NEET (UG) 2024 — Question 86

$2 \mathrm{NO}_{(\mathrm{g})} \rightleftharpoons \mathrm{N}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})}$

$\mathrm{K}_{\mathrm{c}}= \frac{\left[\mathrm{N}_{2}\right]\left[\mathrm{O}_{2}\right]}{[\mathrm{NO}]^{2}}$

$=\frac{3 \times 10^{-3} \times 4.2 \times 10^{-3}}{2.8 \times 10^{-3} \times 2.8 \times 10^{-3}}$

$=1.607$

$2 \mathrm{NO}_{(\mathrm{g})} \rightleftharpoons \mathrm{N}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})}$

$\mathrm{t}=0 \quad 0.1 \quad 0$

$0.1-0.1 \alpha \quad 0.05 \alpha \quad 0.05 \alpha$

$\mathrm{~K}_{\mathrm{c}}=\frac{0.05 \alpha \times 0.05 \alpha}{(0.1-0.1 \alpha)^{2}}$

$\mathrm{~K}_{\mathrm{c}}=\frac{0.05 \alpha \times 0.05 \alpha}{0.01(1-\alpha)^{2}}$

$1.607=\frac{(0.05)^{2} \alpha^{2}}{0.01(1-\alpha)^{2}}$

$\frac{\alpha^{2}}{(1-\alpha)^{2}}=\frac{1.607 \times(0.1)^{2}}{(0.05)^{2}}$

$\frac{\alpha}{1-\alpha}=\frac{1.27 \times 0.1}{0.05}$

$\frac{\alpha}{1-\alpha}=2.54$

$\alpha=2.54-2.54 \alpha$

$3.54 \alpha=2.54$

$\alpha=\frac{2.54}{3.54}=0.717$