Question

The mass of Na2CO3 (91.2% purity) required for the neutralisation of 45.6 mL of 0.25M HC1 solution is

Answer 1

0.663 g

Answer 2

The problem asks for the mass of impure Na₂CO₃ required to neutralize a given volume and concentration of HCl solution.

1. Write the balanced chemical equation for the neutralization reaction:

Sodium carbonate (Na₂CO₃) reacts with hydrochloric acid (HCl) as follows:

$\text{Na}_2\text{CO}_3 (\text{s}) + 2\text{HCl} (\text{aq}) \rightarrow 2\text{NaCl} (\text{aq}) + \text{H}_2\text{O} (\text{l}) + \text{CO}_2 (\text{g})$

From the equation, 1 mole of Na₂CO₃ reacts with 2 moles of HCl.

2. Calculate the moles of HCl:

Given:

Volume of HCl solution = 45.6 mL = 0.0456 L Molarity of HCl solution = 0.25 M

Moles of HCl = Molarity × Volume (in L) Moles of HCl = $0.25 \text{ mol/L} \times 0.0456 \text{ L} = 0.0114 \text{ mol}$

3. Calculate the moles of pure Na₂CO₃ required:

From the stoichiometry of the balanced equation, 1 mole of Na₂CO₃ reacts with 2 moles of HCl.

Moles of Na₂CO₃ = $\frac{\text{Moles of HCl}}{2}$ Moles of Na₂CO₃ = $\frac{0.0114 \text{ mol}}{2} = 0.0057 \text{ mol}$

4. Calculate the molar mass of Na₂CO₃:

Molar mass of Na = 22.99 g/mol Molar mass of C = 12.01 g/mol Molar mass of O = 16.00 g/mol

Molar mass of Na₂CO₃ = $(2 \times 22.99) + 12.01 + (3 \times 16.00)$ $= 45.98 + 12.01 + 48.00 = 105.99 \text{ g/mol} \approx 106 \text{ g/mol}$

5. Calculate the mass of pure Na₂CO₃ required:

Mass of pure Na₂CO₃ = Moles of Na₂CO₃ × Molar mass of Na₂CO₃ Mass of pure Na₂CO₃ = $0.0057 \text{ mol} \times 106 \text{ g/mol} = 0.6042 \text{ g}$

6. Account for the purity of Na₂CO₃:

The Na₂CO₃ sample has 91.2% purity. This means that 91.2 g of pure Na₂CO₃ is present in 100 g of the impure sample.

Let 'X' be the total mass of the impure Na₂CO₃ required.

Mass of pure Na₂CO₃ = X × (Purity / 100) $0.6042 \text{ g} = \text{X} \times \frac{91.2}{100}$ $\text{X} = \frac{0.6042 \text{ g}}{0.912}$ $\text{X} = 0.6625 \text{ g}$

Rounding to three significant figures (consistent with the given data), the mass of Na₂CO₃ required is 0.663 g.