An open-end manometer containing mercury was connected to a vessel holding a gas at a pressure of 720 torr. The atmospheric pressure was 765 torr. Sketch a diagram of the apparatus showing the relative heights of the mercury in the two arms of the manometer. What is the difference in the heights of the mercury expressed in centimeters?

Measuring the pressure of gas is a fundamental task in various scientific and industrial applications. Gas pressure can indicate the state of a reaction in chemistry or ensure proper functioning of equipment in mechanical systems. To measure this pressure, devices such as manometers are utilized. A manometer measures the pressure difference between the gas in a container and the atmosphere by observing the displacement of a liquid column, typically mercury, within a U-shaped tube. The pressure exerted by the gas will either raise or lower the column of mercury in the tube depending on whether it is above or below atmospheric pressure.

Gas pressure can be depicted in several units, with 'torr' being a common one specifically designed for such measurements. The torr is nearly equivalent to the pressure exerted by a millimeter of mercury (mmHg), reflecting the historical use of mercury in barometers and manometers. Crucially, understanding how to read a manometer will allow one to determine the gas pressure either in excess of or below the external atmospheric pressure, which is an essential step in many experimental procedures.

A 'torr' is a unit of pressure that is defined as 1/760 of an atmosphere, which approximately equals the amount of pressure exerted by a one-millimeter column of mercury (1 mmHg) at sea level on Earth. It is named after Evangelista Torricelli, an Italian physicist and mathematician who invented the barometer in the 17th century.

The torr is particularly useful for low pressures found in scientific laboratories, such as when working with gases, and it allows for precise measurements without dealing with large numbers like those in pascal units. When using a mercury manometer, the height of the mercury column can directly provide the gas pressure in torrs, since a change of 1 mm in the mercury column equates to a change of 1 torr in pressure.

A mercury manometer is a device primarily used for determining gas pressure differences. It consists of a U-shaped tube partially filled with mercury. One end of the tube is exposed to the atmosphere, and the other end is connected to the vessel containing the gas whose pressure is being measured.

Due to mercury's high density and relatively low vapor pressure, it is an ideal fluid for precise pressure measurements. As the gas pressure fluctuates relative to the atmospheric pressure, the mercury moves along the tube, providing visual feedback of pressure changes. To read a mercury manometer, you observe the difference in the height of the mercury column between the two arms of the tube. The pressure exerted by the gas can then be calculated based on the height difference, with each millimeter of height representing one torr of pressure difference.

Pressure difference is the driving concept behind how manometers provide valuable measurements. It is simply the difference in pressure between two points, in this case, between the gas in a vessel and the atmospheric pressure. Manometers are designed to visibly show this difference via the movement of a liquid column, like mercury.

The calculation of pressure difference is straightforward but vital for understanding physical phenomena. In the context of the given exercise, the pressure difference is the absolute value of subtracting the gas pressure from atmospheric pressure. This is visually represented in the manometer by the displacement of mercury, allowing for a clear and quantifiable method to measure the unseen force exerted by gases. Converting the pressure difference to a measurable height difference in a mercury column solidifies abstract concepts into concrete readings.