c) Determinar la presion de vapor total 2. Calcular la presión de vapor de una solución que contiene \( 24.5 \mathrm{~g} \) de glicerina \( \left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right) \) en \( 135 \mathrm{~mL} \) de agua a \( 30^{\circ} \mathrm{C} \). La presión de vapor del agua pura a esta temperatura es de \( 31.8 \) torr. Asumir que la glicerina es no volátil y que la densidad del agua es de \( 1.00 \) \( \mathrm{g} / \mathrm{mL} \) 3. Determinar la presión del \( \mathrm{CO}_{2} \) requerida a una concentración de \( 0.36 \mathrm{M} \) y una temperatura de \( 25^{\circ} \mathrm{C} \). La \( \mathrm{Kul} \) del \( \mathrm{CO}_{2} \) es de \( 3.4 \times 10^{-2} \mathrm{M} / \mathrm{atm} \). 4. Un sistema libera \( 622 \mathrm{~kJ} \) de calor y \( 105 \mathrm{~kJ} \) de trabajo para los alrededores. Determinar el cambio en energia interna del sistema. 5. Un gas se expande y realiza trabajo sobre los alrededores de 281 J. Al mismo tiempo absorbe \( 217 \mathrm{~J} \) de calor de los alrededores. Calcule el cambio en energia interna del sistema. 6. El trabajo realizado para comprimir un gas es de 76 J. Como resultado se liberan \( 29 \mathrm{~J} \)
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To calculate the vapor pressure of the solution, we need to use Raoult's law, which states that the vapor pressure of a solution is equal to the mole fraction of the solvent times the vapor pressure of the pure solvent. Since glicerina is non-volatile, we can Show more…
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When heat $d Q$ is given to the vapour its temperature will change by $d T$, pressure by $d p$ and volume by $d V$, it being assumed that the vapour remains saturated. Then by C-C equation $$ \frac{d p}{d T}=\frac{q}{T V^{\prime}}\left(V_{\text {vapour }}^{\prime}>>V_{\mathrm{Lq}}^{\prime}\right), \text { or } d p=\frac{q}{T V^{\prime}} d T $$ on the other hand, $p V^{\prime}=\frac{R T}{M}$ So $$ p d V^{\prime}+V^{\prime} d p=\frac{R d T}{M} $$ Hence $$ p d V^{\prime}=\left(\frac{R}{M}-\frac{q}{T}\right) d T $$ finally $$ \begin{gathered} d Q=C d T=d U+p d V^{\prime} \\ =C_{V} d T+\left(\frac{T}{M}-\frac{q}{T}\right) d T=C_{p} d T-\frac{q}{T} d T \end{gathered} $$ $\left(C_{p}, C_{V}\right.$ refer to unit mass here). Thus $$ C=C_{p}-\frac{q}{T} $$ For water $C_{p}=\frac{R_{\gamma}}{\gamma-1} \cdot \frac{1}{M}$ with $\gamma=1.32$ and $M=18$ So $$ C_{p}=1 \cdot 90 \mathrm{~J} / \mathrm{gm} \mathrm{K} $$ and $\quad C=-4 \cdot 13 \mathrm{~J} / \mathrm{gm}^{\circ} \mathrm{K}=-74 \mathrm{~J} / \mathrm{mole} \mathrm{K}$
Thermodynamics And Molecular Physics
Phase Transformations
An equimolar liquid mixture of $n$ -pentane and $n$ -hexane at $80^{\circ} \mathrm{C}$ and 5.00 atm is fed into a flash evaporator at a rate of $100.0 \mathrm{mol} / \mathrm{s}$. When the feed is exposed to the reduced pressure in the evaporator, a substantial amount is vaporized. The temperature in the tank is maintained at $65^{\circ} \mathrm{C}$ by adding heat. The vapor and liquid phases, which are in equilibrium with each other, are separated and discharged as separate streams. The liquid product stream contains 41.0 mole $\%$ pentane. A flowchart and an inletoutlet enthalpy table for the process are given below. (a) Using Raoult's law for vapor-liquid equilibrium calculations, calculate (i) the system pressure, $P_{0}(\mathrm{atm}),$ (ii) the mole fraction of pentane in the vapor product, $y_{\mathrm{P}},$ (iii) the volumetric flow rate of the vapor product, $\dot{V}(\mathrm{L} / \mathrm{s}),$ and (iv) the fractional vaporization of pentane, $f(\mathrm{mol}$ vaporized/mol fed). (b) Determine values for all the $\dot{n}$ 's and $\hat{H}$ 's in the enthalpy table and calculate the required rate of heat addition to the evaporator, $\dot{Q}(\mathrm{kW}).$ (c) How would each of the variables calculated in Parts (a) and (b) change if the evaporator temperature were increased (increase, decrease, no change, cannot tell)? Explain your reasoning.
A gas containing water vapor has a dry-basis composition of 7.5 mole $\%$ CO, $11.5 \%$ CO $_{2}, 0.5 \%.$ $\mathrm{O}_{2},$ and $80.5 \% \mathrm{N}_{2} .$ The gas leaves a catalyst regeneration unit at $620^{\circ} \mathrm{C}$ and 1 atm with a dew point of $57^{\circ} \mathrm{C}$ at a flow rate of $28.5 \mathrm{SCMH}\left[\mathrm{m}^{3}(\mathrm{STP}) / \mathrm{h}\right] .$ Valuable solid catalyst particles entrained in the gas are to be recovered in an electrostatic precipitator, but the gas must first be cooled to $425^{\circ} \mathrm{C}$ to prevent damage to the precipitator electrodes. The cooling is accomplished by spraying water at $20^{\circ} \mathrm{C}$ into the gas. (a) Use simultaneous material and energy balances on the spray cooler to calculate the required water feed rate ( $\mathrm{kg} / \mathrm{h}$ ). Treat the spray cooler as adiabatic and neglect the heat transferred from the entrained solid particles as they cool. (b) In terms that a high school senior could understand, explain the operation of the spray cooler in this problem. (What happens when the cold water contacts the hot gas?)
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