An open-end mercury manometer was connected to a flask...

An open-end mercury manometer was connected to a flask containing a gas at an unknown pressure. The mercury in the arm open to the atmosphere was $65 \mathrm{~mm}$ higher than the mercury in the arm connected to the flask. The atmospheric pressure was 748 torr. What was the pressure of the gas in the flask (in torr)?

Key Concepts

Pressure Units

Pressure is often measured in units such as torr, mmHg, and atmospheres. In the context of mercury manometers, the vertical displacement in millimeters (mm) directly corresponds to units of torr or mmHg, simplifying the measurement since 1 mm of mercury height is equivalent to 1 torr of pressure.

Gauge Pressure vs Absolute Pressure

Gauge pressure is the pressure measured relative to the atmospheric pressure, whereas absolute pressure is the total pressure including atmospheric pressure. In open-ended manometers, the reading typically indicates a gauge pressure difference, which must be combined with the atmospheric pressure to determine the absolute pressure of the system being measured.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It is directly proportional to both the density of the fluid and the height of the fluid column, following the relationship P = ?gh. This concept is critical in understanding how pressure differences arise in devices like manometers.

Manometer

A manometer is an instrument used to measure pressure differences by comparing the heights of a fluid column between two connected regions. It operates on the principle that the pressure difference causes a difference in the heights of the fluid, which can be read to determine the pressure of a system relative to a reference pressure.

Transcript

00:02 Hi there.

00:02 This is problem number 41.

00:05 It is an open -ended monometer problem.

00:08 A monometer is a glass tube in a u shape, and it typically has some mercury in it.

00:17 So we might start off with maybe that much mercury in this tube.

00:23 All right, for this monometer in this problem, the end that is open to the atmosphere is registering an atmospheric pressure of 748 tor.

00:40 The other end is attached to the container of our gas sample.

00:49 And we do not know the pressure of our gas.

00:52 However, what we do know is when these two are interacting, in other words, the atmospheric pressure and the gas pressure, we find that on the side of the air, the mercury is 6 .5 or 65 millimeters higher.

01:19 So maybe we have something that looks like this, where the difference between the left side and the right side is 65 millimeters.

01:41 And this all represents the mercury.

01:48 Okay, so if we think about what's going on here, we're trying to find the pressure of the gas.

01:54 If we think about what's going on here, if we think about it in terms of the analogy of a teeter -totter.

01:59 If you have a little teeter -totter and it is level, but somebody comes along and takes away, pushes down harder on the right side than another person does on the left side, what's heater -totter is going to do.

02:15 It's going to go down on the right side and up on the left side.

02:20 So that's what we're seeing here.

02:22 The right side is lower than the left side, which is open to the atmosphere.

02:28 That means that the pressure of the gas on the right side must be greater than the pressure of the atmosphere...

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