What is the molar concentration (in \text{mol dm}^{-3}) of a tetraoxosulfate(VI) acid solu… — JAMB UTME

What is the molar concentration (in $\text{mol dm}^{-3}$ ) of a tetraoxosulfate(VI) acid solution if $20.0\text{ cm}^3$ of the acid is required to completely neutralize $25.0\text{ cm}^3$ of a $0.08\text{ mol dm}^{-3}$ sodium hydroxide solution?

Answer: 0.05 mol dm^-3

Answer

The correct molar concentration of the tetraoxosulfate(VI) acid solution is

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

From the balanced chemical equation

\text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}

1\text{ mole}

of tetraoxosulfate(VI) acid reacts with

2\text{ moles}

of sodium hydroxide (

n_a = 1, n_b = 2

). Substituting the given values into the titration equation

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

gives

C_a = \frac{0.08 \times 25.0 \times 1}{20.0 \times 2} = 0.05\text{ mol dm}^{-3}

Step-by-Step Solution

Write the balanced chemical equation for the reaction to find the mole ratio of acid to base.

\text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}

, giving

n_a = 1

and

n_b = 2

Tetraoxosulfate(VI) acid is a dibasic acid and requires two moles of sodium hydroxide for complete neutralization.

Apply the volumetric analysis formula relating concentration, volume, and stoichiometry.

\frac{C_a V_a}{C_b V_b} = \frac{n_a}{n_b} \implies \frac{C_a \times 20.0}{0.08 \times 25.0} = \frac{1}{2}

The standard titration formula relates acid concentration (

C_a

), acid volume (

V_a

), base concentration (

C_b

), base volume (

V_b

), and their mole coefficients.

Rearrange the equation to solve for

C_a

C_a = \frac{C_b \times V_b \times n_a}{V_a \times n_b} = \frac{0.08 \times 25.0 \times 1}{20.0 \times 2} = \frac{2.0}{40.0} = 0.05\text{ mol dm}^{-3}

Simplifying the arithmetic gives the precise molar concentration of the acid.

Key Concept

Volumetric analysis stoichiometry and stoichiometric concentration calculations for acid-base neutralization.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic