Question

What is the pressure (in \(\mathrm{mmHg}\) ) of the gas inside the apparatus below if \(P_{\text {bar. }}=740 \mathrm{mm} \mathrm{Hg}, h_{1}=30 \mathrm{mm}\) and \(h_{2}=50 \mathrm{mm} ?\)

Short answer

The pressure of the gas inside the apparatus is \(760 \mathrm{mmHg}\).

Step-by-step solution

Identify given values

In this problem, we have: Atmospheric pressure \(P_{\text {bar. }}=740 \mathrm{mm} \mathrm{Hg}\), Height \(h_{1}=30 \mathrm{mm}\), and Height \(h_{2}=50 \mathrm{mm}\).

Apply the Barometric Formula

Barometric Pressure Formula is written as \(P_{\text{gas}} = P_{\text {bar. }} - (h_{1} - h_{2})\). Here, \(P_{\text {bar. }}\) is the atmospheric pressure, \(h_{1}\) is the height of mercury level on one side of the manometer, and \(h_{2}\) is the height of the mercury level on one the other side of the manometer.

Substitute given values into the formula

Substitute the given values into the formula to get: \(P_{\text{gas}} = 740 \mathrm{mm} \mathrm{Hg} - (30 \mathrm{mm} - 50 \mathrm{mm})\).

Calculate

Calculate the equation to get the gas pressure: \(P_{\text{gas}} = 740 \mathrm{mm} \mathrm{Hg} - (-20 \mathrm{mm} \mathrm{Hg})\). Thus, \(P_{\text{gas}} = 760 \mathrm{mm} \mathrm{Hg}\).

Key concepts

Barometric Pressure

Barometric pressure, often known as atmospheric pressure, refers to the weight of the air above us in the atmosphere. It is an important concept in understanding how gases behave. Barometric pressure is typically measured in millimeters of mercury (mmHg) or sometimes in atmospheres.
Barometric pressure can change based on altitude and weather conditions. This is because fewer air molecules exert pressure at higher altitudes, leading to lower pressure. When measuring barometric pressure, instruments such as barometers are used, which can either be mercury-based or aneroid.

• Mercury barometers use a column of mercury and measure how high the mercury rises or falls in response to atmospheric changes.
• Aneroid barometers use a small, flexible metal box called an aneroid cell. This box contracts and expands with changes in pressure.

Manometer

A manometer is a device used to measure pressure differences between two points. Often used in laboratories and industries, it is crucial for measuring gas pressures.
There are different types of manometers, but one of the simplest forms is the U-tube manometer. It consists of a U-shaped tube filled with a liquid like mercury. The pressure difference causes the liquid to move within the tube, and this movement measures the pressure of the gas.

• In a closed-end manometer, one side of the U-tube is sealed, thus showing pressure relative to a vacuum.
• An open-end manometer, like in our exercise, shows the gas pressure relative to atmospheric pressure.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the atmosphere above a surface. At sea level, it is standard to state this value as 760 mmHg. However, variations do occur because of weather and altitude.
This pressure can support a column of mercury in a barometer or manometer. The difference in column height indicates pressure differences, which is how atmospheric pressure influences the measure of other pressure types.
Understanding atmospheric pressure is essential for processes in meteorology and various scientific fields, impacting how experiments are conducted and interpreted.

Pressure Measurement

Pressure measurement is a key aspect in science that involves determining the force per unit area exerted by a gas or liquid. It is often measured in units like mmHg, atmospheres, or Pascals.
Instruments like barometers and manometers help measure pressure by comparing an unknown pressure to a known value. By using these devices, you can measure absolute pressure, gauge pressure, and differential pressure.

• Absolute pressure is the total pressure including atmospheric pressure.
• Gauge pressure measures pressure relative to ambient atmospheric pressure.
• Differential pressure is the difference between two pressures.

During experiments and real-world applications, accurate pressure measurement can influence how we understand systems—whether they're atmospheric or industrial.