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For a gaseous reaction, $2 {SO}_{2} + O_{2} ⟶ 2 {SO}_{3} Δ H = - 440 kJ / mole$ mole at a temperature of 300 K. Calculate $Δ U$ when 1 mole of ${SO}_{2}$ is completely reacted with 1 mole of $O_{2}$ in a 10 litre rigid vessel at an initial pressure of 50 bar which decreases to 20 bar.

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$- 410 kJ$

$- 470 kJ$

$- 190 kJ$

$- 250 kJ$

answer is A.

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Detailed Solution

Change in enthalpy when the pressure is changing,

$\begin{array}{l} Δ H = Δ U + V Δ P \\ - 440 \times \frac{1}{2} = Δ U + \frac{10 \times (20 - 50) \times 100}{1000} \Rightarrow Δ U = - 190 kJ \end{array}$

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