Sahana Ansari and Neha Miglani Solutions for Chapter: Thermodynamics, Exercise 4: Chapter Practice

The enthalpy of formation of ${\mathrm{CH}}_4, {\mathrm{C}}_2{\mathrm{H}}_6 \mathrm{and} {\mathrm{C}}_4{\mathrm{H}}_{10}$ are$-74.8,-84.7$ and $-126.1 \mathrm{kJ} {\mathrm{mol}}^{-1}$  respectively
Arrange them in the order of their efficiency as fuel per gram (enthalpy of formation of ${\mathrm{CO}}_2\left(\mathrm{g}\right)$ and ${\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$ are -$393.5$ and $-285.8 \mathrm{kJ} {\mathrm{mol}}^{-1}$ respectively.

It is planned to carry the reaction, ${\mathrm{CaCO}}_3\left(\mathrm{s}\right) \rightleftharpoons \mathrm{CaO}\left(\mathrm{s}\right) + {\mathrm{CO}}_2\left(\mathrm{g}\right)$ at $1273 \mathrm{K}$ and $1 \mathrm{bar}$. 

Calculate the value of partial pressure of ${\mathrm{CO}}_2$, at equilibrium

Given,

$$\begin{gathered} {\mathrm{\Delta }}_{\mathrm{f}}\mathrm{H}° \mathrm{values} (\mathrm{kJ} {\mathrm{mol}}^{-1}): {\mathrm{CaCO}}_3\left(\mathrm{s}\right)=-1206.9,\mathrm{CaO}\left(\mathrm{s}\right)=-635.1, \\ {\mathrm{CO}}_2\left(\mathrm{g}\right)=-393.5 \\ ∆\mathrm{S}° \mathrm{values} \left({\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\right), {\mathrm{CaCO}}_3\left(\mathrm{s}\right)=92.9,\mathrm{CaO}\left(\mathrm{s}\right)=39.8,{\mathrm{CO}}_2\left(\mathrm{g}\right)=213.7. \end{gathered}$$

State the law of thermodynamics that was first formulated by Nernst in 1906. What is the utility of this law? The equilibrium constant for the reaction $\mathrm{A}\rightleftharpoons \mathrm{B}$ is $1.8 \times {10}^{-7}$ at $298 \mathrm{K}$. Calculate the value of $∆\mathrm{G}º$ for the reaction $(\mathrm{R} = 8.314 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1})$. Predict the feasibility of the reaction under standard states.

Two moles of a perfect gas undergo the following processes :

(i) a reversible isobaric expansion from $(1.0 \mathrm{atm}, 20.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$

(ii) a reversible isochoric change of state from $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$ to $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$

(iii) a reversible isothermal compression from $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 20.0\mathrm{L})$

Sketch with labels each of the processes on the same $\mathrm{p}-\mathrm{V}$ diagram.

Two moles of a perfect gas undergo the following processes :

(i) a reversible isobaric expansion from $(1.0 \mathrm{atm}, 20.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$

(ii) a reversible isochoric change of state from $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$ to $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$

(iii) a reversible isothermal compression from $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 20.0\mathrm{L})$

Calculate the total work $\left(\mathrm{W}\right)$ and the total heat change $\left(\mathrm{q}\right)$ involved in the above processes.

Two moles of a perfect gas undergo the following processes :

(i) a reversible isobaric expansion from $(1.0 \mathrm{atm}, 20.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$

(ii) a reversible isochoric change of state from $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$ to $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$

(iii) a reversible isothermal compression from $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 20.0\mathrm{L})$

Sketch with labels each of the processes on the same $\mathrm{p}-\mathrm{V}$ diagram.

Two moles of a perfect gas undergo the following processes :

(i) a reversible isobaric expansion from $(1.0 \mathrm{atm}, 20.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$

(ii) a reversible isochoric change of state from $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$ to $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$

(iii) a reversible isothermal compression from $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 20.0\mathrm{L})$

Sketch with labels each of the processes on the same $\mathrm{P}-\mathrm{V}$ diagram.

Two moles of a perfect gas undergo the following processes :

(i) a reversible isobaric expansion from $(1.0 \mathrm{atm}, 20.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$

(ii) a reversible isochoric change of state from $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$ to $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$

(iii) a reversible isothermal compression from $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 20.0\mathrm{L})$

What will be the value of $∆\mathrm{U}, ∆\mathrm{H}$ and $∆\mathrm{S}$ for the overall process?