Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 3: Level 3

$\mathrm{\Delta G}=\mathrm{\Delta H}-\mathrm{T\Delta S}$ and $\mathrm{\Delta G}=\mathrm{\Delta H}+\mathrm{T}{\left[\frac{\mathrm{d}\left(\mathrm{\Delta G}\right)}{\mathrm{dT}}\right]}_{\mathrm{p}}$ then $\left(\frac{{\mathrm{dE}}_{\mathrm{cell}}}{\mathrm{dT}}\right)$ is :

One mole of an ideal gas $\left({\mathrm{C}}_{\mathrm{v},\mathrm{m}}=\frac{5}{2}\mathrm{R}\right)$ at $300 \mathrm{K}$ and $5 \mathrm{atm}$ is expanded adiabatically to a final pressure of $2 \mathrm{atm}$, against a constant pressure of $2 \mathrm{atm}$. Final temperature of the gas is:

In a fuel cell, methanol is used as a fuel and oxygen gas is used as an oxidizer. The reaction is ${\mathrm{CH}}_3\mathrm{OH}\left(\mathrm{l}\right)+\frac{3}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{CO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$.

At $298 \mathrm{K}$, the standard Gibbs energies of the formation for ${\mathrm{CH}}_3\mathrm{OH}\left(\mathrm{l}\right), {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$ and ${\mathrm{CO}}_2\left(\mathrm{g}\right)$ are $-166.2,-237.2$ and $-394.4 \mathrm{kJ} {\mathrm{mol}}^{-1}$, respectively. If the standard enthalpy of combustion of methanol is $-726 \mathrm{kJ} {\mathrm{mol}}^{-1}$, the efficiency of the fuel cell will be:

One mole of an ideal gas is expanded reversibly and isothermally from $1 {\mathrm{dm}}^3$ to $10 {\mathrm{dm}}^3$ at $300 \mathrm{K}$. $\mathrm{\Delta G}$ will be equal to

A plot of $\ln \mathrm{K}$ against $\frac{1}{\mathrm{T}}$ (abscissa) is expected to be a straight line with intercept on ordinate axis equal to

Two moles of an ideal gas is heated at constant pressure of one atmosphere from $27°\mathrm{C}$ to $127°\mathrm{C}$. If ${\mathrm{C}}_{\mathrm{v},\mathrm{m}}=20+{10}^{-2} \mathrm{T} {\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}$, then $\mathrm{q}$ and $\mathrm{\Delta U}$ for the process are respectively:

The gaseous ozone is bubbled through a water-ice mixture at $0°\mathrm{C}$. As ${\mathrm{O}}_3\left(\mathrm{g}\right)$ decomposes to form ${\mathrm{O}}_2\left(\mathrm{g}\right),$ the enthalpy of the reaction is absorbed by the resulting ice. Given that the heat of fusion of ice is $6.0095 \mathrm{kJ} {\mathrm{mol}}^{-1}$, calculate the mass of ice that melts for each gram of ${\mathrm{O}}_3$ that decomposes.

$2{\mathrm{O}}_3\left(\mathrm{g}\right)\to 3{\mathrm{O}}_2\left(\mathrm{g}\right); \mathrm{\Delta H}=-285.4 \mathrm{kJ}$

Give your answer up to two decimal places.

Water-gas is produced by the reaction $\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\to {\mathrm{H}}_2\left(\mathrm{g}\right)+\mathrm{CO}\left(\mathrm{g}\right)$. The heat required for this endothermic reaction may be supplied by adding a limited amount of air and burning some carbon to carbon dioxide. Calculate the amount of carbon to be burnt to ${\mathrm{CO}}_2$ to provide enough heat for the water- gas $\left({\mathrm{H}}_2+\mathrm{CO}\right)$ conversion of $100 \mathrm{g}$ of carbon. $\mathrm{\Delta H}{°}_{\mathrm{f}}$ for $\mathrm{CO}=-110.53 \mathrm{kJ}, \mathrm{\Delta H}{°}_{\mathrm{f}}$ for ${\mathrm{H}}_2\mathrm{O}=-241.81 \mathrm{kJ}$ and ${\mathrm{\Delta H}}_{\text{combustion }}$ for $\mathrm{C}=-393.51 \mathrm{kJ}.$

Final answer has to be given after rounding-off to the nearest integer.