Question

For a reaction, $${N}_2{O}_5(g) \rightarrow 2{NO}_2(g) + \frac{1}{2} {O}_2(g)$$ in a constant volume container, no products were present initially. The final pressure of the system when 50% of the reaction gets completed is:

• A. $\frac{7}{2}$ times of initial pressure
• B. 5 times of initial pressure
• C. $\frac{5}{2}$ times of initial pressure
• D. $\frac{7}{4}$ times of initial pressure

Hint:

For reactions occurring in a constant volume container, use stoichiometry to calculate the total pressure by considering the moles of reactants and products formed at each step.

Answer 1

The Correct Option is D

Let the initial pressure of $N_2O_5$ be $P_0$.
At 50% reaction completion:
- $\frac{1}{2} P_0$ of $N_2O_5$ decomposes.
- This produces:
    - $P_0$ of $NO_2$,
     - $\frac{P_0}{4}$ of $O_2$.
Thus, the total final pressure is: $$P_{\text{final}} = \frac{P_0}{2} + P_0 + \frac{P_0}{4} = \frac{7P_0}{4}$$ Hence, the final pressure is $\frac{7}{4}$ of the initial pressure.
Thus, the correct answer is: $\boxed{(4)}$.