16 g of oxygen and 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. 50
B. 40
C. 60
D. 70

Explanation

To solve the problem of finding the total pressure of the gas mixture in the flask, we can follow these steps:

### Step 1: Calculate the number of moles of oxygen (O₂)
- Given mass of oxygen = 16 g
- Molar mass of oxygen (O₂) = 32 g/mol

Using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
\[ \text{Moles of O₂} = \frac{16 \, \text{g}}{32 \, \text{g/mol}} = 0.5 \, \text{mol} \]

### Step 2: Calculate the number of moles of hydrogen (H₂)
- Given mass of hydrogen = 4 g
- Molar mass of hydrogen (H₂) = 2 g/mol

Using the same formula:
\[ \text{Moles of H₂} = \frac{4 \, \text{g}}{2 \, \text{g/mol}} = 2 \, \text{mol} \]

### Step 3: Calculate the total number of moles in the mixture
\[ \text{Total moles} = \text{Moles of O₂} + \text{Moles of H₂} = 0.5 \, \text{mol} + 2 \, \text{mol} = 2.5 \, \text{mol} \]

### Step 4: Use the Ideal Gas Law to find the pressure
The Ideal Gas Law is given by:
\[ PV = nRT \]
Where:
- \( P \) = pressure (atm)
- \( V \) = volume (L)
- \( n \) = number of moles
- \( R \) = ideal gas constant = 0.0821 atm·L/(K·mol)
- \( T \) = temperature (K)

Given:
- Volume \( V = 1.12 \, \text{L} \)
- Temperature \( T = 0^\circ C = 273 \, \text{K} \)

Rearranging the Ideal Gas Law to solve for pressure \( P \):
\[ P = \frac{nRT}{V} \]

Substituting the values:
\[ P = \frac{(2.5 \, \text{mol}) \times (0.0821 \, \text{atm·L/(K·mol)}) \times (273 \, \text{K})}{1.12 \, \text{L}} \]

### Step 5: Calculate the pressure
Calculating the numerator:
\[ (2.5) \times (0.0821) \times (273) = 56.30575 \, \text{atm·L} \]

Now, dividing by the volume:
\[ P = \frac{56.30575}{1.12} \approx 50.3 \, \text{atm} \]

### Final Answer
The total pressure of the gas mixture is approximately **50.3 atm**.

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