Two samples of pure sodium chloride obtained from different sources were analyzed quantita… — JAMB UTME

Two samples of pure sodium chloride obtained from different sources were analyzed quantitatively. The first sample contained $4.60\text{ g}$ of sodium combined with $7.10\text{ g}$ of chlorine. If the second sample contains $14.20\text{ g}$ of chlorine, what mass of sodium is present in the second sample to satisfy the Law of Definite Proportions?

A
$4.60\text{ g}$
$9.20\text{ g}$ Answer
C
$11.70\text{ g}$
D
$18.80\text{ g}$

Answer

9.20\text{ g}

According to the Law of Definite Proportions (or Constant Composition), a pure chemical compound always contains its elements combined in a fixed ratio by mass, regardless of its source. Since the chlorine mass in the second sample (

14.20\text{ g}

) is twice that of the first sample (

7.10\text{ g}

), the mass of sodium must also be twice as large, giving

2 \times 4.60\text{ g} = 9.20\text{ g}

Step-by-Step Solution

Determine the mass ratio of sodium to chlorine in the first sample.

The ratio of mass of sodium to mass of chlorine is

\frac{4.60\text{ g}}{7.10\text{ g}} = \frac{46}{71}

The Law of Definite Proportions states that a chemical compound always contains its constituent elements in a fixed ratio by mass.

Set up the proportion for the second sample with

14.20\text{ g}

of chlorine.

\frac{m_{\text{Na}}}{14.20\text{ g}} = \frac{4.60\text{ g}}{7.10\text{ g}}

The mass ratio must remain constant across all samples of the same compound.

Solve for the unknown mass of sodium (

m_{\text{Na}}

m_{\text{Na}} = 4.60\text{ g} \times \left(\frac{14.20\text{ g}}{7.10\text{ g}}\right) = 4.60\text{ g} \times 2 = 9.20\text{ g}

Since

14.20\text{ g}

is exactly twice

7.10\text{ g}

, the mass of sodium required is twice

4.60\text{ g}

Key Concept

Law of Definite Proportions (Law of Constant Composition)

Estimated Time:1m 0s

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