For H2(g) + I2(g) 2HI(g), K_c = 45 at a certain temperature. A 2.0 L vessel holds 1.0 mol H2 and 1.0 mol I2. How many moles of HI must also be present for the mixture to have Q_c = K_c exactly (two decimals)?

JEE Main levelNumerical answerDifficulty 2 of 3ce130

For $H X_{2} (g) + I X_{2} (g) 2 HI (g)$ , $K_{c} = 45$ at a certain temperature. A $2.0 L$ vessel holds $1.0$ mol $H X_{2}$ and $1.0$ mol $I X_{2}$ . How many moles of $HI$ must also be present for the mixture to have $Q_{c} = K_{c}$ exactly (two decimals)?

Numerical answer type, answer in mol, tolerance 0.02.

[H X_{2}] = [I X_{2}] = 0.50 mol L^{- 1}

. Setting

Q_{c} = [HI]^{2} / (0.50 \times 0.50) = 45

gives

[HI] = 45 \times 0.25 = 3.3541 mol L^{- 1}

. Moles of

HI

= 3.3541 \times 2.0 = 6.7082

mol, i.e. 6.71 mol.