The vapour density of a mixture containing `N_(2) (g) and O_(2) (g)` is 14.4. The percentage of `N_(2)` in the mixture is :

Options

A. 0.2
B. 0.8
C. 0.6
D. 0.5

Explanation

To solve the problem of finding the percentage of \( N_2 \) in a mixture of \( N_2 \) and \( O_2 \) with a given vapor density of 14.4, we can follow these steps:

### Step 1: Calculate the Effective Molar Mass
The effective molar mass (\( M_{eff} \)) of the gas mixture can be calculated using the formula:
\[ M_{eff} = 2 \times \text{Vapor Density} \]
Given that the vapor density is 14.4, we can substitute this value into the formula:
\[ M_{eff} = 2 \times 14.4 = 28.8 \, g/mol \]

**Hint:** Remember that vapor density is half the molar mass of the gas.

### Step 2: Set Up the Equation for Molar Mass
Let \( x \) be the mole fraction of \( N_2 \) in the mixture. Therefore, the mole fraction of \( O_2 \) will be \( 1 - x \). The molar masses of the gases are:
- Molar mass of \( N_2 = 28 \, g/mol \)
- Molar mass of \( O_2 = 32 \, g/mol \)

Using the mole fractions and molar masses, we can express the effective molar mass as:
\[ M_{eff} = x \cdot M_{N_2} + (1 - x) \cdot M_{O_2} \]
Substituting the values we have:
\[ 28.8 = x \cdot 28 + (1 - x) \cdot 32 \]

**Hint:** Make sure to distribute the terms correctly when substituting the mole fractions.

### Step 3: Simplify the Equation
Expanding the equation gives:
\[ 28.8 = 28x + 32 - 32x \]
Combining like terms results in:
\[ 28.8 = 32 - 4x \]

**Hint:** Keep track of your variables and constants when combining terms.

### Step 4: Solve for \( x \)
Rearranging the equation to isolate \( x \):
\[ 4x = 32 - 28.8 \]
\[ 4x = 3.2 \]
\[ x = \frac{3.2}{4} = 0.8 \]

**Hint:** Dividing both sides by the coefficient of \( x \) will help you find its value.

### Step 5: Calculate the Percentage of \( N_2 \)
To find the percentage of \( N_2 \) in the mixture, we multiply the mole fraction by 100:
\[ \text{Percentage of } N_2 = x \times 100 = 0.8 \times 100 = 80\% \]

**Hint:** Converting a fraction to a percentage involves multiplying by 100.

### Final Answer
The percentage of \( N_2 \) in the mixture is **80%**.