1.0 mol of H2 and 2.0 mol of I2 are heated in a 1.0 L closed vessel where H2(g) + I2(g) 2HI(g) has K_c = 54. Calculate the amount of HI at equilibrium, in mol, to two decimal places.

JEE Advanced levelNumerical answerDifficulty 3 of 3ce038

1.0 mol of $H X_{2}$ and 2.0 mol of $I X_{2}$ are heated in a 1.0 L closed vessel where $H X_{2} (g) + I X_{2} (g) 2 HI (g)$ has $K_{c} = 54$ . Calculate the amount of $HI$ at equilibrium, in mol, to two decimal places.

Numerical answer type, answer in mol, tolerance 0.005.

Let

x

mol of

H X_{2}

react:

(2 x)^{2} = 54 (1 - x) (2 - x)

, i.e.

50 x^{2} - 162 x + 108 = 0

(all values in mol/L as

V = 1.0

L). The root with

x < 1

x = 0.9385

. Hence

n (HI) = 2 x = 1.877

mol.