What is the pressure in millimeters of mercury inside a container of gas connected to a mercury-filled open-end manometer of the sort shown in Figure 10.5 when the level in the arm connected to the container is 17.6 cm lower than the level in the arm open to the atmosphere and the atmospheric pressure reading outside the apparatus is 754.3 mm Hg?

Verified step by step guidance

1. Identify the type of manometer: This is an open-end manometer, which means the pressure of the gas in the container can be determined by comparing it to the atmospheric pressure.
2. Understand the relationship between the levels in the manometer: Since the level in the arm connected to the container is lower, the gas pressure is greater than the atmospheric pressure.
3. Calculate the difference in mercury levels: Convert the difference in height from centimeters to millimeters. Since 1 cm = 10 mm, the difference is 17.6 cm * 10 mm/cm.
4. Determine the gas pressure: Add the difference in mercury levels to the atmospheric pressure to find the pressure of the gas in the container.
5. Express the final pressure in millimeters of mercury: The result from the previous step gives the pressure in mm Hg, which is the desired unit.

Key Concepts

Manometer Principles

A manometer is a device used to measure the pressure of a gas by comparing it to atmospheric pressure. It typically consists of a U-shaped tube filled with a liquid, often mercury. The difference in height between the two arms of the manometer indicates the pressure difference, allowing for the calculation of the gas pressure in relation to atmospheric pressure.

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of the atmosphere above a given point. It is commonly measured in millimeters of mercury (mm Hg) and is approximately 760 mm Hg at sea level. In calculations involving manometers, the atmospheric pressure is a critical reference point for determining the absolute pressure of the gas in the container.

Pressure Calculation

To find the pressure of the gas in the container using a manometer, one must account for the height difference between the mercury levels in the two arms. If the gas pressure is lower than atmospheric pressure, the height difference is subtracted from the atmospheric pressure. Conversely, if the gas pressure is higher, the height difference is added. This relationship allows for the determination of the gas pressure in mm Hg.