Question

In a closed-end manometer, the mercury level in the arm attached to the flask can never be higher than the mercury level in the other arm, whereas in an open-end manometer, it can be higher. Explain.

Short answer

Closed-end manometer: Mercury in the closed arm can't rise higher due to vacuum pressure. Open-end manometer: Mercury in the open arm can rise higher if flask pressure exceeds atmospheric pressure.

Step-by-step solution

Understand the Closed-End Manometer

In a closed-end manometer, one end of the U-shaped tube is sealed, and the other end is attached to the flask which contains the gas sample. The space above the mercury in the closed arm is a vacuum, meaning it has no pressure.

Compare Pressures in Closed-End Manometer

In a closed-end manometer, the pressure of the gas in the flask is directly measured by the height difference between the mercury levels in the two arms. Since one arm is closed and has no added pressure (vacuum), the gas pressure from the flask pushes the mercury up in the closed arm. The height difference equilibrates the pressure in the flask with the pressure exerted by the mercury column in the open arm, so the mercury level in the closed arm cannot be higher than the open arm.

Understand the Open-End Manometer

In an open-end manometer, one end of the U-shaped tube is open to the atmosphere and the other end is attached to the flask. The pressure of the gas in the flask is compared with the atmospheric pressure.

Compare Pressures in Open-End Manometer

In an open-end manometer, if the gas pressure in the flask is greater than the atmospheric pressure, it will push the mercury level higher in the open end of the manometer. This results in the mercury level in the arm connected to the flask being higher than the mercury level in the open arm.

Summarize the Difference

In summary, in a closed-end manometer, the maximum mercury level in the closed arm reflects a vacuum, so it can't surpass the mercury level in the open arm. However, in an open-end manometer, the mercury level can be higher on the side open to the atmosphere if the gas pressure in the flask exceeds atmospheric pressure.

Key concepts

closed-end manometer

A closed-end manometer is an excellent tool for measuring the pressure of a gas when you need a precise and straightforward approach. This device consists of a U-shaped tube with one end sealed (closed) and the other end connected to a container, typically a flask, containing the gas sample.
In the closed arm of the manometer, there is a vacuum, which means there is no air or any other gas present, resulting in zero pressure. Because of this vacuum, the pressure in the closed arm is always lower than in the arm connected to the gas sample.
The pressure measurement in a closed-end manometer is determined by observing the height difference between the mercury levels in the two arms of the tube. The gas pressure from the flask pushes the mercury upward in the closed arm. The equilibrium occurs when the height difference compensates for the gas pressure from the flask. As a result, the mercury level in the closed arm can never exceed the level in the connected arm.

open-end manometer

The open-end manometer is another tool for measuring gas pressure, but it operates in a slightly different way compared to a closed-end manometer. This manometer also has a U-shaped tube, but instead of one end being sealed, it is open to the atmosphere, making it possible to compare the gas pressure in the flask with the atmospheric pressure.
When using an open-end manometer, the open end experiences atmospheric pressure, while the other end is connected to the gas sample. If the gas pressure in the flask is greater than the atmospheric pressure, the mercury is pushed higher in the arm connected to the flask. Conversely, if the atmospheric pressure is greater, the mercury will rise higher in the open arm.
Thus, the difference in mercury levels in an open-end manometer directly indicates the pressure difference between the gas sample and atmospheric pressure. This makes it useful for situations where knowing the absolute pressure relative to atmospheric conditions is essential.

gas pressure measurement

Gas pressure measurement is crucial in many scientific and industrial applications, and manometers are commonly used instruments for this purpose. The basic principle revolves around balancing the pressure exerted by the gas with that exerted by a column of liquid, often mercury, within the manometer.
In a closed-end manometer, gas pressure is measured against a vacuum, leading to a direct reading of the gas pressure based on the height difference of mercury in the U-tube. This method is highly accurate because it isolates the gas pressure from external variables such as atmospheric pressure.
On the other hand, an open-end manometer measures the gas pressure relative to atmospheric pressure. This allows for understanding how the gas pressure compares to the surrounding environment, which can be critical for processes sensitive to changes in ambient conditions. The height difference in mercury levels indicates whether the gas pressure is higher or lower than the atmospheric pressure.
Overall, understanding how to use and interpret readings from closed-end and open-end manometers is fundamental for accurate gas pressure measurement and has broad applications in chemistry, physics, and engineering fields.