\(\mathrm{X}_{2}(\mathrm{~g})+\mathrm{Y}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{Z}(\mathrm{g})\) \(\mathrm{X}_{2}(\mathrm{~g})\) and \(\mathrm{Y}_{2}(\mathrm{~g})\) are added to a 1 L flask and it is found that the system attains the above equilibrium at \(\mathrm{T}(\mathrm{K})\) with the number of moles of \(\mathrm{X}_{2}(\mathrm{~g}), \mathrm{Y}_{2}(\mathrm{~g})\) and \(\mathrm{Z}(\mathrm{g})\) being 3, 3 and 9 mol respectively (equilibrium moles). Under this conditions of equilibrium, 10 mol of \(\mathrm{Z}(\mathrm{g})\) is added to the flask and the temperature is maintained at \(\mathrm{T}(\mathrm{K})\). Then the number of moles of \(\mathrm{Z}(\mathrm{g})\) in the flask when the new equilibrium is established is \_\_\_\_. (Nearest integer).

JEE Main · 2026 · 23 Jan 2026 · Shift 2 · Equilibrium

X_{2} (g) + Y_{2} (g) ⇌ 2 Z (g)

X_{2} (g)

and

Y_{2} (g)

are added to a 1 L flask and it is found that the system attains the above equilibrium at

T (K)

with the number of moles of

X_{2} (g), Y_{2} (g)

and

Z (g)

being 3, 3 and 9 mol respectively (equilibrium moles). Under this conditions of equilibrium, 10 mol of

Z (g)

is added to the flask and the temperature is maintained at

T (K)

. Then the number of moles of

Z (g)

in the flask when the new equilibrium is established is ____. (Nearest integer).

Answer: 15

At the first equilibrium

K_{C} = \frac{[ Z ] ^{2}}{[ X _{2} ] [ Y _{2} ]} = \frac{9 ^{2}}{3 \times 3} = 9

. Adding

10

mol of Z raises its amount to

19

mol and drives the reaction backward; if

y

mol each of

X_{2}

and

Y_{2}

reform, then

2 y

mol of Z are consumed, giving

[X_{2}] = [Y_{2}] = 3 + y

and

[Z] = 19 - 2 y

in the

1 L

flask. Then

\frac{( 19 - 2 y ) ^{2}}{( 3 + y ) ^{2}} = 9

, so

\frac{19 - 2 y}{3 + y} = 3

and

y = 2

. The amount of Z at the new equilibrium is

19 - 2 (2) = 15

mol.

JEE Main · 2026 · 23 Jan 2026 · Shift 2 · Integer answer