The equilibrium constant for the following reaction is 7.2 x 10-10. What is the [H+] in a solution 1.0 M of this acid?
HCN + H2O --> H3O+ + CN-
To determine the [H+] in a solution of 1.0 M of acid, we can use the equilibrium constant expression and the stoichiometry of the reaction:
HCN + H2O ⇌ H3O+ + CN-
The equilibrium constant expression for this reaction is:
K = [H3O+][CN-] / [HCN][H2O]
Given that the equilibrium constant (K) is 7.2 x 10-10, and the concentration of HCN is 1.0 M, we need to find the concentration of [H3O+].
Let's assume the concentration of [H3O+] is x.
Substituting the known values into the equilibrium constant expression:
7.2 x 10-10 = x [CN-] / [HCN][H2O]
Since the concentration of HCN is 1.0 M, and water concentration remains relatively constant, we can simplify the expression:
7.2 x 10-10 = x [CN-] / 1.0[H2O]
[CN-] / [H2O] = 7.2 x 10-10 / x
Now, since H2O acts as a solvent, its concentration can be considered constant and we can disregard it in the calculation. Therefore, [CN-] / [H2O] ≈ [CN-].
[CN-] ≈ 7.2 x 10-10 / x
Since the reaction involves the loss of one H+ ion from HCN, it can be assumed that [H+] ≈ [CN-].
Therefore, [H+] ≈ 7.2 x 10-10 / x
Now, we can calculate the approximate value of [H+] by substituting the equilibrium constant (K) value:
7.2 x 10-10 = x [H+] / 1.0
x [H+] = 7.2 x 10-10
[H+] ≈ (7.2 x 10-10) / x
To find the final concentration of [H+], we need additional information such as the initial concentrations of HCN and H2O, or the value of x which can be determined from the given conditions of the reaction.
To find the [H+] in a solution of 1.0 M of the acid HCN, we need to use the equilibrium constant and the stoichiometry of the reaction.
The equilibrium constant of a reaction can be expressed as the ratio of the concentration of the products to the concentration of the reactants, with each concentration raised to the power of its respective stoichiometric coefficient.
In the given reaction, the stoichiometric coefficient of H3O+ is 1, meaning it has a power of 1 in the equilibrium constant expression. The stoichiometric coefficient of HCN is 1, so its concentration is also raised to the power of 1.
The equilibrium constant expression for this reaction is as follows:
K = [H3O+] / [HCN]
Given that the equilibrium constant (K) is 7.2 x 10^-10 and the concentration of HCN is 1.0 M, we can rearrange the equation and solve for [H3O+].
7.2 x 10^-10 = [H3O+] / 1.0
Multiply both sides of the equation by 1.0:
7.2 x 10^-10 x 1.0 = [H3O+
..........HCN + H2O ==> H3O^+ + CN^-
initial...1.0M...........0.......0
change.....-x............x.......x
equil.....1.0-x..........x.......x
Substitute into the Ka expression and solve for H3O^+.