3.2 g of oxygen (At. wt. = 16) and 0.2 g of hydrogen (At. wt. = 1) are placed in a `1.12 L` flask at `0^(@)C`. The total pressure of the gas mixture will be

Options

A. 1 atm
B. 4 atm
C. 3 atm
D. 2 atm

Answer

To find the total pressure of the gas mixture of oxygen and hydrogen in a 1.12 L flask at 0°C, we will use the Ideal Gas Law, which is given by the equation:

\[ PV = nRT \]

Where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas (in liters)
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = absolute temperature (in Kelvin)

### Step 1: Calculate the number of moles of oxygen (O₂)
Given:
- Mass of oxygen = 3.2 g
- Molar mass of oxygen = 32 g/mol (since O has an atomic weight of 16, O₂ = 16 * 2)

Using the formula for moles:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]

Calculating the moles of oxygen:
\[ n_{O_2} = \frac{3.2 \, \text{g}}{32 \, \text{g/mol}} = 0.1 \, \text{moles} \]

### Step 2: Calculate the number of moles of hydrogen (H₂)
Given:
- Mass of hydrogen = 0.2 g
- Molar mass of hydrogen = 2 g/mol (since H has an atomic weight of 1, H₂ = 1 * 2)

Calculating the moles of hydrogen:
\[ n_{H_2} = \frac{0.2 \, \text{g}}{2 \, \text{g/mol}} = 0.1 \, \text{moles} \]

### Step 3: Calculate the total number of moles in the mixture
Total moles \( n \) is the sum of moles of oxygen and hydrogen:
\[ n = n_{O_2} + n_{H_2} = 0.1 + 0.1 = 0.2 \, \text{moles} \]

### Step 4: Convert the temperature to Kelvin
Given:
- Temperature = 0°C

Convert to Kelvin:
\[ T = 0 + 273 = 273 \, \text{K} \]

### Step 5: Substitute the values into the Ideal Gas Law
Using the Ideal Gas Law rearranged to solve for pressure \( P \):
\[ P = \frac{nRT}{V} \]

Substituting the values:
- \( n = 0.2 \, \text{moles} \)
- \( R = 0.0821 \, \text{L·atm/(K·mol)} \)
- \( T = 273 \, \text{K} \)
- \( V = 1.12 \, \text{L} \)

Calculating the pressure:
\[ P = \frac{(0.2) \times (0.0821) \times (273)}{1.12} \]

Calculating the numerator:
\[ 0.2 \times 0.0821 \times 273 = 4.48 \]

Now divide by the volume:
\[ P = \frac{4.48}{1.12} = 4 \, \text{atm} \]

### Final Answer:
The total pressure of the gas mixture is **4 atm**.

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