A solution of a monoprotic acid HX contains 3.65\text{ g dm}^{-3} of the acid. If 25.0\tex… — JAMB UTME

A solution of a monoprotic acid $HX$ contains $3.65\text{ g dm}^{-3}$ of the acid. If $25.0\text{ cm}^3$ of this acid solution neutralizes $20.0\text{ cm}^3$ of a $0.125\text{ mol dm}^{-3}$ sodium hydroxide ( $\text{NaOH}$ ) solution, what is the molar mass of the acid $HX$ in $\text{g mol}^{-3}$ ?

Answer: 36.5 g mol^-1

Answer

The molar mass of the acid

HX

36.5\text{ g mol}^{-3}

The reaction of monoprotic acid

HX

with

\text{NaOH}

follows a 1:1 stoichiometric ratio. Applying the titration formula

\frac{C_a V_a}{C_b V_b} = 1

yields an acid concentration of

0.100\text{ mol dm}^{-3}

. Dividing the mass concentration of

3.65\text{ g dm}^{-3}

by this molarity gives a molar mass of

36.5\text{ g mol}^{-3}

Step-by-Step Solution

Determine the stoichiometric mole ratio between acid and base.

The mole ratio

n_a : n_b

for

HX

reacting with

\text{NaOH}

1 : 1

A monoprotic acid donates one proton per molecule to react with one mole of sodium hydroxide.

Calculate the molar concentration of the acid (

C_a

C_a = \frac{0.125\text{ mol dm}^{-3} \times 20.0\text{ cm}^3}{25.0\text{ cm}^3} = 0.100\text{ mol dm}^{-3}

Using the titration relation

\frac{C_a V_a}{C_b V_b} = \frac{n_a}{n_b}

allows determination of the acid molarity.

Calculate the molar mass of the acid.

\text{Molar mass} = \frac{\text{Mass concentration}}{\text{Molarity}} = \frac{3.65\text{ g dm}^{-3}}{0.100\text{ mol dm}^{-3}} = 36.5\text{ g mol}^{-3}

Molar mass is defined as mass of substance per mole.

Key Concept

Determination of molar mass using volumetric titration stoichiometry

Estimated Time:1m 30s

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