Question

The pH meter was mistakenly calibrated to be 1.0 pH unit higher than the buffer.
a. Will this miscalibration result in a reported molar concentration of the weak acid being too high, too low, or unaffected? explain
b. Is the determined pKa of the weak acid too high, too low, or unaffected by the miscalibration? explain

Answer 1

If the pH meter was calibrated wrongly to 1.0 pH unit higher than actual value for the buffer,

a. The molar concentration of the weak acid calculated would be too low. Say we had an actual pH of weak acid be 1 and it shows a value of 2 on the pH meter due to error.

Let the weak acid be acetic acid with Ka 1.8 x 10^-5

When pH = 1, [H+] = [A-] = 0.1 M

[HA] = 0.1 x 0.1/1.8 x 10^-5 = 555.5 M

With error, pH = 2, [H+] = [A-] = 0.01 M

[HA] = 0.01 x 0.01/1.8 x 10^-5 = 5.55 M

So as can be seen the molar concentration of acid calculated with error comes out to be too low in comparison to the actual value without error.

b. pKa is determined by Ka, since equilibrium concentration is a ratio, it remains unaffected by the error in measurement.