3g of `H_(2)` and 24g of `O_(2)` are present in a gaseous mixture at constant temperature and pressure. The partial pressure of hydrogen is

Options

A. 1/3 of total pressure
B. 2/3 of total presure
C. 3/2 of total pressure
D. 1/2 of total pressure

Answer

To find the partial pressure of hydrogen in a gaseous mixture of hydrogen and oxygen, we can follow these steps:

### Step 1: Calculate the number of moles of hydrogen (H₂)
To find the number of moles, we can use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of hydrogen (H₂) is approximately 2 g/mol. Given that we have 3 g of hydrogen:
\[ \text{Number of moles of H₂} = \frac{3 \text{ g}}{2 \text{ g/mol}} = 1.5 \text{ moles} \]

### Step 2: Calculate the number of moles of oxygen (O₂)
The molar mass of oxygen (O₂) is approximately 32 g/mol. Given that we have 24 g of oxygen:
\[ \text{Number of moles of O₂} = \frac{24 \text{ g}}{32 \text{ g/mol}} = 0.75 \text{ moles} \]

### Step 3: Calculate the total number of moles in the mixture
Now, we can find the total number of moles in the mixture:
\[ \text{Total moles} = \text{moles of H₂} + \text{moles of O₂} = 1.5 + 0.75 = 2.25 \text{ moles} \]

### Step 4: Calculate the partial pressure of hydrogen
The partial pressure of a gas in a mixture can be calculated using Dalton's Law of Partial Pressures:
\[ P_{H₂} = \left( \frac{n_{H₂}}{n_{total}} \right) \times P_{total} \]
Where:
- \(P_{H₂}\) is the partial pressure of hydrogen.
- \(n_{H₂}\) is the number of moles of hydrogen.
- \(n_{total}\) is the total number of moles.
- \(P_{total}\) is the total pressure of the gas mixture.

Assuming the total pressure \(P_{total}\) is 1 atm (for simplicity):
\[ P_{H₂} = \left( \frac{1.5}{2.25} \right) \times P_{total} \]
\[ P_{H₂} = \left( \frac{1.5}{2.25} \right) \times 1 \text{ atm} = \frac{2}{3} \text{ atm} \]

### Conclusion
The partial pressure of hydrogen in the mixture is \(\frac{2}{3}\) atm.

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