Write the benzoic acid ionization.
Write the Ka expression.
Use pH = =log(H^+) to calculate (H^+).
Substitute into Ka expression and determine Ka.
Write the Ka expression.
Use pH = =log(H^+) to calculate (H^+).
Substitute into Ka expression and determine Ka.
Ka = [H3O+][C7H5O2-] / [HC7H5O2]
Here, [H3O+] represents the concentration of hydronium ions, [C7H5O2-] represents the concentration of the conjugate base (benzoate ions), and [HC7H5O2] represents the concentration of benzoic acid.
In this case, the concentration of benzoic acid is given as 0.25 mol/L, and the pH is 2.40. To find the concentration of hydronium ions, we need to calculate the antilog of the negative pH value:
[H3O+] = antilog(-pH) = 10^-pH
[H3O+] = 10^(-2.40) = 0.004
Now, we need to find the concentration of benzoate ions, which can be calculated using the equation:
[C7H5O2-] = [H3O+] * (10^-pKa)
To simplify the calculation, we assume that the concentration of benzoate ions is equal to the concentration of hydronium ions:
[C7H5O2-] = 0.004
Finally, substitute the values into the Ka formula:
Ka = [H3O+][C7H5O2-] / [HC7H5O2]
= (0.004) * (0.004) / (0.25)
Ka = 0.000016 / 0.25
Ka = 6.4 x 10^-5
Therefore, the Ka of benzoic acid at SATP is 6.4 x 10^-5.