Sure, let's solve this step-by-step using stoichiometry.
1. Analyze the given chemical reaction:
[tex]\[
\text{Mg} + 2 \text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2
\][/tex]
Here, 1 mole of magnesium (Mg) reacts with 2 moles of hydrochloric acid (HCl) to produce 1 mole of magnesium chloride (MgCl₂) and 1 mole of hydrogen gas (H₂).
2. Understand the relationship from the reaction:
According to the balanced chemical equation:
- 1 mole of Mg produces 1 mole of H₂.
3. Convert the amount of hydrogen gas needed to moles of magnesium:
Given:
[tex]\[
\text{moles of H}_2 \text{ needed} = 0.16 \, \text{mol}
\][/tex]
Since the reaction shows that 1 mole of Mg produces 1 mole of H₂, the moles of Mg required will also be:
[tex]\[
\text{moles of Mg required} = 0.16 \, \text{mol}
\][/tex]
4. Calculate the molar mass of magnesium:
The molar mass of Mg is given as:
[tex]\[
24.3 \, \text{g/mol}
\][/tex]
5. Find the mass of Mg required:
To find the mass of Mg needed, we use the formula:
[tex]\[
\text{mass} = \text{moles} \times \text{molar mass}
\][/tex]
Substituting the values:
[tex]\[
\text{mass of Mg required} = 0.16 \, \text{mol} \times 24.3 \, \text{g/mol} = 3.888 \, \text{g}
\][/tex]
Therefore, the mass of magnesium required to generate 0.16 mol of hydrogen gas is [tex]\(3.888 \, \text{g}\)[/tex].
