Question

Calculate $\Delta _{\text{f}} \text{G}^{^\circ }$ for (NH₄Cl, s) at 310 K.

Given : $\Delta_{ f } H ^{\circ}\left( NH _{4} Cl , s \right)=-314.5\, kJ / mol ; \Delta_{ r } C _{ p }=0$

$S _{ N _{2}( g )}^{\circ}=192 \,JK ^{-1}\, mol ^{-1} ; S _{ H _{2}( g )}^{\circ}=130.5\, JK ^{-1} mol ^{-1}$

$S _{ Cl _{2}( g )}^{\circ}=233 \,JK ^{-1} mol ^{-1} ; S _{ NH _{4} Cl ( s )}^{\circ}=99.5\, JK ^{-1} \,mol ^{-1}$

All given data at $300\, K$.

• A. $- \text{198.56 kJ/mol}$
• B. $- \text{426.7 kJ/mol}$
• C. $- \text{202.3 kJ/mol}$
• D. None of these

Answer 1

Answer: (A)

$\Delta_{ f } S ^{0}\left( NH _{4} Cl , s \right)$ at $300 K$

$= \text{S}_{\text{N} \left(\text{H}\right)_{4} \text{C} \text{l} \left(\right. \text{S} \left.\right)}^{0} - \left[\right. \frac{1}{2} \text{S}_{\left(\text{N}\right)_{2}}^{0} + 2 \text{S}_{\left(\text{H}\right)_{2}}^{0} + \frac{1}{2} \text{S}_{\text{C} \left(\text{l}\right)_{2}}^{0} \left]\right.$

$= \, -374 \, \text{J}\text{K}^{- 1}\text{m}\text{o}\text{l}^{- 1} \, \, $

$\therefore \, \Delta _{\text{f}}\text{C}_{\text{p}}=0$

$\therefore \, \, \Delta _{\text{f}}\text{S}_{310}^{0}=\Delta _{\text{r}}\text{S}_{300}^{0}$

$= \, -374 \, \text{J}\text{K}^{- 1}\text{m}\text{o}\text{l}^{- 1}$

$\Delta _{\text{f}}\text{H}_{310}^{0}=\Delta _{\text{f}}\text{H}_{300}^{0}=-314.5$

$\Delta _{\text{f}}\text{G}_{310}^{0}=\Delta _{\text{f}}\text{H}^{0}-310\Delta _{\text{f}}\text{S}^{0}$

$= \, -314.5-\frac{310 \left(- 374\right)}{1000}$

$-198.56 \, \text{k}\text{J}/\text{m}\text{o}\text{l}$