0.9031 g of a mixture of NaCI and KCI on treatment with `H_2SO_4` yielded 1.0784 g of a mixture of `Na_2SO_4` and `K_2SO_4`.Calculate the percent composition of the mixture.

Explanation

To solve the problem, we need to determine the percent composition of the mixture of NaCl and KCl based on the given data. Here are the steps to arrive at the solution:

### Step 1: Write the Chemical Reactions
The reactions of NaCl and KCl with sulfuric acid (H₂SO₄) are:
1. \( 2 \text{NaCl} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{HCl} \)
2. \( 2 \text{KCl} + \text{H}_2\text{SO}_4 \rightarrow \text{K}_2\text{SO}_4 + 2 \text{HCl} \)

### Step 2: Define Variables
Let:
- \( x \) = mass of NaCl in grams
- \( 0.9031 - x \) = mass of KCl in grams

### Step 3: Calculate the Mass of Na₂SO₄ and K₂SO₄ Produced
From the stoichiometry of the reactions:
- For NaCl:
- 117 g of NaCl produces 142 g of Na₂SO₄.
- Therefore, \( x \) g of NaCl will produce:
\[ \text{Mass of Na}_2\text{SO}_4 = \frac{142}{117} \times x \]

- For KCl:
- 149 g of KCl produces 174 g of K₂SO₄.
- Therefore, \( 0.9031 - x \) g of KCl will produce:
\[ \text{Mass of K}_2\text{SO}_4 = \frac{174}{149} \times (0.9031 - x) \]

### Step 4: Set Up the Equation
According to the problem, the total mass of Na₂SO₄ and K₂SO₄ produced is 1.0784 g. Thus, we can set up the equation:
\[ \frac{142}{117} x + \frac{174}{149} (0.9031 - x) = 1.0784 \]

### Step 5: Solve the Equation
1. Calculate the coefficients:
- \( \frac{142}{117} \approx 1.2145 \)
- \( \frac{174}{149} \approx 1.1678 \)

2. Substitute these values into the equation:
\[ 1.2145x + 1.1678(0.9031 - x) = 1.0784 \]

3. Distributing the second term:
\[ 1.2145x + 1.0563 - 1.1678x = 1.0784 \]

4. Combine like terms:
\[ (1.2145 - 1.1678)x + 1.0563 = 1.0784 \]
\[ 0.0467x + 1.0563 = 1.0784 \]

5. Isolate \( x \):
\[ 0.0467x = 1.0784 - 1.0563 \]
\[ 0.0467x = 0.0221 \]
\[ x = \frac{0.0221}{0.0467} \approx 0.472 \]

### Step 6: Calculate Mass of KCl
Now, calculate the mass of KCl:
\[ \text{Mass of KCl} = 0.9031 - x = 0.9031 - 0.472 \approx 0.4311 \, \text{g} \]

### Step 7: Calculate Percent Composition
1. Percent composition of NaCl:
\[ \text{Percent of NaCl} = \left(\frac{0.472}{0.9031}\right) \times 100 \approx 52.2\% \]

2. Percent composition of KCl:
\[ \text{Percent of KCl} = \left(\frac{0.4311}{0.9031}\right) \times 100 \approx 47.8\% \]

### Final Answer
- Percent composition of NaCl: **52.2%**
- Percent composition of KCl: **47.8%**

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