At a certain temperature the equilibrium constant, Kc, equals 0.11 for the reaction:

What is the equilibrium concentration of ICl if 0.75 mol of I2 and 0.75 mol of Cl2 are initially mixed in a 2.0-L flask?

Question

At a certain temperature the equilibrium constant, Kc, equals 0.11 for the reaction:

What is the equilibrium concentration of ICl if 0.75 mol of I2 and 0.75 mol of Cl2 are initially mixed in a 2.0-L flask?

BlackTom AI · Accepted Answer

First, restate the problem in my own words: We have the equilibrium 2 ICl ⇌ I2 + Cl2 with Kc = 0.11. Initially, I2 = 0.75 mol and Cl2 = 0.75 mol are placed in a 2.0 L flask, and there is no ICl present initially. We need to find the equilibrium concentration of ICl.

Next, set up the change in concentrations using an ICE table. Since the reaction will proceed toward forming ICl from I2 and Cl2, let y be the extent of the forward reaction I2 + Cl2 → 2 ICl. At equilibrium:
- I2: 0.75 − y moles
- Cl2: 0.75 − y moles
- ICl: 0 + 2y moles

Convert to concentrations by dividing by the volume 2.0 L:
- [I2] = (0.75 − y)/2
- [Cl2] = (0.75 − y)/2
- [ICl] = (2y)/2 = y

Now apply the expression for the equilibrium constant in terms of concentrations:
Kc = [I2][Cl2]/[ICl]^2 = [ (0.75 − y)/2 * (0.75 − y)/2 ] / (y^2) = (0.75 − y)^2 / (4 y^2).
Set this equal to 0.11 and solve for y:
(0.75 − y)^2 / (4 y^2) = 0.11
Taking square roots on both sides gives (0.75 − y)/(2y) = √0.11 ≈ 0.33166.
From that, 0.75 − y ≈ 0.66332 y, so 0.75 ≈ 1.66332 y, yielding y ≈ 0.450.
Since [ICl] = y, the equilibrium concentration of ICl is approximately 0.450 M.

A quick consistency check: plug y ≈ 0.450 back into the expressions: [I2] ≈ (0.75 − 0.450)/2 = 0.150 M, [Cl2] ≈ 0.150 M, [ICl] ≈ 0.450 M. Then Kc ≈ (0.150 × 0.150) / (0.450^2) ≈ 0.0225 / 0.2025 ≈ 0.111, which is in line with the given 0.11, validating the calculation.

Therefore, the equilibrium concentration of ICl is about 0.45 M.

At a certain temperature the equilibrium constant, Kc, equals 0.11 for the reaction: What is the equilibrium concentration of ICl if 0.75 mol of I2 and 0.75 mol of Cl2 are initially mixed in a 2.0-L flask?

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