To find the acidic dissociation constant (Ka) for the weak acid HZ, we first need to determine the concentration of hydrogen ions (H+) in the solution.
Given that the pH of the solution is 10.2, we can calculate the concentration of H+ ions using the formula:
H+ concentration = 10-pH
Substituting the given pH value:
H+ concentration = 10-10.2 = 6.31 x 10-11 M
Next, since NaZ is the sodium salt of the weak acid HZ, it will dissociate completely in solution:
NaZ → Na+ + Z–
The concentration of Z– (the conjugate base) will be equal to the initial concentration of NaZ, which is 0.25 M.
Now, we can set up the equilibrium expression for the dissociation of the weak acid HZ:
HZ ⇌ H+ + Z–
The equilibrium constant expression (Ka) for the dissociation of HZ can be written as:
Ka = [H+][Z–]/[HZ]
Assuming that the change in concentration of HZ is negligible (due to the weak nature of the acid), we have the following at equilibrium:
[HZ] ≈ 0.25 M – x (where x is the amount that dissociates, which is equal to [H+])
Since we found that [H+] = 6.31 x 10-11 M and [Z–] equals 0.25 M, we can substitute these values into our Ka expression:
Ka = (6.31 x 10-11)(0.25) / (0.25 – 6.31 x 10-11)
The value of (0.25 – 6.31 x 10-11) is approximately 0.25 since the change is very small in comparison to 0.25.
Thus:
Ka ≈ (6.31 x 10-11)(0.25) / 0.25
Ka ≈ 6.31 x 10-11
In conclusion, the Ka for the weak acid HZ is approximately 6.31 x 10-11.