To determine how many grams of hydrogen gas will be produced when 100 grams of water undergoes electrolysis with 100% efficiency, let's follow these steps:
### Step 1: Understanding the Chemical Reaction
The balanced chemical equation for the electrolysis of water is:
[tex]\[ 2 H_2O \rightarrow 2 H_2 + O_2 \][/tex]
From this equation, it's clear that 2 moles of water (H₂O) produce 2 moles of hydrogen gas (H₂) and 1 mole of oxygen gas (O₂).
### Step 2: Determine the Molar Masses
We need the molar masses of the substances involved:
- Molar mass of water (H₂O): [tex]\(18\)[/tex] g/mol
- Molar mass of hydrogen (H₂): [tex]\(2\)[/tex] g/mol
### Step 3: Calculate the Number of Moles of Water
Given mass of water: [tex]\(100\)[/tex] grams
To find the number of moles of water:
[tex]\[ \text{Moles of H}_2\text{O} = \frac{\text{mass of H}_2\text{O}}{\text{molar mass of H}_2\text{O}} = \frac{100 \text{ grams}}{18 \text{ g/mol}} \][/tex]
[tex]\[ \text{Moles of H}_2\text{O} = 5.555555555555555 \][/tex]
### Step 4: Determine the Number of Moles of Hydrogen Gas Produced
According to the balanced equation, 2 moles of water produce 2 moles of hydrogen gas. Therefore, the number of moles of hydrogen gas (H₂) produced will be the same as the number of moles of water (H₂O) used.
[tex]\[ \text{Moles of H}_2 = \text{5.555555555555555} \][/tex]
### Step 5: Calculate the Mass of Hydrogen Gas Produced
To find the mass of hydrogen gas produced:
[tex]\[ \text{Mass of H}_2 = \text{Moles of H}_2 \times \text{Molar mass of H}_2 \][/tex]
[tex]\[ \text{Mass of H}_2 = 5.555555555555555 \times 2 \text{ g/mol} \][/tex]
[tex]\[ \text{Mass of H}_2 = 11.11111111111111 \text{ grams} \][/tex]
Therefore, the number of grams of hydrogen gas produced is approximately [tex]\(11\)[/tex] grams.
### Conclusion
The correct answer is:
A. [tex]\(11\)[/tex] grams
