Equal weights of two gases of molecular weight 4 and 40 are mixed. The pressure of the mixture is 1.1 atm. The partial pressure of the light gas in this mixture is

Options

A. 0.55 atm
B. 0.11 atm
C. 1 atm
D. 0.25 atm

Explanation

To find the partial pressure of the light gas in a mixture of two gases with molecular weights of 4 and 40, we can follow these steps:

### Step 1: Identify the given information
- Molecular weight of light gas (M1) = 4
- Molecular weight of heavy gas (M2) = 40
- Total pressure of the mixture (P_total) = 1.1 atm
- Equal weights of both gases are mixed.

**Hint:** Start by noting down the molecular weights and the total pressure given in the problem.

### Step 2: Define the weights of the gases
Let the weight of each gas be W. Since equal weights are mixed, we have:
- Weight of light gas = W
- Weight of heavy gas = W

**Hint:** Remember that since the weights are equal, you can use a variable (W) for calculations.

### Step 3: Calculate the number of moles of each gas
The number of moles (n) of a gas can be calculated using the formula:
\[ n = \frac{\text{Weight}}{\text{Molecular Weight}} \]

For the light gas:
\[ n_1 = \frac{W}{4} \]

For the heavy gas:
\[ n_2 = \frac{W}{40} \]

**Hint:** Use the formula for moles to find the number of moles for both gases based on their weights and molecular weights.

### Step 4: Calculate the total number of moles
The total number of moles (N_total) is the sum of the moles of both gases:
\[ N_{\text{total}} = n_1 + n_2 = \frac{W}{4} + \frac{W}{40} \]

To add these fractions, find a common denominator (which is 40):
\[ N_{\text{total}} = \frac{10W}{40} + \frac{W}{40} = \frac{11W}{40} \]

**Hint:** Make sure to find a common denominator when adding fractions.

### Step 5: Calculate the mole fraction of the light gas
The mole fraction (χ) of the light gas is given by:
\[ \chi_1 = \frac{n_1}{N_{\text{total}}} = \frac{\frac{W}{4}}{\frac{11W}{40}} \]

Simplifying this:
\[ \chi_1 = \frac{W}{4} \times \frac{40}{11W} = \frac{10}{11} \]

**Hint:** The mole fraction is a ratio; ensure you simplify correctly.

### Step 6: Calculate the partial pressure of the light gas
Using Dalton's law of partial pressures, the partial pressure (P1) of the light gas can be calculated as:
\[ P_1 = \chi_1 \times P_{\text{total}} \]
\[ P_1 = \frac{10}{11} \times 1.1 \, \text{atm} \]

Calculating this:
\[ P_1 = 1 \, \text{atm} \]

**Hint:** Use the mole fraction you calculated to find the partial pressure by multiplying with the total pressure.

### Final Answer
The partial pressure of the light gas in the mixture is **1 atm**.

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