Volume Change in Gaseous Reaction JEE Main PYQ

 

❓ Question

100 mL of PH₃ gas decomposes to give P₄ and H₂. Find the change in volume.

Reaction:

$$4PH_3(g)\rightarrow P_4(s)+6H_2(g)$$

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✍️ Solution

At constant temperature and pressure, according to Gay-Lussac's law,

$$\text{Volume} \propto \text{Number of moles of gas}$$

From the balanced equation,

$$4\ \text{vol PH}_3 \rightarrow 6\ \text{vol H}_2$$

Since P₄ is a solid, its volume is negligible.

Therefore,

$$4\ \text{mL PH}_3 \rightarrow 6\ \text{mL H}_2$$
$$100\ \text{mL PH}_3 \rightarrow \frac{6}{4}\times100 =150\ \text{mL H}_2$$

Initial gaseous volume,

$$V_i=100\ \text{mL}$$

Final gaseous volume,

$$V_f=150\ \text{mL}$$

Hence,

$$\Delta V=V_f-V_i =150-100 =50\ \text{mL}$$

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✅ Final Answer

$$\boxed{\Delta V=+50\ \text{mL}}$$

The volume increases by $\boxed{50\ \text{mL}}$.