A 0.040M solution of a weak acid has a pH of 3.02 at 25°C . What is the value of Ka for the acid?
...............HA ==> H^+ + A^-
begin.........0.04M....0......0
change..........-x......+x.....+x
final.......0.04-x......x.......x
Ka = (H^+)(A^-)/(HA)
You know pH, convert to (H^+) and that will be x. Substitute into Ka expression and solve for Ka.
To determine the value of Ka for the weak acid, we can use the pH of the solution and the concentration of the acid.
Step 1: Start with the equation for the ionization of the weak acid:
HA ⇌ H+ + A-
Step 2: Since we are given the pH, we can use it to find the concentration of H+ ions in the solution:
pH = -log[H+]
Using the given pH of 3.02, we can calculate the concentration of H+ ions:
[H+] = 10^(-pH)
[H+] = 10^(-3.02)
[H+] = 7.88 x 10^(-4) M
Step 3: Use the concentration of H+ ions to find the concentration of the weak acid.
Since the weak acid is a monoprotic acid, the concentration of H+ ions is equal to the concentration of the weak acid (HA) at equilibrium.
So, [HA] = 7.88 x 10^(-4) M
Step 4: Use the equilibrium concentrations to set up the equation for the ionization constant (Ka):
Ka = [H+][A-]/[HA]
Substituting the known values:
Ka = (7.88 x 10^(-4))^2 / (0.040 - 7.88 x 10^(-4))
Simplifying:
Ka = 6.20 x 10^(-9)
Therefore, the value of Ka for the weak acid is 6.20 x 10^(-9).
To determine the value of Ka (acid dissociation constant) for the weak acid, we can use the pH of the solution and the concentration of the acid.
Ka is a measure of the strength of an acid. It represents the equilibrium constant for the dissociation of the acid into its corresponding ions.
The pH of a solution can be related to the concentration of hydrogen ions (H+) using the logarithmic equation:
pH = -log[H+]
To find the concentration of H+ ions, we need to reverse the equation:
[H+] = 10^(-pH)
Given that the pH of the solution is 3.02, we can calculate the concentration of H+ ions:
[H+] = 10^(-3.02)
[H+] = 7.94 x 10^(-4) M
Since the acidic solution is a weak acid (not fully dissociated), we can assume that the concentration of the acid is approximately equal to the concentration of H+ ions.
Therefore, the concentration of the weak acid is 0.040 M.
Now, we can write the dissociation equation for the weak acid:
HA ⇌ H+ + A-
Using the equilibrium expression for Ka, we have:
Ka = [H+][A-] / [HA]
Substituting the known values, we get:
Ka = (7.94 x 10^(-4))^2 / 0.040
Calculating this expression, the value of Ka for the weak acid is approximately 9.99 x 10^(-5).