A `10 L` flask at `298 K` contains a gaseous mixture of `CO` and `CO_(2)` at a total pressure of `2.0 "bar"` if `0.20 ` mole of `CO` is present, find its partial pressure and also that of `CO_(2)`.

Explanation

To solve the problem, we need to find the partial pressures of carbon monoxide (CO) and carbon dioxide (CO₂) in a gaseous mixture contained in a 10 L flask at 298 K with a total pressure of 2.0 bar. Given that there are 0.20 moles of CO present, we can follow these steps:

### Step 1: Calculate the Partial Pressure of CO
We can use the ideal gas law to calculate the partial pressure of CO. The ideal gas equation is given by:

\[ P = \frac{nRT}{V} \]

Where:
- \( P \) = partial pressure of the gas
- \( n \) = number of moles of the gas
- \( R \) = ideal gas constant (0.083 L·bar/K·mol)
- \( T \) = temperature in Kelvin
- \( V \) = volume in liters

For CO, we have:
- \( n = 0.20 \) moles
- \( R = 0.083 \) L·bar/K·mol
- \( T = 298 \) K
- \( V = 10 \) L

Substituting the values into the equation:

\[ P_{CO} = \frac{0.20 \, \text{mol} \times 0.083 \, \text{L·bar/K·mol} \times 298 \, \text{K}}{10 \, \text{L}} \]

Calculating this gives:

\[ P_{CO} = \frac{0.20 \times 0.083 \times 298}{10} = \frac{4.958}{10} = 0.4958 \, \text{bar} \approx 0.496 \, \text{bar} \]

### Step 2: Calculate the Partial Pressure of CO₂
Next, we can find the partial pressure of CO₂ using the total pressure of the gas mixture. The total pressure is the sum of the partial pressures of CO and CO₂:

\[ P_{total} = P_{CO} + P_{CO₂} \]

Given that the total pressure \( P_{total} = 2.0 \, \text{bar} \) and we have already calculated \( P_{CO} \):

\[ 2.0 \, \text{bar} = 0.496 \, \text{bar} + P_{CO₂} \]

To find \( P_{CO₂} \), we rearrange the equation:

\[ P_{CO₂} = 2.0 \, \text{bar} - 0.496 \, \text{bar} = 1.504 \, \text{bar} \]

### Summary of Results
- Partial Pressure of CO: \( P_{CO} \approx 0.496 \, \text{bar} \)
- Partial Pressure of CO₂: \( P_{CO₂} \approx 1.504 \, \text{bar} \)