320 mg of a sample of magnessium having a coasting of its oxide required 20mL of 0.1M hydrochloric acid for the complete neutralisation of the latter. The composition of the sample is:

Options

A. 87% Mg and 12.5%MgO
B. 12.5% Mg and 87.5 %MgO
C. 80% Mg and 20%MgO
D. 20% Mg and 80%MgO

Answer

To solve the problem step by step, we will follow the outlined process to find the composition of magnesium and magnesium oxide in the sample.

### Step 1: Determine the moles of HCl used
Given:
- Volume of HCl = 20 mL = 0.020 L (since 1 mL = 0.001 L)
- Molarity of HCl = 0.1 M

Using the formula for moles:
\[ \text{Moles of HCl} = \text{Molarity} \times \text{Volume in L} \]
\[ \text{Moles of HCl} = 0.1 \, \text{mol/L} \times 0.020 \, \text{L} = 0.002 \, \text{mol} \]

### Step 2: Relate moles of HCl to moles of magnesium oxide
From the balanced chemical equation:
\[ \text{MgO} + 2 \text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2\text{O} \]
This means that 2 moles of HCl neutralize 1 mole of MgO. Therefore, the moles of MgO can be calculated as:
\[ \text{Moles of MgO} = \frac{\text{Moles of HCl}}{2} = \frac{0.002}{2} = 0.001 \, \text{mol} \]

### Step 3: Calculate the mass of magnesium oxide
The molar mass of magnesium oxide (MgO) is approximately 40 g/mol. To find the mass:
\[ \text{Mass of MgO} = \text{Moles of MgO} \times \text{Molar Mass of MgO} \]
\[ \text{Mass of MgO} = 0.001 \, \text{mol} \times 40 \, \text{g/mol} = 0.04 \, \text{g} = 40 \, \text{mg} \]

### Step 4: Calculate the mass of magnesium in the sample
The total mass of the sample is given as 320 mg. To find the mass of magnesium:
\[ \text{Mass of Mg} = \text{Total mass of sample} - \text{Mass of MgO} \]
\[ \text{Mass of Mg} = 320 \, \text{mg} - 40 \, \text{mg} = 280 \, \text{mg} \]

### Step 5: Calculate the percentage composition of magnesium and magnesium oxide
1. **Percentage of MgO**:
\[ \text{Percentage of MgO} = \left(\frac{\text{Mass of MgO}}{\text{Total mass of sample}}\right) \times 100 \]
\[ \text{Percentage of MgO} = \left(\frac{40 \, \text{mg}}{320 \, \text{mg}}\right) \times 100 = 12.5\% \]

2. **Percentage of Mg**:
\[ \text{Percentage of Mg} = \left(\frac{\text{Mass of Mg}}{\text{Total mass of sample}}\right) \times 100 \]
\[ \text{Percentage of Mg} = \left(\frac{280 \, \text{mg}}{320 \, \text{mg}}\right) \times 100 = 87.5\% \]

### Final Answer
- Percentage of Magnesium Oxide (MgO) = 12.5%
- Percentage of Magnesium (Mg) = 87.5%

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