A sample of gas is collected over water at at a barometric pressure of 751 mm Hg (vapour pressure of water at is 21 mm Hg).The partial pressure of gas in the sample collected is

Options

A. 21 mm Hg
B. 751 mm Hg
C. 0.96 atm
D. 1.02 atm

Answer

To find the partial pressure of the gas collected over water, we can use Dalton's Law of Partial Pressures. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Barometric pressure (total pressure) = 751 mm Hg
- Vapor pressure of water at the given temperature = 21 mm Hg

### Step 2: Apply Dalton's Law of Partial Pressures
According to Dalton's Law, the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas in the mixture. In this case, the total pressure is the sum of the partial pressure of the gas collected and the vapor pressure of water.

The formula can be written as:
\[ P_{\text{total}} = P_{\text{gas}} + P_{\text{water}} \]

### Step 3: Rearrange the equation to solve for the partial pressure of the gas
We can rearrange the equation to find the partial pressure of the gas:
\[ P_{\text{gas}} = P_{\text{total}} - P_{\text{water}} \]

### Step 4: Substitute the known values into the equation
Now, substitute the known values into the equation:
\[ P_{\text{gas}} = 751 \, \text{mm Hg} - 21 \, \text{mm Hg} \]

### Step 5: Calculate the partial pressure of the gas
Perform the subtraction:
\[ P_{\text{gas}} = 751 - 21 = 730 \, \text{mm Hg} \]

### Step 6: Convert the pressure to atmospheres (if needed)
If required, we can convert the pressure from mm Hg to atmospheres using the conversion factor \( 1 \, \text{atm} = 760 \, \text{mm Hg} \):
\[ P_{\text{gas (atm)}} = \frac{730 \, \text{mm Hg}}{760 \, \text{mm Hg/atm}} \approx 0.96 \, \text{atm} \]

### Final Answer
The partial pressure of the gas in the sample collected is **730 mm Hg** or approximately **0.96 atm**.

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