Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 4: EXERCISE-4

Calculate work done in adiabatic compression of one mole of an ideal gas (monoatomic) from an initial pressure of $1\mathrm{atm}$ to final pressure of $2\mathrm{atm}$. Initial temperature $=300\mathrm{K}$

(a) If process is carried out reversibly

(b) If process is carried out irreversible against $2\mathrm{atm}$ external pressure.

Compute the final volume reached by gas in two cases.

A $32\mathrm{g}$ sample of ${\mathrm{CH}}_4$ gas initially at $101.325 \mathrm{kPa}$ and $300\mathrm{K}$ is heated to $550\mathrm{K}$. ${\mathrm{C}}_{\mathrm{p}.\mathrm{m}.}/{\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}=12.552+8.368\times {10}^{-2} \mathrm{T}/\mathrm{K}$. Assuming ${\mathrm{CH}}_4$ behaves ideally, compute $\mathrm{w},\mathrm{q},∆\mathrm{U}$ and $∆\mathrm{H}$ for

(a) an isobaric reversible process and

(b) an isochoric reversible process.

Consider the following thermodynamic data :

Enthalpy of formation of ${\mathrm{CaC}}_2\left(\mathrm{s}\right)=-60 \mathrm{kJ}/\mathrm{mol}$ ;

Enthalpy of sublimation of $\mathrm{Ca}\left(\mathrm{s}\right)=179 \mathrm{kJ}/\mathrm{mol}$ ;

Enthalpy of sublimation of $\mathrm{C}\left(\mathrm{s}\right)=718 \mathrm{kJ}/\mathrm{mol}$ ;

First ionization energy of $\mathrm{Ca} \left(\mathrm{g}\right)=590 \mathrm{kJ}/\mathrm{mol}$ ;

Second ionization energy of $\mathrm{Ca} \left(\mathrm{g}\right)=1143 \mathrm{kJ}/\mathrm{mol}$ ;

Bond energy of ${\mathrm{C}}_2\left(\mathrm{g}\right)=614 \mathrm{kJ}/\mathrm{mol}$ ;

First electron affinity of ${\mathrm{C}}_2\left(\mathrm{g}\right)=+410 \mathrm{kJ}/\mathrm{mol}$ ;

Draw a clear Born-Haber cycle and determine lattice energy of ${\mathrm{CaC}}_2\left(\mathrm{s}\right)$.

A swimmer breath $20$ times in one minute when swimming and inhale $200 \mathrm{mL}$ of air in one breath. Inhalded air contain $20\%$ ${\mathrm{O}}_2$ by volume and exhaled air contain $10\%$ ${\mathrm{O}}_2$ by volume. If all oxygen is consumed in combustion of glucose in the body and $25\%$ of energy obtained from combustion is available for muscular work. Determine the maximum distance this swimmer can swim in one hour if $100 \mathrm{kJ}$ Energy is required for $1.0 \mathrm{km}$ Swimming. Standard molar enthalpy of combustion of glucose is $-2880 \mathrm{kJ}/\mathrm{mol}$ and body temperature is ${37}^{°}\mathrm{C}$.

Use the following enthalpies of combustion in the calculations that follow.

(i) Calculate the enthalpy change for the reaction :

$2\mathrm{C}\left(\mathrm{s}\right)+2{\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{CH}}_3{\mathrm{CO}}_2\mathrm{H}\left(\mathrm{l}\right)$

(ii) Calculate the enthalpy of formation of buta-$1,3$-diene ${\mathrm{C}}_4{\mathrm{H}}_6$.

(iii) Calculate the enthalpy of formation of ethene ${\mathrm{C}}_2{\mathrm{H}}_4$.

(iv) Calculate the enthalpy change for the conversion of ethene ${\mathrm{C}}_2{\mathrm{H}}_4$ to ethane ${\mathrm{C}}_2{\mathrm{H}}_6$.

Enthalpy for the reaction ${\mathrm{Ag}}^{+}\left(\mathrm{aq}\right)+{\mathrm{Br}}^{-}\left(\mathrm{aq}\right)\to \mathrm{AgBr}\left(\mathrm{s}\right)$ is $-84.54 \mathrm{kJ}$. Magnitude of enthalpy of formation of ${\mathrm{Ag}}^{+}\left(\mathrm{aq}\right)$ and ${\mathrm{Br}}^{-}\left(\mathrm{aq}\right)$ are in the ratio $8 : 9$. Formation of ${\mathrm{Ag}}^{+}\left(\mathrm{aq}\right)$ is an endothermic process whereas formation of ${\mathrm{Br}}^{-}$ is an exothermic process. Enthalpy of formation of $\mathrm{AgBr}$ is $-99.54 \mathrm{kJ}/\mathrm{mol}$. Calculate the enthalpy of formation of ${\mathrm{Ag}}^{+}\left(\mathrm{aq}\right)$ in $\mathrm{kJ}/\mathrm{mol}$.

At $25°\mathrm{C},{\mathrm{\Delta H}}_{\mathrm{f}}\left({\mathrm{H}}_2\mathrm{O},\mathrm{l}\right)=-56700 \mathrm{J} \mathrm{mol}$ and energy of ionization of ${\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)=19050 \mathrm{J} \mathrm{mol}$. What will be the reversible EMF at $25°\mathrm{C}$ of the cell,
$\mathrm{Pt}\left|{\mathrm{H}}_2\left(\mathrm{g}\right)(1 \mathrm{atm})\right|{\mathrm{H}}^{+}\left|\right|{\mathrm{OH}}^{-}\left|{\mathrm{O}}_2\left(\mathrm{g}\right)(1 \mathrm{atm})\right|\mathrm{Pt}$, if at $26°\mathrm{C}$ the emf increase by $0.001158 \mathrm{V}$.

Given are the following standard free energies of formation at $298 \mathrm{K}$.

$\begin{array}{lllll}& \mathrm{CO}\left(\mathrm{g}\right)& {\mathrm{CO}}_2\left(\mathrm{g}\right)& {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)& {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\\ \frac{{\mathrm{\Delta }}_{\mathrm{f}}\mathrm{G}°}{{\mathrm{kJmole}}^{-1}}& -137.17& -394.36& -228.57& -237.13\end{array}$

(a) Find ${\mathrm{\Delta }}_{\mathrm{r}}\mathrm{G}°$ and the standard equilibrium constant ${\mathrm{K}}_{\mathrm{p}}^0$ at $298 \mathrm{K}$ for the reaction
$\mathrm{CO}\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{CO}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$

(b) If $\mathrm{CO},{\mathrm{CO}}_2$ and ${\mathrm{H}}_2$ are mixed so that the partial pressure of each is $101.325 \mathrm{kPa}$ and the mixture is brought into contact with excess of liquid water, what will be the partial pressure of each gas when equilibrium is attained at $298 \mathrm{K}$. The volume available to the gases is constant.