When 5.1 g of solid $\mathrm{NH}_{4} \mathrm{HS}$ is introduced into a two litre evacuated flask at $27^{\circ} \mathrm{C}$, 20% of the solid decomposes into gaseous ammonia and hydrogen sulphide. The $\mathrm{K}_{\mathrm{p}}$ for the reaction at $27^{\circ} \mathrm{C}$ is x $\times 10^{-2}$. The value of $x$ is ____ (Integer answer) [Given $\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm}^{-1} \mathrm{~mol}^{-1}$]

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Equilibrium

When 5.1 g of solid

NH_{4} HS

is introduced into a two litre evacuated flask at

2 7^{\circ} C

, 20% of the solid decomposes into gaseous ammonia and hydrogen sulphide. The

K_{p}

for the reaction at

2 7^{\circ} C

is x

\times 1 0^{- 2}

. The value of

x

is ____ (Integer answer)
[Given

R = 0.082 L atm^{- 1} mol^{- 1}

]

Answer: 6

For

N H_{4} HS (s) ⇌ N H_{3} (g) + H_{2} S (g)

, the

5.1 g

of solid is

5.1/51 = 0.1

mol, of which

20%

, i.e.

0.02

mol, decomposes to give

0.02

mol each of ammonia and hydrogen sulphide. Each exerts a partial pressure

p = \frac{n R T}{V} = \frac{0.02 \times 0.082 \times 300}{2} = 0.246 atm,

K_{p} = p_{N H_{3}} p_{H_{2} S} = (0.246)^{2} = 0.0605 at m^{2} = 6 \times 1 0^{- 2},

giving

x = 6

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Integer answer