If a mixture of `CO` and `N_(2)` in equal amount have total 1 atm pressure, then partial pressure of `N_(2)` in the mixture is

Options

A. 1 atm
B. 0.5 atm
C. 2 atm
D. 3 atm

Explanation

To solve the problem of finding the partial pressure of nitrogen gas (N₂) in a mixture of carbon monoxide (CO) and nitrogen (N₂) at a total pressure of 1 atm, we can follow these steps:

### Step 1: Understand Dalton's Law of Partial Pressures
According to Dalton's Law, the partial pressure of a gas in a mixture is equal to the mole fraction of that gas multiplied by the total pressure of the mixture.

### Step 2: Define the Variables
Let’s denote:
- The amount of nitrogen gas (N₂) = W grams
- The amount of carbon monoxide (CO) = W grams
- Total pressure (P_total) = 1 atm

### Step 3: Calculate the Moles of Each Gas
To find the mole fraction, we need to calculate the number of moles of each gas using their molecular weights:
- Molecular weight of N₂ = 28 g/mol
- Molecular weight of CO = 28 g/mol

The number of moles of N₂:
\[ n_{N_2} = \frac{W}{28} \]

The number of moles of CO:
\[ n_{CO} = \frac{W}{28} \]

### Step 4: Calculate Total Moles in the Mixture
Total moles in the mixture:
\[ n_{total} = n_{N_2} + n_{CO} = \frac{W}{28} + \frac{W}{28} = \frac{2W}{28} = \frac{W}{14} \]

### Step 5: Calculate the Mole Fraction of N₂
The mole fraction of N₂ (X_{N₂}) is given by:
\[ X_{N_2} = \frac{n_{N_2}}{n_{total}} = \frac{\frac{W}{28}}{\frac{W}{14}} = \frac{1}{2} \]

### Step 6: Calculate the Partial Pressure of N₂
Using Dalton's Law:
\[ P_{N_2} = X_{N_2} \times P_{total} = \frac{1}{2} \times 1 \text{ atm} = 0.5 \text{ atm} \]

### Final Answer
The partial pressure of nitrogen gas (N₂) in the mixture is **0.5 atm**.

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