Samples of A (1.0 mol) and B (3.5 mol) are placed in a 1 L container and the following reaction takes place: A(g) + B(g) ⇄ 2C(g) At equilibrium, the concentration of A is 0.8 M. What is the value of K to 2 d.p?
Question
Samples of A (1.0 mol) and B (3.5 mol) are placed in a 1 L container and the following reaction takes place:
A(g) + B(g) ⇄ 2C(g)
At equilibrium, the concentration of A is 0.8 M. What is the value of K to 2 d.p?
Solution
To solve this problem, we need to use the formula for the equilibrium constant (K) for the reaction. The equilibrium constant expression for the reaction is:
K = [C]^2 / ([A][B])
Given in the problem, we know that the initial moles of A and B are 1.0 mol and 3.5 mol respectively. Since the volume of the container is 1 L, these are also the initial concentrations in Molarity (M).
At equilibrium, the concentration of A is 0.8 M. This means that 0.2 M of A has reacted.
From the balanced chemical equation, we can see that for every mole of A that reacts, one mole of B also reacts and 2 moles of C are produced. Therefore, at equilibrium, the concentration of B is 3.5 M - 0.2 M = 3.3 M and the concentration of C is 2 * 0.2 M = 0.4 M.
Substituting these equilibrium concentrations into the equilibrium constant expression gives:
K = [C]^2 / ([A][B]) = (0.4 M)^2 / ((0.8 M)(3.3 M)) = 0.16 M^2 / 2.64 M^2 = 0.06
So, the value of K to 2 decimal places is 0.06.
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