Gas Laws I: Fundamental Laws Governing Gases

Gas Laws I

Introduction to Gas Laws

The behavior of gases is described by several fundamental laws that relate pressure, volume, temperature, and amount of gas. These laws are essential for understanding chemical reactions involving gases and for solving practical problems in chemistry and physics.

The Ideal Gas Law

Definition and Formula

The Ideal Gas Law combines several simple gas laws into one equation, relating pressure (P), volume (V), temperature (T), and amount of gas in moles (n).

• Formula: $PV = nRT$

• P: Pressure (atm, Pa, etc.)

• V: Volume (L, m3, etc.)

• n: Amount of gas (mol)

• R: Universal gas constant (0.0821 L·atm·mol−1·K−1)

• T: Temperature (K)

Example: What is the volume occupied by 0.20 mol Rn at 75 °C and 0.85 atm?

• Convert temperature to Kelvin: $T = 75 + 273.15 = 348.15\ K$

• Plug into the formula: $V = \frac{nRT}{P}$

Application: Used to calculate unknown properties of gases under various conditions.

Standard Molar Volume of Gases at STP

At standard temperature and pressure (STP: 0°C, 1 atm), one mole of an ideal gas occupies approximately 22.4 L.

Gas	Molar Mass (g/mol)	Molar V (L/mol) at STP
He	4.003	22.416
O2	32.00	22.414
CO2	44.01	22.425
C3H8	44.09	22.415
SF6	146.1	22.414

Key Point: Most gases have similar molar volumes at STP, regardless of molar mass.

Amontons’s Law (Gay-Lussac’s Law): Pressure and Temperature

Relationship

Amontons’s Law states that the pressure of a fixed amount of gas at constant volume is directly proportional to its absolute temperature.

• Formula: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

• As temperature increases, pressure increases (if volume is constant).

Temperature (°C)	Temperature (K)	Pressure (kPa)
-100	173	36.0
-50	223	46.4
0	273	56.7
50	323	67.1
100	373	77.5
150	423	88.0

Example: If a gas in a steel cylinder has a pressure of 5.50 atm at 25.0°C, what will be the pressure at -45°C?

• Convert temperatures to Kelvin: $T_1 = 298\ K$, $T_2 = 228\ K$

• Use the formula to solve for $P_2$.

Charles’s Law: Volume and Temperature

Relationship

Charles’s Law states that the volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.

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

• As temperature increases, volume increases (if pressure is constant).

Temperature (°C)	Temperature (K)	Volume (L)
-3	270	22
-23	250	21
-53	220	18
-162	111	9

Example: If a balloon has a volume of 2.50 L at 25.0°C, what will be its volume at -78°C?

• Convert temperatures to Kelvin: $T_1 = 298\ K$, $T_2 = 195\ K$

• Use the formula to solve for $V_2$.

Boyle’s Law: Pressure and Volume

Relationship

Boyle’s Law states that the pressure of a fixed amount of gas at constant temperature is inversely proportional to its volume.

• Formula: $P_1V_1 = P_2V_2$

• As volume decreases, pressure increases (if temperature is constant).

Graphical Representation: The relationship is a hyperbola when plotting P vs. V, and a straight line when plotting 1/P vs. V.

Example: If the pressure at sea level is 1 atm, and a diver descends 20 m (adding 2 atm), what is the new volume of a 6 L balloon?

• Total pressure: $P_2 = 1 + 2 = 3\ atm$

• Use Boyle’s Law to solve for $V_2$.

Application in Human Physiology

Boyle’s Law explains how breathing works: when the diaphragm contracts, lung volume increases, pressure decreases, and air flows in.

• Key Point: Pressure changes in the lungs drive airflow during respiration.

Avogadro’s Law: Volume and Amount

Relationship

Avogadro’s Law states that the volume of a gas at constant temperature and pressure is directly proportional to the number of moles of gas present.

• Formula: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• As the amount of gas increases, volume increases (if temperature and pressure are constant).

Example: Doubling the number of moles of gas in a container will double its volume, provided temperature and pressure remain constant.

Summary Table: Gas Laws

Law	Variables Related	Formula	Relationship
Boyle's Law	P, V	$P_1V_1 = P_2V_2$	Inverse
Charles's Law	V, T	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	Direct
Amontons's Law	P, T	$\frac{P_1}{T_1} = \frac{P_2}{T_2}$	Direct
Avogadro's Law	V, n	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	Direct
Ideal Gas Law	P, V, n, T	$PV = nRT$	Combined

Additional info: The notes include graphical and tabular data to illustrate the relationships described by each law, as well as practical examples and physiological applications (e.g., breathing mechanics).