A portable hydrogen generator utilizes the reaction between calcium hydride and water to produce hydrogen. What mass of hydrogen can be produced by 70 g cartridge of calcium hydride?

Options

A. 6.7 g
B. 3.5 g
C. 4.5 g
D. 5.5 g

Explanation

To solve the problem of how much hydrogen can be produced from 70 g of calcium hydride (CaH₂), we will follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between calcium hydride and water can be represented as follows:

\[ \text{CaH}_2 + 2 \text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2 + \text{H}_2 \]

This shows that 1 mole of calcium hydride reacts with 2 moles of water to produce 1 mole of calcium hydroxide and 1 mole of hydrogen gas.

### Step 2: Calculate the molar mass of calcium hydride (CaH₂)
The molar mass of calcium hydride can be calculated as follows:
- Calcium (Ca) = 40 g/mol
- Hydrogen (H) = 1 g/mol (and there are 2 hydrogen atoms in CaH₂)

So, the molar mass of CaH₂ is:
\[ 40 \, \text{g/mol (Ca)} + 2 \times 1 \, \text{g/mol (H)} = 40 + 2 = 42 \, \text{g/mol} \]

### Step 3: Determine the number of moles of calcium hydride in 70 g
To find the number of moles of calcium hydride in 70 g, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

Thus,
\[ \text{Number of moles of CaH}_2 = \frac{70 \, \text{g}}{42 \, \text{g/mol}} \approx 1.67 \, \text{moles} \]

### Step 4: Use the stoichiometry of the reaction to find moles of hydrogen produced
From the balanced equation, we see that 1 mole of CaH₂ produces 1 mole of H₂. Therefore, the number of moles of hydrogen produced is equal to the number of moles of calcium hydride reacted.

Thus,
\[ \text{Moles of H}_2 = 1.67 \, \text{moles} \]

### Step 5: Calculate the mass of hydrogen produced
To find the mass of hydrogen produced, we use the molar mass of hydrogen gas (H₂):
- Molar mass of H₂ = 2 g/mol

Now, we can calculate the mass of hydrogen:
\[ \text{Mass of H}_2 = \text{moles} \times \text{molar mass} \]
\[ \text{Mass of H}_2 = 1.67 \, \text{moles} \times 2 \, \text{g/mol} = 3.34 \, \text{g} \]

### Step 6: Final Answer
The mass of hydrogen produced from 70 g of calcium hydride is approximately **3.34 g**.

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