4.8 g of oxygen and 3.4 g of hydrogen are placed in 1.12 litre flask at `0^∘C`. Find the total pressure in atm of the gas mixture.

Options

A. 37
B. 32
C. 41
D. 50

Explanation

To solve the problem of finding the total pressure of a gas mixture containing 4.8 g of oxygen and 3.4 g of hydrogen in a 1.12-liter flask at 0°C, we will follow these steps:

### Step 1: Calculate the number of moles of oxygen (O₂)
- The molar mass of oxygen (O₂) is approximately 32 g/mol.
- Using the formula:
\[ \text{Number of moles of O₂} = \frac{\text{mass of O₂}}{\text{molar mass of O₂}} = \frac{4.8 \text{ g}}{32 \text{ g/mol}} = 0.15 \text{ moles} \]

### Step 2: Calculate the number of moles of hydrogen (H₂)
- The molar mass of hydrogen (H₂) is approximately 2 g/mol.
- Using the formula:
\[ \text{Number of moles of H₂} = \frac{\text{mass of H₂}}{\text{molar mass of H₂}} = \frac{3.4 \text{ g}}{2 \text{ g/mol}} = 1.7 \text{ moles} \]

### Step 3: Calculate the total number of moles in the mixture
- Total moles (n) = moles of O₂ + moles of H₂
\[ n = 0.15 \text{ moles} + 1.7 \text{ moles} = 1.85 \text{ moles} \]

### Step 4: Use the Ideal Gas Law to find the total pressure
- The Ideal Gas Law is given by the equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure (atm)
- \( V \) = volume (liters)
- \( n \) = number of moles
- \( R \) = ideal gas constant = 0.0821 atm·L/(K·mol)
- \( T \) = temperature in Kelvin
- Convert the temperature from Celsius to Kelvin:
\[ T = 0°C + 273.15 = 273.15 \text{ K} \]

### Step 5: Rearrange the Ideal Gas Law to solve for pressure (P)
- Rearranging gives:
\[ P = \frac{nRT}{V} \]

### Step 6: Substitute the values into the equation
- Substitute \( n = 1.85 \) moles, \( R = 0.0821 \) atm·L/(K·mol), \( T = 273.15 \) K, and \( V = 1.12 \) L:
\[ P = \frac{(1.85 \text{ moles}) \times (0.0821 \text{ atm·L/(K·mol)}) \times (273.15 \text{ K})}{1.12 \text{ L}} \]

### Step 7: Calculate the pressure
- Performing the calculation:
\[ P = \frac{(1.85) \times (0.0821) \times (273.15)}{1.12} \approx \frac{41.78}{1.12} \approx 37.29 \text{ atm} \]

### Final Answer
- The total pressure of the gas mixture is approximately **37.29 atm**.