A 0.25 mol/L solution of benzoic acid, KC7H5O2 and antiseptic also used as a food preservative, has a pH of 2.40. Calculate the Ka of benzoic acid at SATP
Write the benzoic acid ionization.
Write the Ka expression.
Use pH = =log(H^+) to calculate (H^+).
Substitute into Ka expression and determine Ka.
To calculate the Ka of benzoic acid at SATP (Standard Ambient Temperature and Pressure), we can use the pH value and the concentration of the solution. The formula for Ka is:
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.