A \(3.664-\mathrm{g}\) sample of a monoprotic acid was dissolved in water and required \(20.27 \mathrm{~mL}\) of a \(0.1578 \mathrm{M}\) \(\mathrm{NaOH}\) solution for neutralization. Calculate the molar mass of the acid.

Short Answer

Expert verified
The molar mass of the acid is approximately 1145 g/mol.

Step by step solution

01

Calculate moles of $\mathrm{NaOH}$ using concentration and volume

Firstly, calculate the moles (n) of the $\mathrm{NaOH}$ used in the reaction by using the equation n = c × V, where c is the concentration and V is the volume. In this case, c = \(0.1578 \mathrm{M}\) and V = \(20.27 \mathrm{~mL} = 20.27 \times 10^{-3} \mathrm{L}\). Therefore n = \(0.1578 \times 20.27 \times 10^{-3} = 3.200 \times 10^{-3}\) moles.
02

Determine moles of the acid

Since each acid molecule reacts with one $\mathrm{NaOH}$ molecule, the moles of the acid are also \(3.20 \times 10^{-3}\) moles.
03

Calculation of the Molar mass of the acid

Finally, calculate the molar mass (MM) of the acid by using the equation MM = m / n, where m is the mass and n is the moles. In this case m = 3.664 g and n = 3.20 x 10^{-3} mol, hence MM = 3.664 / \(3.20 \times 10^{-3} = 1145 \mathrm{g/mol}\).

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