A gaseous mixture contains 220 g of carbon dioxide and 280 g of nitrogen gas. If the partial pressure of nitrogen gas in the mixture is 1.5 atm then the partial pressure of carbon dioxide gas in the mixture will be

Options

A. 1.25 atm
B. 0.75 atm
C. 0.50 atm
D. 3 atm

Answer

To find the partial pressure of carbon dioxide (CO2) in the gaseous mixture, we can follow these steps:

### Step 1: Calculate the number of moles of CO2
To find the number of moles of CO2, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
Given:
- Mass of CO2 = 220 g
- Molar mass of CO2 = 44 g/mol

Calculating the moles of CO2:
\[ \text{Number of moles of CO2} = \frac{220 \, \text{g}}{44 \, \text{g/mol}} = 5 \, \text{moles} \]

### Step 2: Calculate the number of moles of N2
Using the same formula for nitrogen gas (N2):
Given:
- Mass of N2 = 280 g
- Molar mass of N2 = 28 g/mol

Calculating the moles of N2:
\[ \text{Number of moles of N2} = \frac{280 \, \text{g}}{28 \, \text{g/mol}} = 10 \, \text{moles} \]

### Step 3: Calculate the total number of moles in the mixture
Now, we find the total number of moles:
\[ \text{Total moles} = \text{moles of CO2} + \text{moles of N2} = 5 + 10 = 15 \, \text{moles} \]

### Step 4: Calculate the mole fractions of CO2 and N2
The mole fraction of CO2 is calculated as:
\[ \text{Mole fraction of CO2} = \frac{\text{moles of CO2}}{\text{total moles}} = \frac{5}{15} = \frac{1}{3} \]

The mole fraction of N2 is calculated as:
\[ \text{Mole fraction of N2} = \frac{\text{moles of N2}}{\text{total moles}} = \frac{10}{15} = \frac{2}{3} \]

### Step 5: Use the partial pressure of N2 to find the total pressure
Given that the partial pressure of nitrogen (N2) is 1.5 atm, we can express this as:
\[ P_{N2} = \text{Mole fraction of N2} \times P_{total} \]
Substituting the known values:
\[ 1.5 \, \text{atm} = \frac{2}{3} \times P_{total} \]

To find \( P_{total} \):
\[ P_{total} = \frac{1.5 \, \text{atm}}{\frac{2}{3}} = 1.5 \times \frac{3}{2} = 2.25 \, \text{atm} \]

### Step 6: Calculate the partial pressure of CO2
Now we can find the partial pressure of CO2 using its mole fraction:
\[ P_{CO2} = \text{Mole fraction of CO2} \times P_{total} \]
Substituting the known values:
\[ P_{CO2} = \frac{1}{3} \times 2.25 \, \text{atm} = 0.75 \, \text{atm} \]

### Final Answer
The partial pressure of carbon dioxide (CO2) in the mixture is **0.75 atm**.

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