To solve the problem step by step, let's analyze the given information and perform the necessary calculations.
### Step 1: Write the balanced chemical equation
When magnesium (Mg) reacts with hydrochloric acid (HCl), the balanced chemical equation is:
\[
\text{Mg} + 2 \text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2
\]
### Step 2: Calculate the number of moles of magnesium (Mg)
Given:
- Mass of Mg = 2.4 g
- Atomic mass of Mg = 24 g/mol
Using the formula for moles:
\[
\text{Number of moles of Mg} = \frac{\text{mass}}{\text{molar mass}} = \frac{2.4 \, \text{g}}{24 \, \text{g/mol}} = 0.1 \, \text{mol}
\]
### Step 3: Calculate the number of moles of hydrochloric acid (HCl)
Given:
- Volume of HCl solution = 100 mL = 0.1 L
- Molarity of HCl = 1 M
Using the formula for moles:
\[
\text{Number of moles of HCl} = \text{Molarity} \times \text{Volume} = 1 \, \text{mol/L} \times 0.1 \, \text{L} = 0.1 \, \text{mol}
\]
### Step 4: Determine the limiting reagent
From the balanced equation, we see that:
1 mole of Mg reacts with 2 moles of HCl. Thus, for 0.1 moles of Mg, the required amount of HCl is:
\[
\text{Required moles of HCl} = 2 \times 0.1 \, \text{mol} = 0.2 \, \text{mol}
\]
Since we only have 0.1 moles of HCl available, HCl is the limiting reagent.
### Step 5: Calculate the amount of hydrogen gas produced
From the balanced equation, 2 moles of HCl produce 1 mole of H2. Therefore, 0.1 moles of HCl will produce:
\[
\text{Moles of H}_2 = \frac{0.1 \, \text{mol HCl}}{2} = 0.05 \, \text{mol H}_2
\]
### Step 6: Convert moles of hydrogen gas to volume
At STP, 1 mole of gas occupies 22.4 L. Thus, the volume of hydrogen produced is:
\[
\text{Volume of H}_2 = 0.05 \, \text{mol} \times 22.4 \, \text{L/mol} = 1.12 \, \text{L}
\]
### Step 7: Calculate the amount of magnesium left
Since 0.1 moles of Mg were initially present and 0.05 moles of Mg reacted with the available HCl, the amount of magnesium left is:
\[
\text{Moles of Mg left} = 0.1 \, \text{mol} - 0.05 \, \text{mol} = 0.05 \, \text{mol}
\]
### Conclusion
Now, let's analyze the statements:
1. 1.12 liters of hydrogen is produced at STP - **True**
2. 0.05 moles of magnesium is left behind - **True**
3. HCl is the limiting reagent - **True**
4. 0.005 moles of magnesium is left behind - **False** (it is actually 0.05 moles)
### Final Answer
The wrong statement is the fourth one: **0.005 moles of magnesium is left behind.**
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