In an experiment the equilibrium constant for the reaction is K when t...
Calculating Equilibrium Constant
Equilibrium constant (K) is defined as the ratio of the concentration of reactants and products at equilibrium. It is a constant value for a particular reaction at a specific temperature. The equilibrium constant can be calculated using the following formula:
K = [C]^c[D]^d/[A]^a[B]^b
where [A], [B], [C], and [D] are the concentrations of the reactants and products at equilibrium and a, b, c, and d are the coefficients of the balanced chemical equation.
Solution
In the first experiment, the initial concentration of A and B is 0.1. Let us assume that the balanced chemical equation for the reaction is:
aA + bB ↔ cC + dD
where a, b, c, and d are the coefficients of the balanced chemical equation.
Let us assume that at equilibrium, the concentration of A, B, C, and D is [A], [B], [C], and [D], respectively.
Using the formula for equilibrium constant, we get:
K = [C]^c[D]^d/[A]^a[B]^b = [C]^c[D]^d/(0.1)^a(0.1)^b
Similarly, in the second experiment, the initial concentration of A and B is 2 and 3, respectively.
Using the formula for equilibrium constant, we get:
K' = [C']^c[D']^d/[A']^a[B']^b = [C']^c[D']^d/(2)^a(3)^b
We can see that the only difference between K and K' is the concentration of the reactants and products at equilibrium. To find the value of K' in terms of K, we can use the concept of stoichiometry.
Stoichiometry tells us that the ratio of the moles of reactants and products in a balanced chemical equation is fixed. Therefore, if we know the initial concentrations of the reactants and products, we can use stoichiometry to find the concentrations of the reactants and products at equilibrium.
Let us assume that the moles of A and B in the first experiment are nA and nB, respectively. Similarly, let us assume that the moles of A and B in the second experiment are nA' and nB', respectively.
Using stoichiometry, we can write:
nA/nB = nA'/nB'
Therefore,
nA'/nA = nB'/nB = 2/0.1 = 20
This means that the concentration of A and B in the second experiment is 20 times higher than the concentration of A and B in the first experiment.
Using the formula for equilibrium constant, we get:
K' = [C']^c[D']^