The molar mass of the unknown acid is calculated by dividing the mass of the acid sample by the number of moles of NaOH that reacted in the titration, which should be equal to the number of moles of the acid due to the 1:1 reaction ratio. The closest answer choice to the calculated molar mass is 100.5 g/mol. However, the calculated molar mass does not match any given options exactly.
To calculate the molar mass of the unknown monoprotic acid, we need to find the number of moles of sodium hydroxide that reacted and assume it equates to the number of moles of the unknown acid due to the 1:1 ratio in the reaction. The number of moles of NaOH is given by the formula:
moles NaOH = Volume (L) × Molarity (M)
First, convert mL to L:
31.38 mL × (1 L / 1000 mL) = 0.03138 L
Then, calculate the moles of NaOH that reacted:
moles NaOH = 0.03138 L × 0.1058 M = 0.003320 mol
Since the acid is monoprotic, moles of acid = moles of NaOH.
Now, calculate the molar mass by dividing the mass of the acid sample by the moles of acid:
Molar Mass of the Acid = Mass (g) / # moles
Molar Mass of the Acid = 0.2467 g / 0.003320 mol = 74.34 g/mol
The answer choice that most closely matches our calculated molar mass is option (a) 100.5 g/mol.