Fisicoquímica 1 Unidad I. Relaciones P.V.T. 1.1 Ley cero de de la termodinámi termodinámica. ca. 1.2 Ecuaciones Ecuaciones de estado. estado. 1.2.1. Coeficientes de compresibilidad. 1.2.2. Coeficiente de expansión volumétrica. 1.2.3. Gases ideales. 1.2.4. Gases reales. 1.2.5. Líquidos y sólidos. Unidad II. Primera ley de la termodinámica. 2.1. Energía. 2.2. Trabajo 2.3. Calor Calo r. 2.4. Primera ley de la termodinámica. 2.5. Procesos reversibles e irreversibles. 2.6. Entalpía. 2.7. Cálculos de Q, W, W, ∆U y ∆U, en procesos físicos y químicos.
Unidad III Segunda ley de la termodinámica. 3.1. Procesos espontáneos y no espontáneos. 3.2. Ciclo de Carnot. 3.3. Segunda ley de la termodinámica. 3.4. Cambios de entropía en procesos físicos. Unidad IV. IV. Tercera ley de la termodinámica. 4.1. Entropía y desorden molecular. 4.2. Calculo de entropía absoluta. 4.3. Cambios de entropía en reacciones químicas. Unidad V. Funciones de energía libre. 5.1. Energía libre de Gibas. 5.2. Energía de Helmhotz. 5.3. Cambios de energía libre en procesos físicos y químicos.
1
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Unidad VI. Fugacidad y actividad. 6.1. Propiedades parciales molares. 6.2. Potencial químico. 6.3. Fugacidad. 6.3.1. Cambios de fugacidad. 6.3.2. Métodos para el cálculo de la fugacidad. 6.4. Actividad. 6.4.1. Coeficientes de actividad. Unidad VII. Equilibrio de fases: sistema de un componente. 7.1. Regla de las fases de Gibas. 7.2. Diagrama de equilibrio. 7.3. Ecuación de Clapeyron. 7.4. Equilibrio líquido-vapor, líquido–sólido y sólido-vapor. Unidad VIII. Equilibrio de fases: sistema de dos o más componen tes. 8.1. Soluciones ideales. 8.2. Soluciones ideales de no elecetroitos. 8.3. Ley de Henry. Henry. 8.4. Propiedades coligativas soluciones reales. 8.5. Ley de la distribución de Nernst. 8.6. Equilibrio de fases. 8.6.1. Equilibrio liquido-vapor. liquido-vapor. 8.6.2. Equilibrio sólido-vapor. sólido-vapor. 8.6.3. Equilibrio líquido-líquido. 8.6.4. Equilibrio Eq uilibrio sólido-líquido-vapor.
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Evaluación. Profesor 70%. Primer examen parcial unidades 1 y2 15 puntos. Segundo examen parcial unidades 3, 4 y 5 15 puntos. Tercer examen parcial unidades 6,7 y 8 15 puntos
Una tarea departamental Tareas, investigaciones, prácticas y otros
5 puntos. 20 puntos.
Departamento 30%. Un examen departamental. Examen departamental unidades 1 y 2
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Unidad 1 Relaciones P.V.T
El estado físico de una sustancia generalmente esta definido por las condiciones que lo rodea rodean n (pre (presi sión ón y temp temper erat atur ura) a).. Y como como conse consecue cuenci nciaa el volu volume men n qued quedaa establecido por las anteriores. Una misma sustancia es susceptible de los 3 estados de la materia dependiendo de las condiciones de presión y temperatura. El estado gaseoso se define en función de tres variables P, T y V.
Por lo que es importante entender los conceptos de presión y temperatura.
Para los gases. Propiedades macroscópicas de los gases. V = f(P,T); P = f(V,T), T = f(PV) cuando la masa permanece constante. V = f(P)T=ctte; V = f(T)P=ctte; P = f(V)T=ctte; P = f(T)V=ctte La presión es la fuerza ejercida o aplicada (por un sólido, líquido o gas ) sobre la unidad de superficie.
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Para medir presiones de gases se utiliza generalmente la unidad atmósfera. Para medir presiones de líquidos y sólidos generalmente se utiliza Kg. / cm2. La unidad atmósfera. El experimento de Torricelli (al nivel del mar)
Hg
Hg
Al introducir el tubo de vidrio lleno de mercurio con el extremo sellado hacia arriba y además perpendicular a la superficie, el mercurio de la columna descenderá tanto cuanto sea necesario para que el peso del mercurio ejercido sobre la superficie se iguale al peso ejercido sobre la misma superficie.
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1 atm = 760 mmHg 76 cmHg 29.9 plgHg 14.7Lbf/plg2 1.033 Kgf/cm2 1.0134*105 Pa 1.0134*106 Dinas/cm2 2116.8Lbf/ft2 Para agua al nivel del mar ¿cuál seria la altura de la columna?
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En la siguiente siguiente figura se presenta una presa, calcule la presión ejercida ejercida por el agua en el punto A.
150 m
A
Presión absoluta y presión manométrica. Por lo general el líquido del manómetro es el mercurio cuya densidad es de 13.6 g/cm3. Por lo tanto si la presión de la atmósfera terrestre se puede equiparar a una columna de mercurio de 76 cm de altura, la presión ejercida por la atmósfera es de: Presión Atmosf érica
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= Gas
Gas
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Si tenemos un recipiente cilíndrico como el e l que se describe en la figura: Recipiente cil í ndrico ndrico
Masa = 1000 Kg
20 cm
Recipiente cil í ndrico ndrico
Masa = 1000 Kg
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Temperatura Es el nivel calorífico de los cuerpos Escalas de temperatura Escalas absolutas: El cero es la temperatura mínima que el hombre cree que existe: K grados Kelvin
°R grados Ranking
Escalas relativas: El cero es arbitrario °C grados centí ntígrados °F grados Fahrenheit En la escala centígrada, el cero es la temperatura de equilibrio entre el agua sólida y el agua líquida. Y cien grados es la temperatura de equilibrio entre el agua liquida y el agua vapor a 1 atm de presión. En la escala Fahrenheit el cero se corresponde a la temperatura de congelación de una mezcla de hielo y sal; y los 96 grados es la temperatura de la sangre de un hombre sano. °F ° ° K
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Una forma de evaluar a los gases. Mediante experimentación se determino que algunos gases pueden ser descritos por:
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G.P. baxter y h. W. Starkweather estudiaron la compresibilidad del oxigeno a bajas presiones a 0ºC, los resultados de las mediciones e stán dados en la siguiente tabla: P (atm) 1 .0 0 0 .7 5 0 .5 0 0 .2 5
V(lt) 0.69981 0.93332 1.40027 2.80120
3 2.5 2 m t a P
1.5 1 0.5 0
0
0.2
0.4
0. 6 V (lt)
0.8
1
1.2
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1.- Un mol de hidrog hidrogeno eno se encuent encuentra ra a 25ºC 25ºC y 2 atm, atm, sufre sufre una expans expansión ión hasta hasta una presión de 0.5 atm y 100ºC. Calcule: a) El volume volumen n fina finall del del hidrog hidrogeno. eno. b) Represente Represente este cambio cambio en diagramas diagramas gráficos gráficos de Pvs Pvs T, T, P vs V y V vs T
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2.- ¿Cuál es la presión ejercida por 24 g de CO2 en un recipiente de 5 L a 0°C? a) Una regla aproximada es que 1 mol de gas ocupa 1 ft3 a temperatura y presión atmosférica (25°C y 1 atm). Calcule el error porcentual d e esta regla.
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Ejemplo. Para cierto hidrocarburo gaseoso, 20 mg. ejercen una presión de 24.7 torr en una vasija de 500 cm3 a 25°C. Obtenga la masa molar y peso molecular e identifique el gas.
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Ejemplo. Cierta mezcla de de He y Ne en un bulbo de 356 cm3 pesa 0.1480 g. y se encuentra a 20°C y 748 torr. Calcule la masa y fracción molar del He presente.
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3.- Una mezcla de N2 y O2 tiene una densidad de 1.185 g/L a 25°C y 101.3 KPa. Halle la fracción mol del O2 en la mezcla.
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4.- En la cima de una montaña el termómetro marca 10°C y el barómetro 70 cmHg. En la base de la misma montaña la temperatura es 30°C y la presión de 76cmHg ¿Como es la densidad del aire en la cima con respecto de la densidad del aire en la base?
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5.- Para 1 mol de N2 a 0°C, se miden los siguientes volúmenes en función de la presión: P (atm)
1
3
5
V (cm3)
22405
7461.4
4473.1
Calcule y presenta PV/nT frente a P para estos tres puntos y extrapole a P = 0 para evaluar R.
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6.- La densidad medida de una amina a 0°C en función de la presión es: P (atm)
0.02
0.05
0 .0 8
Ρ (g/L)
0.2796
0.7080
1.1476
Represente P/ρ frente a P y extrapole a P = 0 para obtener un valor exacto del peso molecular, e identifique el gas.
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7.- Después de colocar 1.6 moles de gas amonio en un recipiente de 1600 cm3 a 25°C. Este se calienta a 500 K. a esta temperatura el amoniaco se descompone parcialmente en N2 e H2, y se mide una presión de 4.85 MPa. Calcule el número de moles de cada componente presente a 500 K.
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8.- Cierta mezcla de gas se encuentra a 3450KPa de presión y se compone de 20 g de O2 y 30 g de CO2. Encuentre la presión parcial del CO2.
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9.- Un bulbo bulbo con metano metano de 1Lt a una presión presión de 10KPa, 10KPa, se conecta conecta a un bulbo bulbo con hidrogeno de 3 l y una presión de 20 KPa, ambos bulbos están a la misma temperatura. a) después después de que los los gases gases se han mezclad mezclado o ¿Cuál será será la presión presión total? total? b) ¿Cuál será la fracció fracción n mol de cada cada componente componente??
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10.- Un estudiante estudiante descompone KClO3 y recoge sobre agua a 23°C, 36.5 cm3 de O2. El barómetro indica 751 torr. La presión de vapor del agua a 23°C es de 21.1 torr. Halle el volumen que el oxigeno seco ocuparía a 0°C y 1 atm.
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11.1.- Dos Dos bulb bulbos os vací vacíos os de igua iguall volu volume men n se cone conect ctan an por por un tubo tubo de volu volume men n despreciable. Un bulbo es introducido en un baño de temperatura constante e igual a 200K y el otro en un baño a 300K y se inyecta al sistema 1 mol de gas ideal. Halle el número final de moles en cada bulbo.
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aislante
6.- Estado estacionario. Para sistemas cerrados y abiertos cuando sus propiedades no cambian con respecto del tiempo.
Reactantes 1000Kg/hr
Reactor
Productos 1000Kg/hr
7.- Proceso termodinámico. Es cualquier cambio que sufre un sistema termodinámico que lo lleva a unas condiciones finales diferentes de las condiciones iniciales de dicho sistema.
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Propiedades de los sistemas termodinámicos. Poseen las mismas propiedades extensivas e intensivas de la materia. INTENSIVAS NO DEPENDEN DE LA MASA CONSIDERADA EXTENSIVAS DEPENDEN DE LA MASA CONSIDERADA Funciones de Estado Son aquellas que no dependen de la trayectoria. Son funciones de estado la presión, temperatura, ∆U, cambio de energía interna; ∆H, cambio de entalpía, ∆S, cambio de entropía. energía potencial, energía cinética.
1 Kg
2 m.
10m. Se subirá la caja a la plataforma.
Propiedades.
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2.- Tiene diferencial exacta.
dF
=
∂F ∂F dX + dY ∂X ∂ Y
dF = Mdx + ndY Comprobar que la presión es función de estado.
∂M ∂ N = ∂Y ∂ X
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Formulación de la primera ley de la termodinámica. Primera ley.ley.- De la conservación de la energía. Aunque la energía adopta numerosas formas la cantidad total de energía es constante. Y cuando esta desaparece en una forma aparece simultáneamente en otra. La primera ley de la termodinámica se aplica al sistema y a los alrededores como un todo. La energía no se crea ni se destruye, solo se transforma. ∆(energía del sistema) + ∆(energía de los alrededores)= 0 ∆ (Energía del sistema): Ec = energía cinética Ep = energía potencial U = energía interna. EM = energía mecánica Eel = energía eléctrica ∆(energía de los alrededores): Calor Trabajo ∆Ec + ∆Ep + ∆U + Q + W = 0 ∆Ec + ∆Ep + ∆U = ±Q ±W Primera ley de forma general
En sistemas cerrados no hay cambios de la Ec y la la Ep ∆U = Q + W
1.- En termodinámica el trabajo se define como cualquier cantidad que fluye a través de la frontera de un sistema durante un cambio de estado y que puede usarse por completo para elevar un cuerpo.
2.- En termodinámica se define el calor como la cantidad que fluye a través de la frontera
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La formulación de algunas variables va riables termodinámicas son: 2 Ek = 1/2mv . Ep = mgh W = F*d. En la mayoría de los problemas de fisicoquímica el trabajo se refiere a la expansión o compresión de un gas. y se evalúa.
El calor Q, no tiene formula propia de evaluación, siempre se evalúa a partir de otras variables. Al utilizar utilizar la primera primera ley con esta ecuación: ecuación: ∆Ec + ∆Ep + ∆U = Q + W se debe seguir la siguiente convección.
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Un mol de un gas ideal se somete a varios cambios de estado. ¿Cual es el cambio de energía interna del proceso? a) El sistema cede 512 J de d e calor, y se destruyen 134 J de trabajo b) El sistema absorbe 500 J de calor, y se producen 500 J de trabajo? c) No hay transferencia de calor, se destruyen 126 J de trabajo.
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Un pájaro que pesa 1.5 Kg. se eleva y vuela hasta una altura de 75m, donde alcanza la velocidad de 20m/s. ¿Qué cambio de energía se efectúa en este proceso? (la aceleración de la gravedad es 9.81m/s2).
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Un gas se expande contra una presión de 2 atm de 10 a 20 lt y absorbe 300 cal. ¿Cuál es el cambio de energía interna?
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Si realizamos el estudio desde el punto de vista de pequeños cambios (diferenciales).
Energía interna La energía interna es la suma de las energías del sistema. U = u (V,T) dU
∂U ∂U = ∂V dV + ∂T VdT T
Por definición:
Entonces:
∫
U2
U1
Donde:
dU
=
V2
∫
V1
Cv dT
+
∫
T2
T1
∂U ∂V T
dV
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Procesos termodinámicos. Ciclo termodinámico.
∫
dU
=
∫ δ
Q
+
∫ δ
W
Si un sistema se somete a cualquier transformación cíclica, el trabajo producido en el entorno es igual al calor que fluye desde el entorno. Q = W Para toda función termodinámica
∫ Proceso a volumen constante.
dF
=
0
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Se calientan 100 gramos de agua liquida de 5ºC hasta 50ºC calcule el calor, trabajo y cambio de energía interna del proceso.
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Proceso a presión constante.
m m
CO2
CO2
Calcule el ΔU, Q y W para el proceso mostrado en la figura. El recipiente cilíndrico mostrado en la figura constituido de un embolo, que no es afectado por la fricción con las paredes del recipiente e impide que el gas se escape. Se sabe que el gas es ideal (es decir es descrito por la ecuación de los gases ideales). T =110°C
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Proceso a presión constante. Un gas que es descrito por la ecuación de Van Van der Waals sufre el siguiente cambio de estado. V1 = 10 lt V2 =lt T1 = T2= P1 = 50 atm P2= 50 atm n = 10 mol Calcule Q, W, y ∆H.
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Proceso isotérmico.
V1 = 3lt n = 3mol T1 =
O2 V2 = 8lt Baño de agua a la T
n = 3mol T2 =
El diagrama mostrado en la figura se corresponde a un proceso en el cual se utiliza la presión del gas para producir energía mecánica. Suponiendo comportamiento ideal, Calcule ΔU, Q y W para el proceso.
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Proceso adiabático.
Aislante V1 = 3lt n= T1 = 320 K V2 = 10 lt N2
n= T2 =
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Procesos reversibles e irreversibles. Proceso reversible
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Proceso reversible======= Wmax = Wrev Proceso irreversible====== Wrev > Wirrev Wirrev
w w
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El trabajo realizado en n etapas, es la suma de las pequeñas cantidades de trabajo producido en cada etapa.
Pop = Pgas - dP
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dQ = 0
dU
= δQ −
P dV
0 dU = -PdV ===> nCvdT = -PdV Tenemos enemos dos opciones, opciones, la primer primeraa para para cuando cuando el proces proceso o se desarr desarroll ollaa de forma forma irreversible.
∆U = −W irrev
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Analizando el proceso a presión constante tenemos que: Si el proceso es a presión constante
dU
= δQ − PdV
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Para el Cp se tienen expresiones en función de la temperatura Cp = a + bT + cT2 + dT3 Cp = a + bT + c´/T2 + d´/T3
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Dos litros de N2 a 0°C y 5 atm de presión se expanden isotérmicamente contra una presión de 1 atm hasta que el gas se encuentra también a esta presión. Suponiendo gas ideal, hallar los valores de W, W, ∆U, y q del proceso?
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Tres moles de un gas ideal a 1 atm de presión y 20°C se calientan a presión constante hasta que la temperatura temperatura final es de 80°C. Para el gas Cv = 7.50 +3.2 *10-3 T Cal/molK. Calcúlense w,∆U, ∆H y Q en este proceso.
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Suponiendo que el CO2 es un gas ideal, calcular el trabajo realizado por 10g del mismo en la expansión expansión isotérmica isotérmica reversible reversible desde un volumen de 5 a otro de 10 litros, a 27°C. ¿Cuales son los valores de q, ∆U, ∆H y W en este proceso?
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