60 g of gaseous `C_(2)H_(6)` are mixed with 28 g of carbon monoxide. The pressure of the resulting gaseous mixture is 3 atm. The partial pressure in atm. Of `C_(2)H_(6)` in the mixture is

Answer

To find the partial pressure of \( C_2H_6 \) in the mixture, we will follow these steps:

### Step 1: Calculate the number of moles of \( C_2H_6 \)
The molar mass of \( C_2H_6 \) (ethane) can be calculated as follows:
- Carbon (C) has a molar mass of 12 g/mol.
- Hydrogen (H) has a molar mass of 1 g/mol.

Thus, the molar mass of \( C_2H_6 \) is:
\[ \text{Molar mass of } C_2H_6 = (2 \times 12) + (6 \times 1) = 24 + 6 = 30 \text{ g/mol} \]

Now, we can calculate the number of moles of \( C_2H_6 \):
\[ \text{Moles of } C_2H_6 = \frac{\text{mass}}{\text{molar mass}} = \frac{60 \text{ g}}{30 \text{ g/mol}} = 2 \text{ moles} \]

### Step 2: Calculate the number of moles of carbon monoxide (CO)
The molar mass of carbon monoxide (CO) is:
\[ \text{Molar mass of CO} = 12 + 16 = 28 \text{ g/mol} \]

Now, we can calculate the number of moles of CO:
\[ \text{Moles of CO} = \frac{\text{mass}}{\text{molar mass}} = \frac{28 \text{ g}}{28 \text{ g/mol}} = 1 \text{ mole} \]

### Step 3: Calculate the total number of moles in the mixture
Now, we can find the total number of moles in the mixture:
\[ \text{Total moles} = \text{Moles of } C_2H_6 + \text{Moles of CO} = 2 + 1 = 3 \text{ moles} \]

### Step 4: Calculate the mole fraction of \( C_2H_6 \)
The mole fraction of \( C_2H_6 \) is given by:
\[ \text{Mole fraction of } C_2H_6 = \frac{\text{Moles of } C_2H_6}{\text{Total moles}} = \frac{2}{3} \]

### Step 5: Calculate the partial pressure of \( C_2H_6 \)
The partial pressure of \( C_2H_6 \) can be calculated using Dalton's Law of Partial Pressures:
\[ \text{Partial pressure of } C_2H_6 = \text{Mole fraction of } C_2H_6 \times \text{Total pressure} \]
Given that the total pressure \( P_T \) is 3 atm:
\[ \text{Partial pressure of } C_2H_6 = \left(\frac{2}{3}\right) \times 3 \text{ atm} = 2 \text{ atm} \]

### Final Answer:
The partial pressure of \( C_2H_6 \) in the mixture is **2 atm**.

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