What is value of PV type of work for following reaction at 1 bar?

What is value of PV type of work for following reaction at 1 bar?
  1. $3.5 \mathrm{~J}$
  2. $4.5 \mathrm{~J}$
  3. $9.0 \mathrm{~J}$
  4. $15 \mathrm{~J}$

Solution

$\begin{aligned} & 1 \text { mole of } \mathrm{C}_2 \mathrm{H}_4 \text { reacts with } 1 \text { mole of } \mathrm{HCl} \text { to } \\ & \text { produce } 1 \mathrm{~mole} \text { of } \mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl} \text {. } \\ & \text { Hence, } 150 \mathrm{~mL} \text { of } \mathrm{HCl} \text { would react with only } \\ & 150 \mathrm{~mL} \text { of } \mathrm{C}_2 \mathrm{H}_4 \text { to produce } 150 \mathrm{~mL} \text { of } \mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl} . \\ & \mathrm{V}_1=150 \mathrm{~mL}+150 \mathrm{~mL}=300 \mathrm{~mL}=0.3 \mathrm{dm}^3 \\ & \mathrm{~V}_2=150 \mathrm{~mL}=0.15 \mathrm{dm}^3 \\ & \mathrm{~W}=-\mathrm{P}_{\text {ext }} \Delta \mathrm{V}=-\mathrm{P}_{\text {ext }}\left(\mathrm{V}_2-\mathrm{V}_1\right) \\ & \therefore \quad \mathrm{W}=-1 \text { bar }\left(0.15 \mathrm{dm}^3-0.3 \mathrm{dm}^3\right) \\ & \therefore \quad \mathrm{W}=0.15 \mathrm{dm}^3 \text { bar } \\ & \therefore \quad W=0.15 \mathrm{dm}^3 \text { bar } \times 100 \frac{\mathrm{J}}{\mathrm{dm}^3 \text { bar }} \\ & \therefore \quad W=15 \mathrm{~J} \end{aligned}$ The PV work in joules is $15 \mathrm{~J}$.

Asked in: MHT CET 2023 (11 May Shift 1)

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