Gases: Pressure, Measurement, and Gas Laws

Gases and Pressure

Definition of Pressure

Pressure is defined as the amount of force exerted per unit area. In the context of gases, pressure is the result of gas particles colliding with the surfaces of their container. The force exerted by these collisions, divided by the area of the surface, gives the pressure.

• Formula: $P = \frac{F}{A}$, where P is pressure, F is force, and A is area.

• Units: The SI unit of pressure is the pascal (Pa), but other common units include atmosphere (atm), millimeter of mercury (mmHg), and torr.

• Example: Atmospheric pressure at sea level is approximately 1 atm or 760 mmHg.

Pressure Units

Pressure can be measured in several units, each useful in different contexts. The millimeter of mercury (mmHg) is commonly used in laboratory settings, originating from the use of a barometer.

Unit	Symbol	Equivalent to 1 atm
Pounds per square inch	psi	14.7
Torr (mmHg)	torr	760
Inches of mercury	in Hg	29.92
Atmosphere	atm	1

Example: To convert 1.32 atm to mmHg: $1.32 \text{ atm} \times \frac{760 \text{ mmHg}}{1 \text{ atm}} = 1003 \text{ mmHg}$

Measuring Pressure: Barometers and Manometers

The Barometer

A barometer is an instrument used to measure atmospheric pressure. It typically consists of a column of mercury in a glass tube. The height of the mercury column is proportional to the atmospheric pressure.

• Atmospheric pressure: At sea level, the mercury column rises to about 760 mm.

• Principle: The pressure exerted by the atmosphere supports the column of mercury against gravity.

The Manometer

A manometer is used to measure the pressure of a gas sample in the laboratory. It consists of a U-shaped tube containing a dense liquid, usually mercury.

• Types: Closed-end and open-end manometers.

• Measurement: The difference in height between the two columns of liquid indicates the pressure of the gas relative to atmospheric pressure.

• Formula for open-end manometer: $P_{\text{gas}} = P_{\text{atm}} \pm h$ (where h is the height difference)

• Example: If the mercury column is 200 mm higher on the open side, $P_{\text{gas}} = P_{\text{atm}} + 200 \text{ mmHg}$

The Simple Gas Laws

Boyle's Law: Volume and Pressure

Boyle's Law describes the relationship between the pressure and volume of a gas at constant temperature. As the pressure on a gas increases, its volume decreases proportionally, and vice versa.

• Mathematical expression: $P_1 V_1 = P_2 V_2$

• Graph: The relationship is a hyperbola when plotting pressure versus volume.

• Example: If a gas at 1.02 atm occupies 2.75 L, and the volume increases to 3.25 L, the new pressure is: $P_2 = \frac{P_1 V_1}{V_2} = \frac{1.02 \times 2.75}{3.25} = 0.863 \text{ atm}$

Charles's Law: Volume and Temperature

Charles's Law states that the volume of a gas is directly proportional to its temperature (in Kelvin) at constant pressure.

• Mathematical expression: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Graph: Volume increases linearly with temperature.

• Example: If a gas occupies 1.0 L at 273 K, it will occupy 2.0 L at 546 K, assuming constant pressure.

Applications of Gas Laws

Molar Volume, Density, and Molar Mass of a Gas

The molar volume is the volume occupied by one mole of a substance. For gases at standard temperature and pressure (STP: 0°C or 273 K, 1 atm), the molar volume is 22.4 L.

• Molar volume at STP: 22.4 L/mol

• Density of a gas: $d = \frac{PM}{RT}$, where P is pressure, M is molar mass, R is the gas constant, and T is temperature.

• Molar mass from gas properties: $M = \frac{dRT}{P}$

• Example: At STP, 1 mole of any ideal gas occupies 22.4 L.

Summary Table: Gas Laws

Law	Relationship	Equation	Constant
Boyle's Law	Pressure vs. Volume	$P_1 V_1 = P_2 V_2$	Temperature
Charles's Law	Volume vs. Temperature	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	Pressure
Avogadro's Law	Volume vs. Moles	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	Pressure, Temperature

Additional info: Avogadro's Law relates the volume of a gas to the number of moles at constant temperature and pressure.