A gas mixture 44g of `CO_(2)` and 14g of `N_(2)`, what will be fraction of `CO_(2)` in the mixture

Options

A. `1//5`
B. `1//3`
C. `2//3`
D. `1//4`

Explanation

To find the fraction of \( CO_2 \) in the gas mixture of \( CO_2 \) and \( N_2 \), we will calculate the mole fraction of \( CO_2 \). The mole fraction is given by the formula:

\[ X_{CO_2} = \frac{n_{CO_2}}{n_{CO_2} + n_{N_2}} \]

where \( n_{CO_2} \) is the number of moles of \( CO_2 \) and \( n_{N_2} \) is the number of moles of \( N_2 \).

**Step 1: Calculate the number of moles of \( CO_2 \)**

The number of moles is calculated using the formula:

\[ n = \frac{W}{M} \]

where \( W \) is the weight of the substance and \( M \) is the molar mass.

For \( CO_2 \):
- Weight \( W_{CO_2} = 44 \, g \)
- Molar mass \( M_{CO_2} = 12 + (16 \times 2) = 44 \, g/mol \)

Calculating the moles of \( CO_2 \):

\[ n_{CO_2} = \frac{W_{CO_2}}{M_{CO_2}} = \frac{44 \, g}{44 \, g/mol} = 1 \, mol \]

**Step 2: Calculate the number of moles of \( N_2 \)**

For \( N_2 \):
- Weight \( W_{N_2} = 14 \, g \)
- Molar mass \( M_{N_2} = 14 \times 2 = 28 \, g/mol \)

Calculating the moles of \( N_2 \):

\[ n_{N_2} = \frac{W_{N_2}}{M_{N_2}} = \frac{14 \, g}{28 \, g/mol} = 0.5 \, mol \]

**Step 3: Calculate the total number of moles in the mixture**

\[ n_{total} = n_{CO_2} + n_{N_2} = 1 \, mol + 0.5 \, mol = 1.5 \, mol \]

**Step 4: Calculate the mole fraction of \( CO_2 \)**

Now we can substitute the values into the mole fraction formula:

\[ X_{CO_2} = \frac{n_{CO_2}}{n_{total}} = \frac{1 \, mol}{1.5 \, mol} = \frac{1}{1.5} = \frac{2}{3} \]

Thus, the fraction of \( CO_2 \) in the mixture is:

\[ X_{CO_2} = \frac{2}{3} \]

**Final Answer: \( \frac{2}{3} \)**

---