The vapour pressure of water at `80^(@)C` is 355 mm of Hg. 1 L vessel contains `O_(2)` at `80^(@)C`, which is saturated with water and the total pressure being 760 mm of Hg. The contents of the vessel were pumped into 0.3 L vessel at the same temperature. What is the partial presure of `O_(2)`?

Options

A. 1350 Hg
B. 2178.3 Hg
C. 121.5 Hg
D. 355 Hg

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the given data
- The vapor pressure of water at 80°C is 355 mm Hg.
- The total pressure in the 1 L vessel is 760 mm Hg.
- The contents are transferred to a 0.3 L vessel at the same temperature.

### Step 2: Calculate the partial pressure of oxygen in the 1 L vessel
The total pressure in the vessel is the sum of the partial pressures of the gases present. Since the vessel contains both oxygen (O₂) and water vapor, we can express this as:

\[ P_{\text{total}} = P_{\text{O}_2} + P_{\text{H}_2O} \]

Where:
- \(P_{\text{total}} = 760 \, \text{mm Hg}\)
- \(P_{\text{H}_2O} = 355 \, \text{mm Hg}\)

Now, we can rearrange the equation to find the partial pressure of oxygen:

\[ P_{\text{O}_2} = P_{\text{total}} - P_{\text{H}_2O} \]

Substituting the values:

\[ P_{\text{O}_2} = 760 \, \text{mm Hg} - 355 \, \text{mm Hg} = 405 \, \text{mm Hg} \]

### Step 3: Use the ideal gas law to find the new pressure in the 0.3 L vessel
Since the temperature and the number of moles of gas remain constant, we can use the relationship of pressure and volume:

\[ P_1 V_1 = P_2 V_2 \]

Where:
- \(P_1 = 405 \, \text{mm Hg}\) (initial partial pressure of O₂)
- \(V_1 = 1 \, \text{L}\) (initial volume)
- \(V_2 = 0.3 \, \text{L}\) (final volume)
- \(P_2\) is what we need to find.

Rearranging the equation to solve for \(P_2\):

\[ P_2 = \frac{P_1 V_1}{V_2} \]

Substituting the known values:

\[ P_2 = \frac{405 \, \text{mm Hg} \times 1 \, \text{L}}{0.3 \, \text{L}} = \frac{405}{0.3} \, \text{mm Hg} \]

Calculating \(P_2\):

\[ P_2 = 1350 \, \text{mm Hg} \]

### Final Answer
The partial pressure of oxygen in the 0.3 L vessel is **1350 mm Hg**.

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