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Nitrogen gas was collected over water at \(25^{\circ} \mathrm{C}\) . If the vapor pressure of water at \(25^{\circ} \mathrm{C}\) is 23 \(\mathrm{mmH}\) g, and the total pressure in the container is measured at 781 \(\mathrm{mmH} \mathrm{g}\) , what is the partial pressure of the nitrogen gas? \(\begin{array}{ll}{\text { (A) }} & {46 \mathrm{mmH} \mathrm{g}} \\ {\text { (B) }} & {551 \mathrm{mmH} \mathrm{g}} \\ {\text { (C) }} & {735 \mathrm{mmH} \mathrm{g}} \\ {\text { (D) }} & {758 \mathrm{mmH} \mathrm{g}}\end{array}\)

Short Answer

Expert verified
The partial pressure of the nitrogen gas is \(758 mmHg\). So, the answer is (D) \(758 mmHg\).

Step by step solution

01

Understand the total pressure

The total pressure inside the container is a sum of the pressure of the nitrogen and the vapor pressure of the water. This is given as 781 mmHg.
02

Note the vapor pressure of water

We are told that the vapor pressure of water at the given temperature (25°C) is 23 mmHg. This is the pressure that the water exerts in the container.
03

Calculate the partial pressure of the nitrogen gas

The partial pressure of the nitrogen gas can now be found by subtracting the vapor pressure of the water from the total pressure. Mathematically, this can be expressed as: \( P(N_{2}) = P(total) - P(water) \) Substituting the given values: \( P(N_{2}) = 781 mmHg - 23 mmHg = 758 mmHg \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Partial Pressure
Partial pressure refers to the pressure that a single gas in a mixture would exert if it occupied the entire volume by itself. It's an important concept in understanding gas mixtures, like when collecting gases over water.
Gases in a mixture each contribute to the total pressure based on their individual pressures. Imagine each gas behaving as if the others weren't there, pushing against the walls of their container.
To find the partial pressure of a gas, you generally subtract the pressures of all other gases from the total pressure. It's like peeling back layers to see the contribution from each gas.
In the exercise, determining the partial pressure of nitrogen meant removing the contribution from water vapor pressure, leaving behind only what's due to nitrogen.
Dalton's Law of Partial Pressures
Dalton's Law of Partial Pressures helps us make sense of multi-gas systems, like a container with both nitrogen and water vapor. This law states that the total pressure exerted by a mixture of non-reacting gases can be calculated by adding up all their individual, or partial, pressures.
For example: If you know total pressure and one gas's pressure, you can easily find the other. It's like a simple arithmetic problem involving addition or subtraction.
In our scenario, the total pressure was measured as 781 mmHg, and when we subtracted the water vapor's partial pressure of 23 mmHg (given for 25°C), we easily arrived at the nitrogen's partial pressure. This is a classic application of Dalton's Law! Remember, it's always about piecing together or breaking apart the components of the total pressure.
Vapor Pressure
Vapor pressure is when a liquid transitions into a vapor within a closed system. It refers to the pressure exerted by the vapor in equilibrium with its liquid form at a given temperature.
Vapor pressure is specific to each substance and temperature. For instance, as temperature increases, so does vapor pressure. At 25°C, water has a vapor pressure of 23 mmHg.
In practical terms, knowing vapor pressure lets you measure how much a liquid 'wants' to become gas at a given temperature.
In the exercise, vapor pressure was crucial because it helped determine how much of the total pressure was due to nitrogen after accounting for the water vapor. Knowing these pressures helps in scenarios like predicting how a gas behaves in changing temperatures.

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