The equilibrium constant $\mathrm{K}_{\mathrm{c}}$ at 298 K for the reaction A + B ⇌ C + D is 100. Starting with an equimolar solution with concentrations of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D all equal to 1 M, the equilibrium concentration of D is $\_\_\_\_$ $\times 10^{-2} \mathrm{M}$. (Nearest integer)

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Equilibrium

The equilibrium constant

K_{c}

at 298 K for the reaction
A + B ⇌ C + D
is 100. Starting with an equimolar solution with concentrations of

A, B, C

and D all equal to 1 M, the equilibrium concentration of D is

____

\times 1 0^{- 2} M

. (Nearest integer)

Answer: 182

All four species start at

1

M, so the reaction quotient is

1

, far below

K_{c}

, and the reaction runs forward. If

x

M of A and of B are consumed, then at equilibrium

K_{c} = \frac{( 1 + x ) ^{2}}{( 1 - x ) ^{2}} = 100

Taking the positive square root,

\frac{1 + x}{1 - x} = 10

, so

1 + x = 10 - 10 x

11 x = 9

and

x = 0.818

M. The equilibrium concentration of D is

1 + 0.818 = 1.818

M, that is

181.8 \times 1 0^{- 2}

M, which to the nearest integer is

182 \times 1 0^{- 2}

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Integer answer