Video: Calculating Atmospheric Pressure at the Open End of an Open-Ended Manometer Given the Pressure of the Sample and the Height Differential of the Mercury Column

In an open-ended manometer, a gas sample is trapped, causing the mercury to rise as seen on the diagram. What is the atmospheric pressure if the pressure of the gas inside the manometer is 750 torr? [A] 705 torr [B] 740 torr [C] 760 torr [D] 795 torr [E] 815 torr

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Video Transcript

In an open-ended manometer, a gas sample is trapped, causing the mercury to rise as seen in the diagram. What is the atmospheric pressure if the pressure of the gas inside the manometer is 750 torr? (A) 705 torr, (B) 740 torr, (C) 760 torr, (D) 795 torr, or (E) 815 torr.

A manometer is a device that’s used to measure the pressure. Usually, it’s used to measure the pressure of a sample of gas, unlike a barometer which is usually used to measure the pressure of the atmosphere. In this question, we’ve been tasked with finding the atmospheric pressure. And we’ve been given the pressure of the gas inside the manometer, which is 750 torr. So, we need to come up with some kind of expression that’s going to relate the pressure of the gas inside the manometer to the atmospheric pressure outside the manometer.

Since the level of mercury within the manometer is no longer changing, the manometer must be at equilibrium. So, all of the pressures involved in the manometer are balancing each other out. So, that means if we zoom in on the part of the manometer that’s closest to the container of gas, the pressure of the gas is pushing down on the liquid mercury. And that pressure must be balanced by the pressure from the atmosphere and the pressure from the mercury on the other side.

Another way to think about this would be to recognize that the level of mercury, which I’ve marked here on the diagram, represents the pressure of the gas. The level of mercury on the other side represents the pressure of the atmosphere. And the 45 millimeters of mercury would exert its own pressure. Either way, the pressure of the gas is going to be equal to the pressure of the atmosphere plus the pressure of the remaining column of mercury.

We’re looking to solve for the pressure of the atmosphere, so we can do that by subtracting the pressure of mercury from both sides of the equation. The question tells us that the pressure of the gas is 750 torr, but what’s the pressure of the mercury? Well, each millimeter of mercury is equal to one unit of pressure expressed in torr. So, the pressure of the mercury is 45 millimeters of mercury or 45 torr. Now, we can put that in for the pressure of the mercury and solve for the pressure of the atmosphere. Subtracting these two numbers, we’ll get 705 torr, which matches answer choice (A).

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