At 25oC, the value of Kc for the following reaction is 82. 𝐼2(𝑔) + 𝐶𝑙2(𝑔) ⇌ 2𝐼𝐶𝑙(𝑔) 0.83 mol of I2(g) and 0.83 mol of Cl2(g) are placed in a 10 L container at 25oC. What is the concentration of the three gases at equilibrium?

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Answer 1 · 2018-05-17T16:57:14

Consider,

$I_{2} (g) + C l_{2} (g) ⇌ 2 I C l (g)$ $I_2(g) + Cl_2(g) rightleftharpoons 2ICl(g)$

where, $K_{c} = 82$ $K_"c" = 82$ at $298.15 K$ $298.15"K"$

Given,

${[I_{2}]}_{i} = {[C l_{2}]}_{i} \approx 8.3 \cdot 10^{- 2} M$ $[I_2]_"i" = [Cl_2]_"i" approx 8.3*10^-2"M"$

Using an ICE table,

$I_{2} (g) + C l_{2} (g) ⇌ 2 I C l (g)$ $I_2(g) + Cl_2(g) rightleftharpoons 2ICl(g)$
puu.sh

$K_{c} = \frac{{(8.3 \cdot 10^{- 2} - x)}^{2}}{{(2 x)}^{2}} = 82$ $K_c = (8.3*10^-2 - x)^2/(2x)^2 = 82$

$\Rightarrow x = 4.34 \cdot 10^{- 3}$ $=> x = 4.34*10^-3$

Hence,

${[I_{2}]}_{eq} = {[C l_{2}]}_{eq} \approx 7.87 \cdot 10^{- 2} M$ $[I_2]_"eq" = [Cl_2]_"eq" approx 7.87*10^-2"M"$ , and

${[I C l]}_{eq} = 2 x \approx 8.69 \cdot 10^{- 3} M$ $[ICl]_"eq" = 2x approx 8.69*10^-3"M"$