Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 5: Exercise 5

The heat of reaction for

${\mathrm{C}}_{10}{\mathrm{H}}_8\left(\mathrm{s}\right)+12{\mathrm{O}}_2\left(\mathrm{g}\right)⟶10{\mathrm{CO}}_2\left(\mathrm{g}\right)+4{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$ at constant volume is $-1228.2 \mathrm{kcal}$ at ${25}^0\mathrm{C}$. The heat of reaction at constant pressure and same temperature is

Internal energy is:

For the reaction, ${\mathrm{N}}_2+3{\mathrm{H}}_2\rightleftharpoons 2{\mathrm{NH}}_3$, which one of the following is correct regarding $\mathrm{\Delta H}$?

A gas expands adiabatically at a constant pressure, such that $\mathrm{T}\propto {\mathrm{V}}^{-1/2}$. The value of $\mathrm{\gamma }\left({\mathrm{C}}_{\mathrm{p},\mathrm{m}}/{\mathrm{C}}_{\mathrm{v},\mathrm{m}}\right)$ of the gas will be:

${\mathbf{S}}_{\mathbf{1}}:$ Molar heat at a constant pressure $=$ Molar heat at a constant volume $+\mathrm{P\Delta V}$
${\mathbf{S}}_{\mathbf{2}}: {\mathrm{\Delta H}}_{\mathrm{sub}}={\mathrm{\Delta H}}_{\mathrm{fusion} }+{\mathrm{\Delta H}}_{\mathrm{vap} }$
${\mathbf{S}}_{\mathbf{3}}:$ Pressure is an intensive property.
${\mathbf{S}}_{\mathbf{4}}:$ For reaction $2\mathrm{A}\left(\mathrm{g}\right)+\mathrm{B}\left(\mathrm{g}\right) ⟶\left(\mathrm{g}\right) \mathrm{\Delta H}=-\mathrm{x} \mathrm{kJ}$, then for reaction
$\frac{3}{2}\mathrm{C}\left(\mathrm{g}\right)-\mathrm{A}\left(\mathrm{g}\right)+\frac{\mathrm{B}}{2}\left(\mathrm{g}\right) \mathrm{\Delta H}=\frac{\mathrm{X}}{2}\mathrm{kJ}$

Stearic acid $\left[{\mathrm{CH}}_3{\left({\mathrm{CH}}_2\right)}_{16}{\mathrm{CO}}_2\mathrm{H}\right)$ is a fatty acid, the part of fat that stores most of the energy. $1.0 \mathrm{g}$ of stearic acid was burned in a bomb calorimeter. The bomb had a heat capacity of $652 \mathrm{J}/{}^{\circ }\mathrm{C}.$ If the temperature of $500 \mathrm{g}$ water $\left(\mathrm{c}=4.18 \mathrm{J}/\mathrm{g}{}^{\circ }\mathrm{C}\right)$ increase from $25.0$ to $39.3°\mathrm{C},$ how much heat was released when the stearic acid was burned? $[\mathrm{Given}\left.{\mathrm{C}}_{\mathrm{p}}\left({\mathrm{H}}_2\mathrm{O}\right)=4.18 \mathrm{J}/8°\mathrm{C}\right]$

Use the following data to calculate the enthalpy of formation of ${\mathrm{As}}_2{\mathrm{O}}_3$:
(i) ${\mathrm{As}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)+\left[\left(3{\mathrm{H}}_2\mathrm{O}+\mathrm{aq}\right)\right]⟶2{\mathrm{H}}_3{\mathrm{AsO}}_3\left(\mathrm{aq}\right)$ $\mathrm{\Delta H}=+7550$ $\mathrm{cal}$
(ii) $\mathrm{As}\left(\mathrm{s}\right)+\frac{3}{2}{\mathrm{Cl}}_2\left(\mathrm{g}\right)⟶{\mathrm{AsCl}}_3\left(\mathrm{\ell }\right)$ $\mathrm{\Delta H}=-71390$ $\mathrm{cal}$
(iii) ${\mathrm{AsCl}}_3\left(\mathrm{\ell }\right)+\left(3{\mathrm{H}}_2\mathrm{O}+\mathrm{aq}\right)⟶{\mathrm{H}}_3{\mathrm{AsO}}_3\left(\mathrm{aq}\right)+3\mathrm{HCl}\left(\mathrm{aq}\right); \mathrm{\Delta H}=-17580\mathrm{cal}$
(iv) $\mathrm{HCl}\left(\mathrm{g}\right)+\mathrm{aq}⟶\mathrm{HCl}\left(\mathrm{aq}\right)$ $\mathrm{\Delta H}=-17315 \mathrm{cal}$
(v) $\frac{1}{2}{\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{Cl}}_2\left(\mathrm{g}\right)⟶\mathrm{HCl}\left(\mathrm{g}\right)$ $\mathrm{\Delta H}=-22000 \mathrm{cal}$
(vi) ${\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)⟶{\mathrm{H}}_2\mathrm{O}\left(\ell \right)$ $\mathrm{\Delta H}=-68360$ $\mathrm{cal}$

From the following data calculate the enthalpy change for the sublimation of ice at $223 \mathrm{K}$ [mean heat capacity of ice $=2 {\mathrm{JK}}^{-1}{\mathrm{gm}}^{-1},$ mean heat capacity of ${\mathrm{H}}_2\mathrm{O}\left(\ell \right)=4.2 {\mathrm{JK}}^{-1}{\mathrm{gm}}^{-1},$ mean heat capacity of ${\mathrm{H}}_2\mathrm{O}\left(\mathrm{v}\right)=1.85 {\mathrm{JK}}^{-1}{\mathrm{gm}}^{-1},$ enthalpy of fusion of ice at $0°\mathrm{C}=334 {\mathrm{Jgm}}^{-1},$ enthalpy of evaporation of water
at $\left[100°=2255 \text{ J }{\mathrm{gm}}^{-1}\right]$