ECTS GUIDE CHEMICAL ENGINEERING DEGREE CURRICULUM

Transcripción

1 ECTS GUIDE CHEMICAL ENGINEERING DEGREE CURRICULUM PROGRAMS OF SUBJECTS 2009/2010

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3 Programs of subjects Chemical Engineering Degree 1 In this document there are summarized the programs of the subjects of the Chemical Engineering Degree of the USC. The intention is to be a brief guide about the objectives, contents and skills to be developed by each subject. For more information (instructors, bibliography, recommendations for the study, etc.), please refer to the guide of the subject in the web page of the USC, where for each subject the available languages are indicated.

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5 3 1 ST YEAR SUBJECT DISTRIBUTION FIRST SEMESTER SECOND SEMESTER Subject T P CT ECTS Subject T P CT ECTS Physical Foundations of 4,5 4,5 9 8 Physics 4,5 1,5 6 5,5 Engineering Algebra 3 1,5 4,5 4 Statistics 3 1,5 4,5 4 Differential Calculus 3 1,5 4,5 4 Integral Calculus 3 1,5 4,5 4 Fundamentals of Chemical 3 1,5 4,5 4 Fundamentals of Chemical 3 1,5 4,5 4 Engineering I Engineering II Introduction to Chemistry 4,5 3,5 8 7 Inorganic Chemistry 6 1,5 7,5 6,5 Fundamentals of Computing Analytical Chemistry 4,5 1,5 6 5,5 Total 21 15,5 36,5 37 Total ,5 T: theory credits (hours=t*10) P: practice/laboratory credits (hours=p*10) CT: credits (total hours=ct*10) ECTS: European credits

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7 Programs of subjects Chemical Engineering Degree 1 st year Physical Foundations of Engineering Core subject 1 st semester 1 st course 8 ECTS (45h theory, 45h practical) Course objectives (translated with Google Translate) The objectives of this subject are summarized in the following points: That the students apply the concepts and dimensional analysis vector analysis in this matter, physics and other curriculum subjects. That the students acquire basic knowledge of mechanics and mostly Fluid Mechanics needed to apply them in this matter, physics and other curriculum subjects. That the students begin to apply physics to real practical problems. The student becomes familiar with the measurement of physical quantities through the use of tools and techniques of measurement used in a laboratory, planning, knowledge about the experience. To learn to appreciate the uncertainty of the result obtained directly or indirectly from experimental measurements to have a clear which of the deductions made from the experimental data are true, what values fall between the actual value of the magnitude that and want to determine what degree of probability will be found between the limit values. Contents (in Spanish) THEORY AND PROBLEMS UNIDAD TEMÁTICA I: CONCEPTOS PREVIOS Tema 1: Magnitudes físicas Tema 2: Análisis vectorial Tema 3: Sistemas de coordenadas UNIDAD TEMÁTICA II: PRINCIPIOS FUNDAMENTALES DE LA MECÁNICA Tema 4: Cinemática del punto material Tema 5: Cinemática del solido rígido y movimiento relativo Tema 6: Teoría elemental de campos Tema 7: Dinámica de la partícula Tema 8: Dinámica de los sistemas de partículas Tema 9: Dinámica del sólido rígido UNIDAD TEMÁTICA III: FLUIDOS Tema 10: Estática de fluidos Tema 11: Dinámica de fluidos Tema 12: Fluidos reales Tema 13: Fenómenos de superficie en los líquidos UNIDAD TEMÁTICA IV Tema 14: Óptica geométrica LABORATORY 1. Introducción a la teoría de incertidumbres. Métodos de medida de una magnitud. Clasificación de las incertidumbres. Cifras significativas. Reglas de redondeo. Teoría de errores. Medidas directas. Medidas indirectas. Media pesada o ponderada. 2. Análisis de regresión. Regresión lineal. Aceptación o rechazo de valores discordantes. 3. Fundamentos teóricos. Breve descripción de cada una de las prácticas. 4. Practice sessions: Determinación de la gravedad por la caída libre de un cuerpo. Análisis de las Leyes de Newton. Conservación de la energía mecánica. Determinación de la gravedad mediante el péndulo de Kater. Caracterización de un muelle mediante su estudio estático y dinámico. Medida de la densidad. Determinación de momentos de inercia. Comprobación del teorema de Steiner. Momento angular. Comportamiento pvt. Medida de viscosidades, densidades y tensión superficial. Espejos. Refracción. Angulo límite. Lentes. Competences (translated with Google Translate) The skills that students should acquire are described in paragraphs 1, 2, 3 and 4 of the goals. So here's some more specific: Distinguish between scalar vectorial and tensorial magnitudes Learn to correctly operate with quantities expressed in different units Learn to describe any movement of a particle. Distinguish between different types of movement Working in spherical, cylindrical and polar coordinates

8 6 1 st year Programs of subjects Chemical Engineering Degree Distinguish between different types of motion of a solid. Easily handle the concepts of rotational axis, instantaneous axis of rotation and instantaneous center of rotation. Be able to describe the motion of simple machines That the students be able to describe a movement with respect to a reference system from the description of the same movement through other systems that reference to the previous moves. To know how to apply Newton's equations and conservation theorems of particle systems and rigid solids, That students could calculate moments of inertia and centers of masses of various shapes That the student knows how to vary the pressure in fluids at rest and in motion To distinguish between stationary and non-stationary state To learn to apply the mechanic laws to fluids Being able to determine the way of the motion of a fluid in a pipe To know where the surface forces come from and what implications have in natural and engineering To know how to deflect the rays of light when passing through media of different refractive index or affecting mirrors. To determine the uncertainty aware of experimental results determined directly or indirectly Knowing how to do linear regressions to identify the parameters with their uncertainty To know how to present a good essay with analysis of their experimental data, consistent with the physics of practice and conclusions To begin the preparation of technical reports Improve your oral communication skills and ability to work in groups

9 Programs of subjects Chemical Engineering Degree 1 st year Algebra Core subject 1 st semester 1 st course 4 ECTS (30h theory, 15h practical) Course objectives The overall aim of the course is to introduce the student to some basic topics in Linear Algebra insisting on: how to relate different concepts (linear transformations, matrices, resolution of simple systems of linear equations ). how to use the notion of matrix of a linear transformation to decide whether two matrices are similar. By the end of this course, the student should: be familiar with the concept of a matrix and be able to manipulate them freely. have a clear understanding of the importance of matrices and the application to the solving of systems of linear equations. Contents 1. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Matrices of systems of linear equations. Matrix operations. Elementary Matrices and Inverses. Solving systems of linear equations: Gaussian Elimination. 2. DETERMINANTS. Definition and properties. Inverse Matrix. Cramer s Rule. 3. VECTOR SPACES. Real Vector Spaces: first notions and examples. Subspaces. Linear Independence. Basis and Dimension. 4. LINEAR TRANSFORMATIONS AND MATRICES. Linear transformations. Kernel and range. Matrices of Linear Transformations. Relation with the problem of solving systems of linear equations. 5. MATRIX DIAGONALIZATION. Eigenvalues and Eigenvectors. Characteristic polynomial. Diagonalization. Competences By the end of this course, the student should: be able to solve Systems of Linear Equations have a working knowledge of algorithms to reduce a matrix to row-echelon form and their uses in solving systems of linear equations, finding basis, etc. be familiar with the Matrix Diagonalization Problem. have a clear understanding of the relation between matrices, linear transformations and systems of linear equations.

10 8 1 st year Programs of subjects Chemical Engineering Degree Differential Calculus Core subject 1 st semester 1 st course 4 ECTS (30h theory, 15h practical) Course objectives To introduce students to the differential calculus of multivariable functions in order to master the basic problem-solving techniques. To know and handle the basic concepts related to the differential calculus and their applications to real problems and other areas of the degree. To introduce students to MATLAB software as an extra support for the theoretical classes. To introduce students to the e-learning using USC_VIRTUAL. Contents 1. Multivariable functions. Scalar and vector functions. Domain, image, graph and level set of a multivariable function. Examples. Limits and continuity. 2. Differential calculus for multivariable functions: partial derivatives. Gradient and Jacobian matrix. Tangent plane. Chain rule. Directional derivatives. 3. Higher order derivatives: hessian matrix. Taylor's theorem. Critical points of multivariable functions: classification and characterization. Constraint extrema: Lagrange multipliers. 4. Vector fields. Divergence and curl operator. 5. MATLAB practices. Display of curves and surfaces. Symbolic calculation of derivatives and partial derivatives. Numerical approximation of first and second order derivatives. Numerical solution of non-linear equations: Newton's method. Competences To identify the analytical properties of elementary functions. To compute and interpret derivatives, partial derivatives and directional derivatives correctly. To relate concepts as gradient, level set, etc, to the previously studied courses of the degree. To find and classify critical points (with or without constraints) of multivariable functions. To know the MATLAB functions in order to practice on computer the skills acquired in the theoretical classes. To numerically solve non-linear equations in one variable and to approximate derivatives using tabular values. To use the course webpage through the VIRTUAL_USC, in such a way that e-learning is incorporated to the student s day to day capabilities.

11 Programs of subjects Chemical Engineering Degree 1 st year Fundamentals of Chemical Engineering I Core subject 1 st semester 1 st course 4 ECTS (30h theory, 15h practical) Course objectives (translated with Google Translate) As it is an introductory course and the first subject of this area of knowledge, two are the main objectives set out in the program: Place the Chemical Engineering degree as indicating their interest and need for a Chemical Engineer, his field of activity and the professional work to develop. We also emphasize the social interest, the importance of the economy and the basic tools necessary to justify the program title and the sequence of their development. Identify the need to know and introduce the student to the basic terminology with the understanding and application of some concepts in everyday life and in the chemical industry. Following the presentation of each principle and to strengthen the learning, it will be presented examples and illustrations to apply to specific situations. Contents (in Spanish) 1. LA INGENIERÍA QUÍMICA. La Ingeniería Química como disciplina. La profesión de Ingeniero Químico. La industria química. La titulación de Ingeniero Químico. 2. LOS PROCESOS QUÍMICOS EN LA INDUSTRIA. Un proceso industrial: La fabricación de ácido sulfúrico. Aspectos químico-físicos. Diagrama de flujo. La unidad de operación. Operaciones unitarias. Reactores químicos. Análisis y síntesis de procesos. Economía. Simulación y control de procesos. Desarrollo de proyectos. 3. UNIDADES Y ASPECTOS RELACIONADOS. Sistemas de unidades. Conversión de valores numéricos y de ecuaciones. Análisis dimensional. Semejanza y cambio de escala. 4. GASES, VAPORES Y LÍQUIDOS. Regla de las fases. Gases ideales. Líquidos y presión de vapor. Correlación y predicción. Saturación y equilibrios líquido vapor y gas líquido. Humedad. 5. INTRODUCCIÓN A LOS BALANCES. Base de cálculo. Reacción química y estequiometría. Reactivo limitante, conversión, selectividad y rendimiento. Balances aplicados a proceso de vaporización y condensación. Competences (translated with Google Translate) As stated in the objectives, it is essential that students acquire in the first place, aware of his professional future. It is therefore necessary to justify the need for Chemical Engineering, field of activity and develop the professional work. Parallel emphasis on its social, justifying the program qualified and the sequence of their development. It is therefore essential to introduce the student to the basic terminology that allows understanding of the fundamentals and operation of the units to be used in the chemical industry. Following the presentation of each principle and to reinforce learning are illustrations and examples applied to specific situations apply to both the industry (where the chemical engineer will screen their work) as usual in daily life.

12 10 1 st year Programs of subjects Chemical Engineering Degree Introduction to Chemistry Core subject 1 st semester 1 st course 7 ECTS (45h theory, 35h practical) Course objectives To acquire basic concepts related to atomic structure and some notions on quantum chemistry. Be able to solve numerical problems related to chemical equilibrium, from the schematic vision of the problem to the determination of possible factors that could modify the equilibrium. Application of learned concepts to important natural chemical systems, industrial processes or highly topical questions To be familiar with the concepts that will serve as the basis to other subjects, related to chemistry, during the whole career Contents THEORY 1. CHEMICAL EQUILIBRIUM. Equilibrium concept. Equilibrium constant. Different forms of the equilibrium constant. Information derived from equilibrium constants. Reaction quotient. Factors affecting the equilibrium. Le Chatelier's principle. 2. ACIDS AND BASES. Brönsted and Lowry theory for acids and bases. Autoionization of water. The ph concept. Relative strength of acids and bases. Poliprotic acids. Acid-base properties of salts. 3. ACID-BASE REACTIONS. The common ion effect in acid-base equilibria. Buffer solutions. Buffer capacity. Henderson-Hassselbalch equation. Acid-base indicators. Neutralization reactions and titration curves. Poliprotic acid titrations. 4. PRECIPITATION EQUILIBRIA. Solubility product constant. Common ion effect in precipitation reactions. Precipitation and crystallization. Fractionated precipitation. Solubility and ph. Equilibria involving complex ions. 5. ELECTROCHEMISTRY. Electrochemical cells. Standard electrode potentials. Changes in the Gibbs free energy. Nernst equation. Batteries and accumulators. Electrolysis. 6. ELECTRONIC STRUCTURE OF THE ATOMS. The discovery of the electron. Black-body radiation. Photoelectric effect. Atomic spectra. Bohr's atom. De Broglie's hypothesis. Schrödinger equation. Uncertainty principle. The particle in a box. 7. QUANTUM MECHANICS. Description of the hydrogen atom. Quantum numbers. Atomic orbitals. Spin. Multielectronic atoms. Electronic configuration of the elements. Pauli exclusion principle. Aufbau principle. 8. PERIODIC PROPERTIES. The periodic table of elements. Families of elements. Ionization potential and electronic affinity. 9. CHEMICAL BOND. Lewis' theory. Lewis structures. Resonance. Lewis' acids and bases. Bond order. Bond energy. 10. BOND THEORIES. Molecular geometry. Molectular orbitals theory. Valence-bond theory. Hybrid orbitals. Multiple bonds. Delocalization. Resonance. The chemical bond in metals. 11. INTERMOLECULAR FORCES. Properties of the liquids. Solid state. Crystal lattice structures. Lattice energy. LABORATORY EXPERIMENTS 1. Precipitation 2. Redox systems metal/solution: electrolytic cell 3. Influences on chemical equilibrium 4. Acid-base titration 5. Calorimetry: Reaction enthalpy Competences To know how to obtain the electronic configuration of atoms and to predict some periodic properties base on that. To easily use the concept of resonant structures. To obtain basic knowledge of bond theories. To predict the molecular geometry. To solve problems related with all types of chemical equilibria: acid-base, precipitation, electrochemical. To learn how to solve numerical questions individually. To be able of interpret the graphics and to predict the fulfilment of some equilibrium laws. To acquire laboratory skills with the instrumentation and learn how to make the final laboratory summary. It is obligatory to know and to follow the USC safety procedure.

13 Programs of subjects Chemical Engineering Degree 1 st year Fundamentals of Computing Core subject 1 st semester 1 st course 5.5 ECTS (30h theory, 30h practical) Course objectives This course makes an introduction to Computer Science and to PC MATLAB programming with applications to chemical engineering problems. Contents THEORY PROGRAMMME (30 HOURS) 1. INTRODUCTION TO COMPUTER SCIENCE 2. MATLAB PROGRAMMING LANGUAGE. Constants and variables. Basic types: float, character and complex. Basic expressions: Arithmetic expressions. Assignment expression. A basic programme. Basic Input/Output functions. Selection structures: Logical expressions. Simple selection. Multiple selection. Switch sentence Repetitive structures: while loop. for loop Variable groupings: Homogeneous groupings: vectors and matrices. Strings. Heterogeneous groupings: cells and structures Modular programming: user-defined functions Input/Output. File input/output. Other output functions: graphical representation PRACTICE PROGRAMME 1. INTRODUCTION TO WINDOWS O.S. (4 HOURS) PC architecture and performance. Folders and files: Windows explorer. Edition of text files. Introduction to Internet: file transfer. Introduction to e-class tools 2. PROGRAMMING ENVIRONMENTS: MATLAB LANGUAGE (26 HOURS) Fundaments. MATLAB interpreter and file editor. Basic operations in command line. Structured programming in MATLAB. Program debugging. Modular design: functions. File input/output. Final project applied to one problem belonging to the field of Chemical Engineering. Competences Once finished this course, students should be capable to implement structured programming problems of medium difficulty using MATLAB. These programs are expected to include basic functions of the MATLAB library, mainly Input/Output functions such as: data streams from/to files, basic data processing and graphic representation. Students should also be capable of understanding MATLAB help and documentation on any other function they may need to use in the future (syntax, prototype...). The competences to develop will be collaborative work in small groups, capacity of analysis and synthesis and capacity of organization and planning.

14 12 1 st year Programs of subjects Chemical Engineering Degree Physics Core subject 2 nd semester 1 st course 5.5 ECTS (45h theory, 15h practical) Course objectives (translated with Google Translate) The aim of this course is to provide the student a broad introduction to Electromagnetism, both in vacuum and in media materials, and since this area is part of physics, this subject must be regarded as one of science subjects in that technological knowledge and guide are based. Accordingly, in this discipline do not arise as a finalist in the training of students, but as a basic discipline and preparation for the understanding of the various materials, both as a technological foundation that students of this degree be given. It is intended, first, to make known the physical principles of electrostatic or magnetostatic highlighting the limits of applicability and, secondly, to develop in the students both analytical skills such as problem solving in addition to introducing them in the handling of laboratory equipment, which will allow them to learn and try to take experimental data and develop a scientific report, but according to this level and therefore not exhaustive. The vast scientific discipline associated with this classic subject, besides the time constraints imposed, necessarily requires the difficult task of sorting, reflection and synthesis, in order to select the content and cutting themes. It is thus striking a balance between the depth and breadth of treatment of the subject under study, ensuring that the requirements inherent in the mathematical development of the subject matches the knowledge of the subject should have acquired the students of this level. Contents (in Spanish) Según BOE (02/08/2003): Ampliación de Mecánica, Electromagnetismo y Óptica. Según Comisión de Docencia (14/02/2005) de la ETSE: Electromagnetismo. El contenido de la asignatura se desarrollará de la forma que se detalla a continuación: 1. CAMPO ELECTROSTÁTICO EN EL VACÍO. Introducción. Carga eléctrica. Ley de Coulomb. Campo electrostático. Potencial electrostático. Dipolo eléctrico. Flujo eléctrico. Teorema de Gauss integral y diferencial. Algunas aplicaciones del teorema de Gauss. Energía de un sistema de cargas. 2. CONDUCTORES EN EQUILIBRIO ELECTROSTÁTICO. Conductores. Conceptos fundamentales. Conductor único aislado. Sistema de conductores. Coeficientes de influencia y capacidad. Condensadores. Estudio de algunos casos particulares. Energía de un sistema de conductores. Energía de un condensador. Fuerzas electrostáticas sobre conductores. Asociación de condensadores. 3. CAMPO ELECTROSTÁTICO EN MEDIOS DIELÉCTRICOS. Dieléctricos. Polarización eléctrica. Campo y potencial en el exterior de un medio dieléctrico. Campo y potencial en el interior de un medio dieléctrico. Desplazamiento eléctrico. Ley de Gauss en un dieléctrico. Susceptibilidad eléctrica. Clasificación de dieléctricos. Influencia del dieléctrico en un condensador. Energía de una distribución de carga en presencia de dieléctricos. Fuerzas sobre el dieléctrico en un condensador. Ferroeléctricos. 4. CORRIENTE ELÉCTRICA. Corriente eléctrica. Densidad de corriente. Ecuación de continuidad. Ley de Ohm. Conductividad y resistencia. Fuerza electromotriz. Ley de Ohm generalizada. Redes de resistencias. Leyes de Kirchhoff. 5. CAMPO MAGNÉTICO EN EL VACÍO. Fuerza entre dos circuitos completos. Inducción magnética. Ley de Biot y Savart. Algunas aplicaciones de la ley de Biot y Savart. Fuerza sobre una carga puntual que se mueve en un campo magnético. Propiedades del campo magnético. Ley de Ampère de la circulación. Potencial vectorial magnético. 6. INDUCCIÓN ELECTROMAGNÉTICA. Inducción electromagnética. Ley de Faraday. Inducción mutua. Autoinducción. Asociación de inductancias: serie y paralelo. Energía magnética. PRÁCTICAS DE LABORATORIO 1. Medida de pequeñas resistencias. 2. Condensador de placas plano-paralelas. 3. Determinación de la constante dieléctrica de diferentes materiales. 4. Curva de carga de un capacitor. 5. Circuitos de corriente continua 6. Circuitos de corriente continua. Resistividad de un conductor Campo magnético creado por distintas distribuciones de corriente. 8. Campo magnético creado por bobinas de Helmholtz. 9. Momento magnético en el campo magnético. 10. Balanza electrodinámica: fuerza sobre un conductor de corriente.

15 Programs of subjects Chemical Engineering Degree 1 st year 13 Competences (translated with Google Translate) Specific skills Manage properly the specific language of electromagnetism, to know their concepts and physical principles which underpin highlighting their limits of applicability. Develop the ability to model the physical reality consistent at this level, those who build quality needed in physics or any other part of the Science and Technology. Develop the capacity for analysis and resolution of basic problems, both foundations and applications related to basic electromagnetic theory and how to approach, when and what. Become familiar with the specific and general infrastructure of a laboratory of electromagnetism and acquire the basic notion of uncertainty inherent in any experiment. Be able to produce a scientific report, represent a set of data as tables, graphs... summarized by a few parameters and draw conclusions consistent with the level of these studies. General skills Capacity for analysis and synthesis. Management of library and computer resources. Management of scientific material. Ability to work as a team. Skill in data processing. Preparation of technical reports.

16 14 1 st year Programs of subjects Chemical Engineering Degree Statistics Core subject 2 nd semester 1 st course 4 ECTS (30h theory, 15h practical) Course objectives Introduction to the basic models and techniques used in Statistics. Exploratory and inferential analysis of data for chemical engineers. Contents 1. DESCRIPTIVE STATISTICS: Introduction to Statistics. Types of statistical variables. Frequency distributions. Graphical representation of data. Statistical measures: measures of location, measures of dispersion. 2. DESCRIPTIVE STATISTICS WITH TWO VARIABLES: Bidimensional statistical variable. Frequency distributions: joint distribution, marginal distributions and conditional distributions. Graphical representation of data. Statistical measures: mean vector. variances and covariances matrix. correlations matrix. Linear dependence. Linear regression. 3. PROBABILITY: Historical introduction. Basic concepts. Probability experiment, sample space, events. Interpretations of probability: classical (Laplace), empirical or relative frequency, mathematical or axiomatic. Conditional probability. Independence. Probability theorems: product rule, law of total probability, and Baye's theorem. 4. UNIDIMENSIONAL RANDOM VARIABLES: Definition of random variable. Discrete random variable: Probability mass function and distribution function. Continuous random variable: Density function and distribution function. Functions of random variables. Moments of a distribution function: expectation, variance and standard deviation. Standardized random variables. Some moment inequalities: Markov and Tchebychev. 5. SOME SPECIAL DISTRIBUTIONS: Discrete distributions: The uniform distribution of n points. Bernoulli distribution and Binomial distribution. The Poisson distribution. The Hypergeometric distribution. Continuous distributions: The uniform distribution. The exponential distribution. The normal distribution. Approximations to other distributions. The Central Limit Theorem. 6. STATISTICAL INFERENCE: POINT AND INTERVAL ESTIMATION: Basic concepts. Approach to the problem of statistical inference: random sample, estimator. Sample proportions and point estimation. Properties of an estimator: bias, variance, mean squared error. Confidence interval. Confidence interval for a proportion. Estimation of parameters of a normal population. Point estimation of the mean and variance of a normal population. Confidence intervals for the mean and variance in normal populations. 7. HYPOTHESIS TESTING: Introduction. Terminology in statistical test of hypothesis. Error of type I and error of type II, critical value or p-value. Hypothesis test for one and two proportions. Hypothesis test for one and two normal populations. Relation between confidence intervals and hypothesis tests. 8. ONE-WAY ANALYSIS OF VARIANCE: The model. Variance decomposition. F test. Competences Formulation of problems which can be solved using statistical techniques. Knowledge of Statistics and Probability for Engineering Applications. Knowledge of how to assigns probability to events. Random variable and types of random variables. Learn how to use probability distribution tables. Calculate coefficients that measure the degree of dependence between two variables. Interpret the regression line as a model of linear dependence. Knowledge of basic concepts in statistical inference. Use MATLAB to carry out a statistical analysis.

17 Programs of subjects Chemical Engineering Degree 1 st year Integral Calculus Core subject 2 nd semester 1 st course 4 ECTS (30h theory, 15h practical) Course objectives To know the basic tools of integration in single variable and multivariable Calculus, its definition from a physical and geometric perspective and the calculation techniques. To know some basic methods of numerical approximation of single variable definite integrals. To know line and surface integration tools, as well as their meaning. To use all these tools to analyze and recognize some concepts involved in chemical processes. To use the MATLAB program to carry out numerical and symbolic calculations and to obtain graphical plots. Contents 1. SINGLE VARIABLE INTEGRAL CALCULUS. The definite integral: geometrical meaning and properties. Fundamental Theorem of Integral Calculus. The indefinite integral: calculation of primitives. Improper integrals. Numerical integration. Some Applications. 2. MULTIVARIABLE INTEGRAL CALCULUS. Integration over rectangular parallelepipeds and elementary regions. The geometric meaning. Iterated integrals. Fubini's Theorem. Change of variables Theorem. Polar, cylindrical and spherical coordinates. Some Applications. 3. LINE AND SURFACE INTEGRATION. Parameterization of regular curves in space. The tangent vector to a curve. Integral of a scalar function over a curve. Integral of a vector function over a curve. Parameterized surfaces in space. The tangent plane and the normal vector to a surface. The orientation of a surface. Integral of a scalar function over a surface. Integral of a vector function over a surface. Classical Theorems of Vector Analysis: Green's Theorem, Stokes' Theorem and the divergence Theorem. Some Applications Competences GENERAL COMPETENCES: To improve the development of the scientific reasoning. To develop the ability to solve a problem and to explain its resolution. SPECIFIC COMPETENCES: To learn the calculation techniques of integration in single variable and multivariable Calculus. To learn how to model a problem and how to solve it with integral and numerical techniques. To use the MATLAB program in integral Calculus.

18 16 1 st year Programs of subjects Chemical Engineering Degree Fundamentals of Chemical Engineering II Core subject 2 nd semester 1 st course 4 ECTS (30h theory, 15h practical) Course objectives (translated with Google Translate) Become familiar with the construction of balances in the field of chemical engineering Notes the importance of these balances for engineering analysis Acquire the ability to approach balances in any system and Apply various techniques for calculating the settlement of balances brought Contents (in Spanish) PRINCIPIOS DE CONSERVACION 1. INTRODUCCIÓN. Principios de conservación. Conservación de una propiedad extensiva. Ecuación general de conservación. Balances macroscópicos. Técnicas para la resolución de problemas. Resolución gráfica de balances. Análisis de variables. BALANCES MACROSCOPICOS DE MATERIA 2. SISTEMAS SIN GENERACIÓN. Balances en régimen estacionario. Ecuación de continuidad. Base de cálculo. Recirculación. Purga. By-pass. Balances en régimen no estacionario. 3. SISTEMAS CON GENERACIÓN. El término de generación en la ecuación de balance. Conversión. Velocidad de reacción. Ecuación cinética. Balances en régimen estacionario. Balances en régimen no estacionario. BALANCES MACROSCOPICOS DE ENERGIA 4. SISTEMAS SIN GENERACIÓN. Introducción. Calores específicos. Estimación de calores específicos. Entalpía. Estimación de entalpías sin y con cambio de fase. Ecuación general del balance de energía. Balance entálpico. Balance de energía mecánica. Ecuación de Bernouilli. 5. SISTEMAS CON GENERACIÓN. Calores de reacción. Calores de formación y de combustión. Temperatura de referencia. Temperatura de reacción. Calores de mezcla. Diagramas entalpía-composición. BALANCES MACROSCOPICOS DE CANTIDAD DE MOVIMIENTO 6. SISTEMAS CON GENERACIÓN. Ecuación general del balance de cantidad de movimiento. Aplicación a diferentes situaciones de interés.

19 Programs of subjects Chemical Engineering Degree 1 st year Inorganic Chemistry Core subject 2 nd semester 1 st course 6.5 ECTS (60h theory, 15h practical) Course objectives General objectives: To explain and predict properties of substance families and their periodical variation on the base of knowledge about bond and chemical periodicity. To establish relations between the structure and the physical and chemical properties of elements and compounds. To formulate chemical equations that reflect general methods for obtaining inorganic elements and compounds that are important for industry, and the properties of compounds families, by means of a theoretical analysis or as a result of experimental data. To describe the applications of those elements and compounds interesting for Chemical Engineering. Contents 1. Introduction to Inorganic Chemistry. Concept, methodology and importance of Inorganic Chemistry. Bases for the systematic study of the elements and their compounds. 2. Systematic study of hydrogen and its compounds. General study of hydrides. 3. Systematic study of the elements from group 18. The noble gases and their compounds. 4. Systematic study of the elements from group 17. Halogens and their compounds. General study of halides. 5. Systematic study of the elements from group 16. Chalcogens and their compounds. General study of oxides. Water. 6. Systematic study of the elements from group 15. Pnicogens and their compounds. Ammonia. 7. Systematic study of the elements from group 14. Carbonoids and their compounds. General study of silicates. 8. Systematic study of the elements from group 13. Boron, aluminium and their compounds. 9. Systematic study of the elements from group 12. Zinc, cadmium, mercury and their compounds. 10. Systematic study of alkaline and alkaline-earth metals and their compounds. 11. General characteristics of transition metals. 12. Chemistry of the elements of the first transition serial. Elements and their most important compounds. 13. Chemistry of the elements of the second and third transition series. Elements and their most important compounds. 14. General characteristics of the lanthanide and actinide elements. Competences To systematize the study of the chemical elements and their most important compounds, paying special attention to hydrogen, noble gases and the elements from the main groups. For that group of elements, the students will learn to systematize the comparative study of the general characteristics of those elements, their natural state and the main extraction methods, the study of the physical and chemical properties and the most important compounds, specially their structure and bond, the preparation, the physical properties and the chemical behaviour as well as the most significant and current applications.

20 18 1 st year Programs of subjects Chemical Engineering Degree Analytical Chemistry Core subject 2 nd semester 1 st course 5.5 ECTS (45h theory, 15h practical) Course objectives The aim of this subject is to introduce at the student in the problems of the sampling and sample preparations, in the volumetric and gravimetric analysis and a short introduction to the instrumental analysis. The basic aim is that the student learn to solve analytical problems. Contents I. INTRODUCTION 1. Introduction to analytical chemistry: history, concept and division. The analytical process. Previous operations: sampling and sample preparation. 2. Data treatment in analytical chemistry II. IONIC EQULIBRIUM IN SOLUTION 3. Acid-base equilibrium I. Introduction to chemical equilibrium: kinetic and thermodynamic aspects. Activity. Concentrations in equilibrium for solutions acid-base. 4. Acid-base equilibrium II. Introduction to volumetric analysis. Acid-base titrations: titrations curves, indicators, applications. 5. Complex equilibrium I. Introduction to complex formation: inorganic and organic ligands. Equilibrium constants. Factors that affect the equilibrium: secondary reactions. 6. Complex equilibrium II. Complex titrations : curves of titration, indicators, applications. 7. Heterogeneous equilibrium I. Solubility of precipitates. Characteristics of the precipitates : formation and properties of the precipitates. Contamination, dry and stability of precipitates. Introduction to gravimetric analysis. Applications. 8. Heterogeneous equilibrium II. Precipitation titrations: curves of titration, indicators, applications. 9. Redox equilibrium I. Introduction. Nerst equation, potential of electrode, equilibrium constant. 10. Redox equilibrium II. Redox titartions: curves of titrations, indicators, previous oxidation and reduction. Applications. III. INTRODUCTION TO INSTRUMENTAL ANALYSIS 11. Spectroscopic techniques. Classification. Molecular Spectroscopy: foundations, instrumentation and analytical methodology. 12. Electrochemical techniques. Foundation of electrochemistry. Electrodes and potentiometry. Electrogravimetry. Culombimetry. Voltamperometry. 13. Chromatographic techniques. Definition and classification of chromatographic techniques. Resolution and efficacy. Instrumentation in liquid and gas chromatography. Applications. Competences At the end of this course the student will have competences in relation about the problems of the chemical equilibrium, its foundations, calculus and their applications to volumetric and gravimetric analysis. On the other hand, also will have information about the sampling and the pretreatment of the sample and a short introduction to the instrumental analysis. Other competences will be the capacity to work autonomous and capacity to solve problems and to take decisions

21 19 2 nd YEAR SUBJECT DISTRIBUTION FIRST SEMESTER SECOND SEMESTER Subject T P CT ECTS Subject T P CT ECTS Organic Chemistry I 4,5 1,5 6 5,5 Organic Chemistry II 3 1,5 4,5 4 Chemical Thermodynamics 4,5 1,5 6 5,5 Physical Chemistry 4,5 1,5 6 5,5 Chemistry Laboratory I ,5 Chemistry Laboratory II ,5 Basic Operations in Transport Phenomena 4,5 1,5 6 5,5 Chemical Engineering Laboratory ,5 Differential Equations 4,5 1,5 6 5,5 Chemical Engineering Thermodynamics 4,5 1,5 6 5,5 Total ,5 Total 12 16, 5 28,5 26 T: theory credits (hours=t*10) P: practice/laboratory credits (hours=p*10) CT: credits (total hours=ct*10) ECTS: European credits

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23 Programs of subjects Chemical Engineering Degree 2 nd year Organic Chemistry I Core subject 1 st semester 2nd course 5.5 ECTS (45h theory, 15h practical) Course objectives Learning and comprehension of the proposed contents. Study of the basic aspects relative to the structure, reactivity and industrial importance of the organic compounds. Contents 1. ORGANIC COMPOUNDS: STRUCTURE AND BONDING. ALKANES. Structural characteristics and nomenclature of hydrocarbons. Functional groups with simple bonds and with multiple bonds. Representation of the organic compounds. Acids and bases. Electronic effects. 2. ALKANES. STEREOCHEMISTRY. Structure and properties of alkanes. Conformacional analysis. Stereochemistry. Optical activity. Quirality. Configuration. Diastereoisomerism. General aspects of organic reactions; kinetics and thermodynamics. Reactivity of alkanes. 3. HALOGENATED ORGANIC COMPOUNDS. Structural characteristics and properties. Nucleophilicity and electrophilicity. Reactions of alkyl halides: nucleophilic substitution and elimination. Organometallic compounds. 4. ALCOHOLS AND ETHERS. Alcohols and alkoxides; structure and properties. Oxidation. Ethers. Reactions of epoxides. 5. AMINES. Structure and properties of amines. Amines as nucleophiles. Quaternary ammonium salts. 6. ALKENES AND ALKYNES. Structure and properties. Electrophilic Aaddition. Oxidation. Reduction. Delocalized systems. Dienes. Kinetic and thermodynamic control. Diels-Alder's reaction. Polimerization. 7. AROMATIC COMPOUNDS. Structure and properties. Reactions of aromatic compounds: electrophilic aromatic substitution. Competences To be able to represent organic compounds and the most important functional groups using Lewis's and Kekule's structures and structural and estereochemical formulas (Newman, Fischer perspective, etc). To adequately perform the conformational analysis of organic compounds. To predict similarities and differences in physical properties (melting and boiling points, solubility, acidity, etc.) on the basis of the functional groups present in a given molecule. To assign correct iupac names to organic compounds, including notation for stereogenic centers and the configuration of double bonds, and deduce a correct structure from a given name. To know the main chemical reactions of the most important functional groups. To know and to handle chemical kinetics and thermodynamics (rate and equilibrium constants, reaction mechanism, elementary step, reaction intermediate, transition state, potential-energy diagrams, ratedetermining step, overall rate, etc) of the studied transformations. To be capable of apply the above-referred knowledge to a given compound, with particular emphasis on chemo, regio and estereoselectivity issues. To develop skills for oral communication and team-work in organic chemistry issues.

24 22 2 nd year Programs of subjects Chemical Engineering Degree Chemical Thermodynamics Core subject 1 st semester 2nd course 5.5 ECTS (45h theory, 15h practical) Course objectives Thermodynamics is related to the transformations of energy from one to another type. So, notions as heat, work, phase transitions and energy of chemical reactions are included in it. When it is applied to chemical systems, Thermodynamics is a quite useful tool for predicting, for example, the spontaneity of a chemical reaction, the relationship between reactants and products when the chemical equilibrium is reached and the amount of energy absorbed or released during the reaction. Nevertheless, it is not possible to predict the reaction mechanism and the chemical reaction rate, two notions studied by the Chemical Kinetics. Therefore, the main objectives of this course are to learn the thermodynamic method and to apply it to different chemical systems. All along this course, special attention will be paid to the use of the computer as learning tool, mainly through the use of the WebCT, math worksheets (as Excel, for example) and web browsers (as Internet Explorer, Netscape or similar). Moreover, the reasoning capabilities of the students will be developed through the answer to questions related to the Thermodynamics. The students will have to argue about their truthfulness or falseness, or to propose a reasonable solution. Contents 1. INTRODUCTION TO CHEMICAL THERMODYNAMICS. (5 HOURS). Outline of the Thermodynamics. Physical magnitudes. 2. THE FIRST LAW OF THERMODYNAMICS AND OTHER BASIC CONCEPTS. (10 HOURS). Internal energy. The first Law. Thermodynamic properties, thermodynamic state and state functions. Enthalpy. Flow processes in steady state. Equilibrium. The phase rule. Phase equilibrium in one-component system. The reversible process. Processes at constant V and T. Heat capacity. 3. VOLUMETRIC PROPERTIES OF PURE FLUIDS. (10 HOURS). PVT behaviour of pure substances. Virial equation. The perfect gas. Applications of the virial equations. Cubic equations of state. Generalised correlations for gases. Generalised correlations for liquids. 4. THERMOCHEMISTRY. (6 HOURS). Latent heat of pure substances. Standard enthalpies of reaction, formation and combustion. Hess Law. Calorimetry. Dependence of enthalpy with temperature. 5. THE SECOND AND THIRD LAWS OF THERMODYNAMICS (10 HOURS). Formulations of the second Law. Thermal Engines. Temperature scales: thermodynamic and perfect gas. Entropy. Changes of entropy for a perfect gas. Mathematical formulation of the second Law. Conditions for spontaneous evolution and equilibrium. The third Law of Thermodynamics. 6. THERMODYNAMIC PROPERTIES OF FLUIDS. (10 HOURS). Gibbs and Helmholtz functions. Thermodynamic reactions of a system in equilibrium. Residual properties. Two-phase systems (Clapeyron and Clausius- Clapeyron equations). Thermodynamic diagrams. Tables of thermodynamic properties. Generalised correlations of thermodynamic properties for gases. 7. CHEMICAL EQUILIBRIUM OF A MIXTURE OF PERFECT GASES. (9 HOURS). Chemical equilibrium. Chemical potentials in a mixture of ideal gases (chemical potential of a pure perfect gas). Temperature dependence of the equilibrium constant. Equilibrium calculations in perfect gases. Competences During this course, a lot of new notions for the student are introduced. So, special attention will be devoted to solve questions and exercises that help the better understanding of those notions. The student has to be able to use correctly the most important thermodynamic equations in the different conditions they can be used. Ability to correlate different fields of the science, specially Physics, Chemistry, Engineering and Mathematics. A good background in Mathematics (derivation, integration, etc.) is very advisable because mathematical calculus is used for introducing some notions. Use of the WebCT platform and some informatics programs (worksheets as Microsoft Excel or similar ones). Resolution of theoretical and practical exercises.

25 Programs of subjects Chemical Engineering Degree 2 nd year Chemistry Laboratory I Core subject 1 st semester 2nd course 5.5 ECTS (60h practical) Course objectives To acquaint the students with the development of the chemical analysis of different materials. To use the classical analysis techniques applied to real samples. To acquaint the students with the basic laboratory material. To train students in the basic synthesis techniques in Inorganic Chemistry. Contents PRACTICES ANALYTIC CHEMISTRY LABORATORY 1. Determination of the organic matter of a freshwater. 2. Determination of calcium, magnesium and hardness in a water. 3. Determination of the carbonate-bicarbonate content in a synthetic sample. 4. Spectrophotometric determination of copper in soils. 5. Determination of chlorides in waters. 6. Determination of the acidity constant in a weak acid. 7. Determination of sulphur in a soluble sulphate. 8. Determination of nickel in a steel. 9. Determination of the content in hypochlorite and active chlorine in a sample of bleach. 10. Determination of the total acidity of a vinegar. 11. Determination of phosphate in river waters. 12. Determination of chrome (VI) with diphenilcarbazide in polluted waters. PRACTICES. INORGANIC CHEMISTRY LABORATORY. 1. Preparation of iron sulphate (II) and hexahydrated ammonium. (Mohr salt). 2. Preparation of tin (II) iodide. 3. Preparation of chromium alum. 4. Preparation of boric acid. 5. Preparation of lead (II) chloride. 6. Preparation of lead (II) nitrate. 7. Preparation of iron alum. 8. Preparation of dehydrated iron (II) oxalate. 9. Preparation of monohydrated tetra-amin-copper (II) sulphate. 10. Preparation of copper and ammonium sulphate. 11. Preparation of lead (II) thiosulphate. 12. Obtaining copper by cementation. 13. Obtaining metallic iron. Competences It is supposed a minimum knowledge of the basic operations to be carried out in a laboratory of Chemistry. In the part corresponding to Analytic Chemistry basic abilities will be developed for doing an analysis by using the conventional techniques. At finishing the practices in the Inorganic Chemistry laboratory, students must be able to: Isolate compounds by using different separation techniques. Do laboratory assemblies. Do calculations referred to the experiments that have been done.

26 24 2 nd year Programs of subjects Chemical Engineering Degree Basic Operations in Chemical Engineering Core subject 1 st semester 2nd course 5.5 ECTS (45h theory, 15h practical) Course objectives This course aims at the study of basic concepts which will be applied along the degree. Once the concepts and applications of balances of mass, energy and momentum are known from the previous courses (Introduction and Fundamentals of Chemical Engineering), microscopic balances of property are considered The mechanisms of molecular and turbulent transport are introduced and the combination of balances with velocity equations is proposed. The concept of transport coefficient (individual and global) is also introduced. A major objective of the course is to connect theoretical concepts to their practical application and for this purpose a number of practical examples are analyzed. Contents 1. MACROSCOPIC BALANCES. Levels of description. Macroscopic balances. Concept of vector and tensor calculus. Direct deduction of microscopic balances. Deduction from macroscopic balances. The equation of continuity. Microscopic momentum balance. Microscopic heat energy balance. 2. VELOCITY EQUATIONS. Transport mechanisms. Velocity laws in molecular transport: Newton s law. Viscosity. Tensions: sign criteria. Non-Newtonian fluids; Fourier s law. Thermal conductivity; Fick s law. Diffusivity. 3. CONSERVATION EQUATIONS. Mass conservation equations. The movement equation for isothermal flow. Navier-Stokes equation. The heat energy conservation equation. 4. ESTIMATION OF TRANSPORT PROPERTIES. Viscosity of gases and liquids. Thermal conductivity of gases, liquids and solids. Diffusivity of gases, liquids and solids. 5. MOLECULAR TRANSPORT IN STEADY-STATE REGIME. Momentum molecular transport: study of fluids flow in simple geometries. Heat energy molecular transport: systems without generation, systems with generation. Mass molecular transport. Simple transport: single component transport, contradiffusion. Transport with generation: homogeneous reaction, heterogeneous reaction. 6. UNSTEADY STATE MOLECULAR TRANSPORT. Approach of the variation equations. Semi-infinite solids. Unidirectional transport in solids with finite thickness: general conditions, analytical solutions, graphic solutions. Application to three-dimensional solids: Newman s rule. Numerical methods: Schmidt s method. 7. TURBULENT TRANSPORT. Description of turbulence. Conservation equations averaged respect to time. Theoretical treatment of turbulence: turbulent diffusivity, Prandtl s length of mixture. Velocities distribution: universal profile. 8. BOUNDARY LAYER. Qualitative study. Boundary layer thickness: laminar flow, turbulent flow. Entrance length. Drag force. Separation of the limit layer in round solids: applications. Quantitative aspects. Prandtl s equation. 9. TRANSPORT BETWEEN PHASES: TRANSPORT COEFFICIENTS. Individual coefficients. Determination of the transport coefficients. Friction coefficient. Application to the calculus of pressure drops in tubes. Convection coefficients. Mass transport coefficient. Global coefficients. Heat transmission global coefficient: application to the calculus of heat exchangers. Mass transfer global coefficient: application to the calculus of gas adsorption equipments. Competentes (translated with Google Translate) Aims at the strengthening of the technical approach to problems, and initiatives in the area earlier, and developing skills for conflict resolution. (Objective: Result orientation). An additional objective is learning to read "physical" of the equations, including complex, looking for their understanding and simplification in the case. (Goal: Capacity of abstraction). It is intended that the student use the concepts to explain observed facts in daily life and in industrial processes. (Goal: Capacity of relationship). Eventually seek to increase the active participation of students in class. (Goal: improving communication skills)