A sample of nitrogen gas is collected over water at a total pressure of 760\text{ mmHg}. I… — JAMB UTME

A sample of nitrogen gas is collected over water at a total pressure of $760\text{ mmHg}$ . If the saturated vapor pressure of water at the collection temperature is $24\text{ mmHg}$ , what is the partial pressure of the dry nitrogen gas?

$736\text{ mmHg}$ Answer
B
$784\text{ mmHg}$
C
$760\text{ mmHg}$
D
$24\text{ mmHg}$

Answer

The partial pressure of the dry nitrogen gas is

736\text{ mmHg}

According to Dalton's Law of Partial Pressures, the total pressure of a gas collected over water is the sum of the partial pressure of the dry gas and the vapor pressure of water (

P_{\text{total}} = P_{\text{dry gas}} + P_{\text{water}}

). To find the pressure of the dry gas alone, subtract the saturated water vapor pressure from the total pressure:

760\text{ mmHg} - 24\text{ mmHg} = 736\text{ mmHg}

Step-by-Step Solution

State Dalton's Law of Partial Pressures for a gas collected over water.

P_{\text{total}} = P_{\text{dry gas}} + P_{\text{H}_2\text{O}}

When a gas is collected over water, the measured total pressure is the sum of the partial pressure of the dry gas and the saturated vapor pressure of water.

Rearrange the equation to solve for the partial pressure of the dry nitrogen gas.

P_{\text{dry gas}} = P_{\text{total}} - P_{\text{H}_2\text{O}}

To isolate the pressure exerted by the dry gas, the water vapor pressure (aqueous tension) must be subtracted from the total pressure.

Substitute the given values into the formula and calculate.

P_{\text{dry gas}} = 760\text{ mmHg} - 24\text{ mmHg} = 736\text{ mmHg}

Performing simple subtraction gives the final partial pressure of dry nitrogen.

Key Concept

Dalton's Law of Partial Pressures and Collection of Gas over Water

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