Question

Oxygen gas is collected by downward displacement of water in a jar. The level of water inside the jar is adjusted to the height of water outside the jar. When the adjustment is made the pressure exerted by the oxygen is (1) equal to the atmospheric pressure (2) equal to the vapour pressure of oxygen at that temperature (3) equal to the atmospheric pressure plus aqueous tension at that temperature (4) equal to the atmospheric pressure minus aqueous tension at that temperature

Short answer

The pressure exerted by the oxygen is equal to the atmospheric pressure minus aqueous tension at that temperature (Option 4).

Step-by-step solution

Understanding the Displacement Method

When oxygen gas is collected by downward displacement of water, the gas pushes water out of the jar. This process captures the gas above the water. The height of water inside the jar being adjusted to the height outside implies equilibrium, eliminating pressure difference contributed by water column height.

Identify Total Pressure Components

The total pressure inside the jar is composed of the pressure due to the oxygen gas and the vapor pressure (aqueous tension) exerted by water vapor present along with the oxygen. This is because water evaporates and contributes to the pressure in the jar.

Equation Setup and Calculation

The total pressure inside the jar must equal the atmospheric pressure outside, therefore:\[ P_{total} = P_{oxygen} + P_{aqueous tension} \]Here, \( P_{total} \) is the atmospheric pressure. Rearranging the equation for the oxygen pressure, we get:\[ P_{oxygen} = P_{atmospheric} - P_{aqueous tension} \]

Conclusion

This yields that the pressure exerted by the oxygen gas is equal to the atmospheric pressure minus the aqueous tension at that temperature.

Key concepts

Displacement Method

When we use the displacement method to collect gas, we rely on a simple but effective technique. This involves collecting the gas over water. As the gas enters the jar, it displaces the water, effectively pushing it out. The gas then settles above the water.
Importantly, adjusting the water level to match the outside water level ensures there’s no pressure difference caused by the water column. This equilibrium is crucial for accurate pressure readings.
By using this method, we can capture lighter gases like oxygen without contamination. Making sure no water remains also prevents inaccuracies in pressure measurement.

Aqueous Tension

Aqueous tension, or water vapor pressure, is the pressure exerted by water vapor present alongside the collected gas.
When oxygen is collected over water, some water evaporates into the space above the liquid, even in the presence of the gas. This contributes to the total pressure inside the jar.
Thus, the measured pressure inside the jar isn’t just from oxygen; it also includes the vapor pressure of water, known as aqueous tension. It’s essential to account for this when calculating the pressure of the collected gas to avoid errors.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air in the Earth's atmosphere.
At sea level, this pressure is approximately 101.3 kPa. It acts uniformly in all directions and is an essential factor in gas collection.
In our setup, the total pressure inside the jar matches the atmospheric pressure outside when we adjust the water levels. This balancing act makes sure we properly account for all pressure components.
Knowing the atmospheric pressure helps us calculate the actual pressure of the gas by subtracting the aqueous tension.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid form. For water, at a given temperature, a certain amount of water will evaporate and exert a specific pressure in the space above it.
This pressure is called vapor pressure. It increases with temperature since higher temperatures cause more water molecules to evaporate.
In the context of gas collection, the vapor pressure of water contributes to the total pressure inside the jar. Hence, it is crucial to subtract this aqueous tension from the total pressure to determine the gas pressure accurately.