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 carbon dioxide (CO2)
The formula to calculate the number of moles is:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

For CO2:
- Mass = 220 g
- Molar mass of CO2 = 12 (C) + 16×2 (O) = 44 g/mol

Calculating the number of 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 nitrogen gas (N2)
Using the same formula for nitrogen:
- Mass = 280 g
- Molar mass of N2 = 14×2 = 28 g/mol

Calculating the number of 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
Total moles = moles of CO2 + moles of N2:
\[ \text{Total moles} = 5 + 10 = 15 \text{ moles} \]

### Step 4: Use the partial pressure of nitrogen to find total pressure
The partial pressure of nitrogen (N2) is given as 1.5 atm. The relationship between partial pressure and mole fraction is:
\[ P_{N2} = X_{N2} \times P_{total} \]
Where \(X_{N2}\) is the mole fraction of nitrogen.

Calculating the mole fraction of N2:
\[ X_{N2} = \frac{\text{moles of N2}}{\text{total moles}} = \frac{10}{15} = \frac{2}{3} \]

Now substituting into the equation for partial pressure:
\[ 1.5 = \left(\frac{2}{3}\right) \times P_{total} \]

Solving for \(P_{total}\):
\[ P_{total} = 1.5 \times \frac{3}{2} = 2.25 \text{ atm} \]

### Step 5: Calculate the partial pressure of carbon dioxide (CO2)
Using the mole fraction of CO2:
\[ X_{CO2} = \frac{\text{moles of CO2}}{\text{total moles}} = \frac{5}{15} = \frac{1}{3} \]

Now we can find the partial pressure of CO2:
\[ P_{CO2} = X_{CO2} \times P_{total} \]
\[ P_{CO2} = \left(\frac{1}{3}\right) \times 2.25 = 0.75 \text{ atm} \]

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

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