A cylinder is filled with a gaseous mixture containing equal masses of `CO` and `N_(2)`. The partial pressure ratio is:

Options

A. `P_(N_2) = P_(CO)`
B. `P_(CO) = 0.875P_(N_2)`
C. `P_(CO) = 2P_(N_2)`
D. `P_(CO) = 0.5 P_(N_2)`

Answer

To solve the problem of finding the partial pressure ratio of a gaseous mixture containing equal masses of CO and N₂, we can follow these steps:

### Step 1: Calculate the Molar Masses
- The molar mass of Carbon Monoxide (CO) is calculated as follows:
- Molar mass of Carbon (C) = 12 g/mol
- Molar mass of Oxygen (O) = 16 g/mol
- Therefore, Molar mass of CO = 12 + 16 = 28 g/mol

- The molar mass of Nitrogen (N₂) is calculated as follows:
- Molar mass of Nitrogen (N) = 14 g/mol
- Therefore, Molar mass of N₂ = 14 × 2 = 28 g/mol

### Step 2: Determine Moles of Each Gas
Since the problem states that equal masses of CO and N₂ are present, we can assume a mass of 28 grams for each gas for simplicity:
- Moles of CO = Mass / Molar mass = 28 g / 28 g/mol = 1 mol
- Moles of N₂ = Mass / Molar mass = 28 g / 28 g/mol = 1 mol

### Step 3: Calculate Mole Fractions
- The total number of moles in the mixture = Moles of CO + Moles of N₂ = 1 mol + 1 mol = 2 mol
- Mole fraction of CO (X_CO) = Moles of CO / Total moles = 1 mol / 2 mol = 1/2
- Mole fraction of N₂ (X_N₂) = Moles of N₂ / Total moles = 1 mol / 2 mol = 1/2

### Step 4: Calculate Partial Pressures
Using Dalton's Law of Partial Pressures, the partial pressure of each gas can be expressed as:
- Partial pressure of CO (P_CO) = X_CO × P_total
- Partial pressure of N₂ (P_N₂) = X_N₂ × P_total

### Step 5: Calculate the Ratio of Partial Pressures
The ratio of the partial pressures can be calculated as follows:
- Ratio of partial pressures = P_CO / P_N₂
- Substituting the expressions we have:
- Ratio = (X_CO × P_total) / (X_N₂ × P_total)
- The total pressure (P_total) cancels out:
- Ratio = X_CO / X_N₂ = (1/2) / (1/2) = 1

### Conclusion
Thus, the partial pressure ratio of CO to N₂ is 1:1.

### Final Answer
The partial pressure ratio is 1:1.

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