Alright, let's go through a step-by-step solution to determine the mass of magnesium (Mg) required to generate 0.16 moles of hydrogen gas (H₂).
### Step 1: Understanding the Reaction
The balanced chemical equation for the reaction between magnesium (Mg) and hydrochloric acid (HCl) is:
[tex]\[ \text{Mg} + 2 \text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2 \][/tex]
This equation shows that 1 mole of magnesium reacts with 2 moles of hydrochloric acid to produce 1 mole of magnesium chloride (MgCl₂) and 1 mole of hydrogen gas (H₂).
### Step 2: Relating Moles of Reactants to Products
According to the stoichiometry of the reaction:
- 1 mole of Mg produces 1 mole of H₂ gas.
### Step 3: Using Given Information
We are given that 0.16 moles of H₂ gas are needed. Based on the stoichiometry of the reaction, we can determine that:
- 0.16 moles of H₂ gas requires 0.16 moles of Mg (because the ratio is 1:1).
### Step 4: Calculating the Mass of Magnesium
Next, we need to find out the mass of magnesium corresponding to 0.16 moles.
The molar mass of Mg (given) is 24.3 g/mol.
### Step 5: Applying the Formula
To find the mass, we use the formula:
[tex]\[ \text{Mass} = \text{Moles} \times \text{Molar Mass} \][/tex]
So, we calculate:
[tex]\[ \text{Mass of Mg} = 0.16 \text{ moles} \times 24.3 \text{ g/mol} \][/tex]
### Step 6: Final Result
Performing the multiplication:
[tex]\[ \text{Mass of Mg} = 0.16 \times 24.3 = 3.888 \text{ grams} \][/tex]
Thus, 0.16 moles of Mg are needed, and the mass of magnesium required to generate 0.16 moles of hydrogen gas [tex]\( H_2 \)[/tex] is 3.888 grams.
