A polythene bag 3 litre capacity is partially filled by 1 liter of Helium gas at 0.3 atm at 300K. Subsequently, enough Ne gas is filled to make total pressure 0.4 atm at 300K. Calculate ratio of moles of Ne to He in the container.

Options

A. `1/2`
B. `1/3`
C. `1/4`
D. `3/4`

Explanation

To solve the problem, we need to calculate the number of moles of Helium (He) and Neon (Ne) gas in the container and then find the ratio of moles of Ne to He.

### Step-by-Step Solution:

1. **Calculate the moles of Helium (He)**:
We can use the Ideal Gas Law, which states:
\[ PV = nRT \]
Where:
- \( P \) = Pressure (in atm)
- \( V \) = Volume (in liters)
- \( n \) = Number of moles
- \( R \) = Ideal gas constant (0.0821 atm·L/(K·mol))
- \( T \) = Temperature (in Kelvin)

Given:
- \( P = 0.3 \, \text{atm} \)
- \( V = 3 \, \text{L} \)
- \( T = 300 \, \text{K} \)

Rearranging the Ideal Gas Law to solve for \( n \):
\[ n = \frac{PV}{RT} \]

Plugging in the values for Helium:
\[ n_{He} = \frac{(0.3 \, \text{atm}) \times (3 \, \text{L})}{(0.0821 \, \text{atm·L/(K·mol)}) \times (300 \, \text{K})} \]
\[ n_{He} = \frac{0.9}{24.63} \approx 0.0365 \, \text{moles} \]

2. **Calculate the total pressure after adding Neon (Ne)**:
The total pressure after adding Neon gas is given as \( 0.4 \, \text{atm} \).

3. **Calculate the moles of Neon (Ne)**:
Let \( n_{Ne} \) be the number of moles of Neon gas. The total pressure can be expressed as:
\[ P_{total} = P_{He} + P_{Ne} \]
We know:
\[ P_{total} = 0.4 \, \text{atm} \]
The partial pressure of Helium is:
\[ P_{He} = 0.3 \, \text{atm} \]
Therefore, the partial pressure of Neon can be calculated as:
\[ P_{Ne} = P_{total} - P_{He} = 0.4 \, \text{atm} - 0.3 \, \text{atm} = 0.1 \, \text{atm} \]

Now, using the Ideal Gas Law again for Neon:
\[ n_{Ne} = \frac{P_{Ne} \cdot V}{R \cdot T} \]
Plugging in the values:
\[ n_{Ne} = \frac{(0.1 \, \text{atm}) \times (3 \, \text{L})}{(0.0821 \, \text{atm·L/(K·mol)}) \times (300 \, \text{K})} \]
\[ n_{Ne} = \frac{0.3}{24.63} \approx 0.0122 \, \text{moles} \]

4. **Calculate the ratio of moles of Neon to Helium**:
The ratio can be calculated as:
\[ \text{Ratio} = \frac{n_{Ne}}{n_{He}} = \frac{0.0122}{0.0365} \]
\[ \text{Ratio} \approx \frac{1}{3} \]

### Final Answer:
The ratio of moles of Neon to Helium in the container is \( \frac{1}{3} \).