Heat of formation of $C O$ gas at $300 K$ is $- 110 k J$ at constant pressure. Its heat of formation at the same temperature but at the constant volume is : (Given : $R = 8.344 J K^{- 1} {m o l}^{- 1}$ )

- 108.753 k J

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- 110 k J

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- 111.247 k J

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- 112.249 k J

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Solution

The correct option is B $- 108.753 k J$
Heat of reaction at constant volume $=$ Change in internal energy
$q_{v} = Δ E$

Heat of reaction at constant pressure $=$ Change in enthalpy energy
$q_{p} = Δ H = - 110 k J$

The formation of carbon monoxide involves the following reaction :
$C (s) G r a p h i t e + \frac{1}{2} O_{2} (g) O x y g e n ⟶ C O (g) C a r b o n m o n o x i d e$

We know that heat of reaction at constant volume and pressure are related by the following equation :
$Δ H = Δ E + Δ n R T$
where,
$Δ n =$ change in the number of moles $=$ number of moles of product $-$ number of moles of reactants
$1 - (1 + \frac{1}{2})$
$= - \frac{1}{2}$

$R = 8.314 J K^{- 1} {m o l}^{- 1} = 0.008314 k J K^{- 1} {m o l}^{- 1}$
$T =$ temperature $= 300 K$

Putting the values in the equation
$- 110 = Δ E + (- \frac{1}{2}) \times 0.008314 \times 300$

$Δ E = - 110 + 1.2471$

$Δ E = - 108.753 k J$

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Heat of formation of CO gas at 300 K is −110 kJ at constant pressure. Its heat of formation at the same temperature but at the constant volume is : (Given : R=8.344 JK−1mol−1)

Heat of formation of $C O$ gas at $300 K$ is $- 110 k J$ at constant pressure. Its heat of formation at the same temperature but at the constant volume is : (Given : $R = 8.344 J K^{- 1} {m o l}^{- 1}$ )