JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Equilibrium

For a reaction

X + Y = 2 Z

1.0 mol

X

1.5 mol

Y

and

0.5 mol

Z

were taken in a

1 L

vessel and allowed to react. At equilibrium, the concentration of

Z

was

1.0 mol L^{- 1}

. The equilibrium constant of the reaction is

\frac{x}{15}

. The value of

x

is ______.

Answer: 16

Solution

Begin with

1.0

mol

X

1.5

mol

Y

and

0.5

mol

Z

in a

1

L flask, and let the reaction consume

α

mol each of

X

and

Y

to make

2 α

mol of

Z

. Since

[Z]

climbs from

0.5

1.0

2 α = 0.5

, so

α = 0.25

. At equilibrium

[X] = 0.75

[Y] = 1.25

and

[Z] = 1.0

, giving

K = \frac{[ Z ] ^{2}}{[ X ] [ Y ]} = \frac{1}{0.75 \times 1.25} = \frac{1}{0.9375} = \frac{16}{15}

. Comparing with

\frac{x}{15}

x = 16

JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Integer answer