70 g of a sample of magnesite on treatment with excess of HCl gave 11.2 L of `CO_(2)` at STP. The percentage purify of the sample

Options

A. 80
B. 70
C. 60
D. 50

Answer

To find the percentage purity of the magnesite sample, we can follow these steps:

### Step 1: Write the reaction
Magnesite is magnesium carbonate (MgCO₃). When treated with hydrochloric acid (HCl), it decomposes to produce magnesium chloride (MgCl₂), water (H₂O), and carbon dioxide (CO₂). The balanced chemical equation is:

\[ \text{MgCO}_3 (s) + 2 \text{HCl} (aq) \rightarrow \text{MgCl}_2 (aq) + \text{H}_2\text{O} (l) + \text{CO}_2 (g) \]

### Step 2: Calculate the molar mass of magnesite (MgCO₃)
- Atomic mass of Magnesium (Mg) = 24 g/mol
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Oxygen (O) = 16 g/mol (and there are 3 O atoms)

Molar mass of MgCO₃ = 24 + 12 + (3 × 16) = 24 + 12 + 48 = 84 g/mol

### Step 3: Calculate the number of moles of CO₂ produced
At STP (Standard Temperature and Pressure), 1 mole of gas occupies 22.4 L. Given that 11.2 L of CO₂ was produced:

\[ \text{Number of moles of CO}_2 = \frac{\text{Volume of CO}_2}{\text{Molar volume at STP}} = \frac{11.2 \, \text{L}}{22.4 \, \text{L/mol}} = 0.5 \, \text{mol} \]

### Step 4: Determine the moles of MgCO₃ required
From the balanced equation, 1 mole of MgCO₃ produces 1 mole of CO₂. Therefore, 0.5 moles of CO₂ will require:

\[ \text{Moles of MgCO}_3 = 0.5 \, \text{mol} \]

### Step 5: Calculate the mass of MgCO₃ required
Using the molar mass calculated earlier:

\[ \text{Mass of MgCO}_3 = \text{Moles} \times \text{Molar mass} = 0.5 \, \text{mol} \times 84 \, \text{g/mol} = 42 \, \text{g} \]

### Step 6: Calculate the percentage purity of the sample
The percentage purity is given by the formula:

\[ \text{Percentage purity} = \left( \frac{\text{Required mass of MgCO}_3}{\text{Total mass of sample}} \right) \times 100 \]

Substituting the values:

\[ \text{Percentage purity} = \left( \frac{42 \, \text{g}}{70 \, \text{g}} \right) \times 100 = 60\% \]

### Final Answer
The percentage purity of the magnesite sample is **60%**.

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