The density of a gaseous mixture of He and `N_2` is found to be `(10)/(22.4) g//1` at STP. The percentage composition of He and `N_2` in this mixture respectively will be

Options

A. 75%, 25%
B. 25%, 75%
C. 30%, 70%
D. 40%, 60%

Answer

To solve the problem of finding the percentage composition of helium (He) and nitrogen (N2) in a gaseous mixture with a given density at STP, we can follow these steps:

### Step 1: Understand the Given Data
The density of the gaseous mixture is given as \( \frac{10}{22.4} \, \text{g/L} \) at Standard Temperature and Pressure (STP). At STP, 1 mole of any gas occupies 22.4 liters.

### Step 2: Calculate the Mass of the Mixture
Using the density formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
We can rearrange this to find the mass of the mixture:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
Assuming the volume is 22.4 L (the volume of 1 mole of gas at STP):
\[ \text{Mass} = \frac{10}{22.4} \times 22.4 = 10 \, \text{g} \]

### Step 3: Set Up the Moles of Gases
Let \( x \) be the number of moles of helium (He) in the mixture. Then, the number of moles of nitrogen (N2) will be:
\[ 1 - x \]
since the total moles of the mixture is 1 mole at STP.

### Step 4: Express Masses in Terms of Moles
The mass of helium can be expressed as:
\[ \text{Mass of He} = x \times 4 \, \text{g/mol} = 4x \, \text{g} \]
The mass of nitrogen can be expressed as:
\[ \text{Mass of N2} = (1 - x) \times 28 \, \text{g/mol} = 28(1 - x) \, \text{g} \]

### Step 5: Set Up the Total Mass Equation
The total mass of the mixture is the sum of the masses of helium and nitrogen:
\[ 4x + 28(1 - x) = 10 \]

### Step 6: Solve for \( x \)
Expanding the equation:
\[ 4x + 28 - 28x = 10 \]
Combining like terms:
\[ -24x + 28 = 10 \]
Rearranging gives:
\[ -24x = 10 - 28 \]
\[ -24x = -18 \]
\[ x = \frac{18}{24} = \frac{3}{4} \]

### Step 7: Calculate Moles of N2
Now, substituting back to find the moles of nitrogen:
\[ \text{Moles of N2} = 1 - x = 1 - \frac{3}{4} = \frac{1}{4} \]

### Step 8: Calculate the Percentage Composition
To find the percentage composition of helium:
\[ \text{Percentage of He} = \left( \frac{3}{4} \right) \times 100 = 75\% \]
To find the percentage composition of nitrogen:
\[ \text{Percentage of N2} = \left( \frac{1}{4} \right) \times 100 = 25\% \]

### Final Answer
The percentage composition of helium and nitrogen in the mixture is:
- Helium (He): 75%
- Nitrogen (N2): 25%

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