Equal mass of oxygen and helium gases are mixed in a container at 27°C Fraction of total pressure exerted by helium gas is

Options

A. `1/8`
B. `8/9`
C. `1/4`
D. `3/4`

Answer

To find the fraction of total pressure exerted by helium gas when equal masses of oxygen and helium gases are mixed in a container at 27°C, we can follow these steps:

### Step 1: Define the Masses
Let the mass of oxygen (O₂) be \( m \) grams and the mass of helium (He) also be \( m \) grams.

### Step 2: Calculate Moles of Each Gas
- The molar mass of oxygen (O₂) is 32 g/mol.
- The molar mass of helium (He) is 4 g/mol.

Using the formula for moles:
\[ \text{Moles of O₂} = \frac{m}{32} \]
\[ \text{Moles of He} = \frac{m}{4} \]

### Step 3: Calculate Total Moles
Now, we can calculate the total number of moles in the container:
\[ \text{Total moles} = \text{Moles of O₂} + \text{Moles of He} = \frac{m}{32} + \frac{m}{4} \]

To add these fractions, we need a common denominator. The common denominator of 32 and 4 is 32:
\[ \text{Total moles} = \frac{m}{32} + \frac{8m}{32} = \frac{9m}{32} \]

### Step 4: Calculate Mole Fraction of Helium
The mole fraction of helium (He) is given by:
\[ \text{Mole fraction of He} = \frac{\text{Moles of He}}{\text{Total moles}} = \frac{\frac{m}{4}}{\frac{9m}{32}} \]

This simplifies to:
\[ \text{Mole fraction of He} = \frac{m}{4} \times \frac{32}{9m} = \frac{32}{36} = \frac{8}{9} \]

### Step 5: Calculate Fraction of Total Pressure Exerted by Helium
According to Dalton's Law of Partial Pressures, the partial pressure of a gas is equal to its mole fraction multiplied by the total pressure:
\[ \text{Partial pressure of He} = \text{Mole fraction of He} \times P_{\text{total}} \]

Since we are interested in the fraction of total pressure exerted by helium:
\[ \text{Fraction of total pressure exerted by He} = \text{Mole fraction of He} = \frac{8}{9} \]

### Final Answer
The fraction of total pressure exerted by helium gas is \( \frac{8}{9} \).

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