1.1 mol of A mixed with 2.2 mol of B and the mixture is kept in a 1 L flask and the equilibrium,A + 2B 2C + D is reached. If at equilibrium 0.2 mol of C is formed then the value of KC will be.
Question
1.1 mol of A mixed with 2.2 mol of B and the mixture is kept in a 1 L flask and the equilibrium,A + 2B 2C + D is reached. If at equilibrium 0.2 mol of C is formed then the value of KC will be.
Solution
To solve this problem, we first need to understand the reaction and what is happening at equilibrium. The reaction is:
A + 2B ⇌ 2C + D
We are given that initially we have 1.1 mol of A and 2.2 mol of B in a 1 L flask. At equilibrium, 0.2 mol of C is formed.
Step 1: Calculate the initial concentrations of A, B, C and D.
Since the volume of the flask is 1 L, the initial concentrations are:
[A] = 1.1 mol / 1 L = 1.1 M [B] = 2.2 mol / 1 L = 2.2 M [C] = 0 (since C is a product and we are given that it is formed at equilibrium) [D] = 0 (for the same reason as C)
Step 2: Calculate the change in concentrations to reach equilibrium.
Since the reaction shows that 1 mol of A reacts with 2 mol of B to produce 2 mol of C and 1 mol of D, the changes in concentrations are:
Δ[A] = -0.2 M (since 0.2 mol of C is formed, 0.1 mol of A is used up) Δ[B] = -0.4 M (since 2 mol of B react for every 1 mol of A) Δ[C] = +0.2 M (since 0.2 mol of C is formed) Δ[D] = +0.1 M (since 1 mol of D is formed for every 1 mol of A)
Step 3: Calculate the equilibrium concentrations.
[A]eq = [A]initial + Δ[A] = 1.1 M - 0.2 M = 0.9 M [B]eq = [B]initial + Δ[B] = 2.2 M - 0.4 M = 1.8 M [C]eq = [C]initial + Δ[C] = 0 + 0.2 M = 0.2 M [D]eq = [D]initial + Δ[D] = 0 + 0.1 M = 0.1 M
Step 4: Substitute the equilibrium concentrations into the expression for Kc.
Kc = ([C]^2[D]) / ([A][B]^2) = (0.2^2 * 0.1) / (0.9 * 1.8^2)
Step 5: Calculate the value of Kc.
Kc = 0.004 / 2.916 = 0.00137
So, the value of Kc for this reaction under these conditions is approximately 0.00137.
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