QUESTION 9 [ 14 marks] The balanced equation for the reaction of sodium chloride, NaCl , with sulphuric acid, $$ \mathrm{H}_{2} \mathrm{SO}_{4} $$, is as follows: $$ 2 \mathrm{NaCl}(\mathrm{s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})+2 \mathrm{HCl}(\mathrm{g}) $$ Sindile wants to find the percentage purity of a sodium chloride sample she has. She reacts $$ 1,5 \mathrm{~g} $$ of an impure sample of sodium chloride with $$ 100 \mathrm{~cm}^{3} $$ sulphuric acid of concentration 0,1 mol $$ \cdot d \mathrm{~m}^{3} $$ at room temperature.

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UpStudy AI · Accepted Answer

To find the percentage purity of the sodium chloride sample, we will follow these steps:

1. **Calculate the number of moles of sulfuric acid (H₂SO₄) used.**
2. **Determine the number of moles of sodium chloride (NaCl) that reacted based on the stoichiometry of the balanced equation.**
3. **Calculate the mass of pure sodium chloride that reacted.**
4. **Determine the percentage purity of the sodium chloride sample.**

### Step 1: Calculate the number of moles of sulfuric acid (H₂SO₄)

The concentration of sulfuric acid is given as $$ 0.1 \, \text{mol/dm}^3 $$ and the volume is $$ 100 \, \text{cm}^3 $$. We need to convert the volume from cm³ to dm³:

$$
\text{Volume in dm}^3 = \frac{100 \, \text{cm}^3}{1000} = 0.1 \, \text{dm}^3
$$

Now, we can calculate the number of moles of sulfuric acid:

$$
\text{Moles of } \text{H}_2\text{SO}_4 = \text{Concentration} \times \text{Volume} = 0.1 \, \text{mol/dm}^3 \times 0.1 \, \text{dm}^3
$$

### Step 2: Determine the number of moles of sodium chloride (NaCl) that reacted

From the balanced equation:

$$
2 \, \text{NaCl} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2 \, \text{HCl}
$$

We see that 2 moles of NaCl react with 1 mole of H₂SO₄. Therefore, the number of moles of NaCl that reacted can be calculated as follows:

$$
\text{Moles of NaCl} = 2 \times \text{Moles of } \text{H}_2\text{SO}_4
$$

### Step 3: Calculate the mass of pure sodium chloride that reacted

The molar mass of NaCl is approximately $$ 58.44 \, \text{g/mol} $$. The mass of NaCl that reacted can be calculated using:

$$
\text{Mass of NaCl} = \text{Moles of NaCl} \times \text{Molar mass of NaCl}
$$

### Step 4: Determine the percentage purity of the sodium chloride sample

The percentage purity can be calculated using the formula:

$$
\text{Percentage purity} = \left( \frac{\text{Mass of pure NaCl}}{\text{Mass of impure sample}} \right) \times 100
$$

Now, let's perform the calculations step by step.

1. Calculate the moles of H₂SO₄.
2. Calculate the moles of NaCl that reacted.
3. Calculate the mass of NaCl that reacted.
4. Calculate the percentage purity.

Let's execute these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(2\left(0.1\times 0.1\right)\right)\times 58.44$$
- step1: Remove the parentheses:
  $$2\times 0.1\times 0.1\times 58.44$$
- step2: Multiply the terms:
  $$0.2\times 0.1\times 58.44$$
- step3: Multiply the terms:
  $$0.02\times 58.44$$
- step4: Multiply the numbers:
  $$1.1688$$
Calculate or simplify the expression $$ 0.1 * 0.1 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$0.1\times 0.1$$
- step1: Multiply the numbers:
  $$0.01$$
Calculate or simplify the expression $$ 2 * (0.1 * 0.1) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$2\left(0.1\times 0.1\right)$$
- step1: Remove the parentheses:
  $$2\times 0.1\times 0.1$$
- step2: Multiply the terms:
  $$0.2\times 0.1$$
- step3: Multiply the numbers:
  $$0.02$$
### Step 1: Calculate the number of moles of sulfuric acid (H₂SO₄)

The number of moles of H₂SO₄ is:

$$
\text{Moles of } \text{H}_2\text{SO}_4 = 0.1 \, \text{mol/dm}^3 \times 0.1 \, \text{dm}^3 = 0.01 \, \text{mol}
$$

### Step 2: Determine the number of moles of sodium chloride (NaCl) that reacted

Using the stoichiometry from the balanced equation:

$$
\text{Moles of NaCl} = 2 \times 0.01 \, \text{mol} = 0.02 \, \text{mol}
$$

### Step 3: Calculate the mass of pure sodium chloride that reacted

The mass of NaCl that reacted is calculated as follows:

$$
\text{Mass of NaCl} = 0.02 \, \text{mol} \times 58.44 \, \text{g/mol} = 1.1688 \, \text{g}
$$

### Step 4: Determine the percentage purity of the sodium chloride sample

The mass of the impure sample is $$ 1.5 \, \text{g} $$. Now we can calculate the percentage purity:

$$
\text{Percentage purity} = \left( \frac{1.1688 \, \text{g}}{1.5 \, \text{g}} \right) \times 100
$$

Let's calculate the percentage purity.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{1.1688}{1.5}\right)\times 100$$
- step1: Divide the terms:
  $$\frac{487}{625}\times 100$$
- step2: Reduce the numbers:
  $$\frac{487}{25}\times 4$$
- step3: Multiply:
  $$\frac{487\times 4}{25}$$
- step4: Multiply:
  $$\frac{1948}{25}$$
The percentage purity of the sodium chloride sample is calculated as follows:

$$
\text{Percentage purity} = \left( \frac{1.1688 \, \text{g}}{1.5 \, \text{g}} \right) \times 100 \approx 77.92\%
$$

### Final Answer:
The percentage purity of the sodium chloride sample is approximately $$ 77.92\% $$.
The sodium chloride sample is approximately 77.92% pure.

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