To find the molar mass of a monoprotic acid from titration data, the first thing we need to do is look at the units we need to find. In this case, we need molar mass so we need to know grams of the acid and moles of the acid. The grams are given so we just need to find moles from the titration data provided in the problem.
To find moles we need to first look at the balanced chemical equation. Since we don't know the formula of the acid, we'll use the generic "HA" to represent the monoprotic acid. For the base, we'll use the generic "BOH".
HA + BOH --> H2O + BA
Since we have a monoprotic acid, we can write a balanced reaction which gives us a 1:1 ratio between the acid and base. If it were something different, then additional information would have to be provided in the problem.
Since we know the volume of base and the molarity of the base, we can use that information to find moles. We will set up a titration calculation much like we set up for other stoichiometry problems.
10 mL (1 L / 1000 mL) (0.20 mol/L base) (1 mol HA / 1 mol BOH)
= 0.002 moles HA
Now we know the mass of HA and the moles of HA so we can find the molar mass
0.281 g HA / 0.002 mol HA = 141 g/mol
Given a selection of acids, we could also identify the acid by comparing molar masses of the options to the molar mass determined experimentally.