Gas Laws and Kinetic Molecular Theory

Gases Unit #5: Gas Laws

Learning Objectives

• Use the Kinetic Molecular Theory of Gases to explain gas behavior

• Explain the relationship between the kinetic molecular theory of gases and physical properties

• Identify and convert between units of pressure

• Describe the behavior of gases using the gas laws (Boyle’s, Charles’, Gay-Lussac’s, Combined, Avogadro’s, Ideal Gas, and Dalton’s Laws)

• Use gas law equations to calculate initial and final conditions of gases and the ideal gas law to calculate pressure (P), volume (V), temperature (T), and amount of substance (n)

• Use standard temperature and pressure to determine the volume of a gas sample

• Use Dalton’s Law of Partial Pressures to calculate the total pressure of a mixture of gases

Gases and the Kinetic Molecular Theory

Ideal Gas Concept

• Definition: An ideal gas is a model that describes the behavior of gas particles at the microscopic level, assuming a number of ideal conditions.

Properties of Gases

• Key measurable properties of gases include:

  • Temperature

  • Volume

  • Pressure

  • Mass

• Gases can be systematically altered in one property to observe effects on the others.

Kinetic Molecular Theory (KMT) of Gases

1. Gases consist of small particles (atoms or molecules) in constant, random motion.

2. Large distances separate gas particles compared to their size, resulting in gases being mostly empty space.

3. Gas particles behave independently with no attractive or repulsive forces between them.

4. Collisions between gas particles and the walls of their container are perfectly elastic, meaning no energy is lost in collisions.

5. The average kinetic energy of gas particles is proportional to the absolute temperature (Kelvin).

   • As temperature increases, particle speed increases.

Implications of KMT

• Compressibility: Gases are easily compressible due to their mostly empty space.

• Expansion: Gases expand to fill any given volume, overcoming attractive forces as they move freely.

• Density: Gases have low density, characterized by low mass per unit volume.

• Diffusion: Gases readily diffuse through one another due to their continuous motion; paths between particles facilitate movement.

• Pressure: Gases exert pressure on their containers, resulting from collisions with container walls.

• Ideal Behavior: Gases behave most ideally at low pressures and high temperatures, where forces between particles are minimal due to increased distances and rapid motion.

Gas Diffusion Example

Ammonia vs. Hydrogen Chloride

• Molar Mass:

  • Ammonia: 17.0 g/mol

  • Hydrogen chloride: 36.5 g/mol

• Result: Ammonia diffuses farther than Hydrogen chloride in the same timeframe due to its lower molar mass.

Measurement of Gases: Pressure Units

Learning Objectives

• Identify and convert between units of pressure.

• Use standard temperature and pressure to determine the volume of gas samples.

Nature of Gas Pressure

• Gases exert pressure on container walls, and atmospheric pressure applies uniformly on the earth's surface.

Variables Influencing Gas Behavior

• Key variables include:

  • Number of moles (n)

  • Volume (V)

  • Temperature (T)

  • Pressure (P)

• Pressure Definition: Force per unit area.

• Gas pressure derives from collisions of particles against the walls of their container.

Barometer: Measure of Atmospheric Pressure

• Inventor: Evangelista Torricelli

• Common Pressure Units:

  • Atmosphere (atm)

  • Torr (named after Torricelli)

  • Pascal (Pa)

• Pressure Conversion:

  • 1 atm = 760 mmHg = 760 torr = 76 cmHg = 101 kPa

Standard Temperature and Pressure (STP)

• STP Definitions:

  • Temperature: 273 K (0 °C)

  • Pressure: 1 atm

• At STP, the molar volume of any gas is 22.4 L.

Practice Problems Related to STP

1. Volume Calculation:

   • At STP, what is the volume of 4.50 moles of nitrogen gas?

2. Mass to Volume:

   • Calculate the volume of 76.0 g of fluorine gas at STP.

Gas Laws

Learning Objectives ̵

• Describe gas behavior based on gas laws: Avogadro’s, Boyle’s, Charles’, Gay-Lussac’s, Ideal Gas, Combined, and Dalton’s Laws.

• Use gas law equations for calculating initial and final conditions, and apply the ideal gas law accordingly.

Avogadro’s Law

• Definition: Equal volumes of ideal gases contain equal numbers of moles if measured at the same temperature and pressure.

• Equation: Rewritten as
  $rac{V<em>i}{n</em>i} = rac{V<em>f}{n</em>f}$

Study Check Example

• If 5.50 mol of CO occupies 20.6 L, determine volume occupied by 16.5 mol of CO.

  • $V_f = rac{20.6 L imes 16.5 mol}{5.50 mol} = 61.8 L$

Boyle’s Law: Relation Between Volume and Pressure

• Definition: Volume of a gas varies inversely with the pressure exerted by the gas when temperature and quantity (moles) of gas remain constant.

  • Equation:
    $PV = k_1$

Boyle’s Law Application Example

• A gas occupies 10.0 L at 1.00 atm:

  • Product, $PV = (10.0 L)(1.00 atm) = k_1$

  • When pressure doubles to 2.0 atm, volume decreases to 5.0 L

  • $P<em>fV</em>f = P<em>iV</em>i$

Charles’s Law: Relation between Volume and Temperature

• Definition: Volume of a gas varies directly with the absolute temperature (K) when pressure and amount of gas are constant.

• Equation:
  $rac{V}{T} = k_2$

Charles’s Law Application Example

• A gas occupies 1.0 L at 200 K; when the temperature is doubled to 400 K, the new volume is 2.0 L.

Gay-Lussac’s Law: Relation Between Pressure and Temperature

• Definition: Pressure of a gas is directly related to its Kelvin temperature, with volume and the amount of gas held constant.

• Equation:
  $rac{P}{T} = k_3$

The Combined Gas Law

• Definition: Describes a gas sample under simultaneous changes in volume, pressure, and temperature.

• Derived from Boyle’s law and Charles’s law.

• Equation:
  $rac{P<em>iV</em>i}{T<em>i} = rac{P</em>fV<em>f}{T</em>f}$

Ideal Gas Law

• Definition: Integrates Boyle’s, Charles’s, and Avogadro’s laws into one equation.

• Equation: $PV = nRT$

  • Where:

  • R = 0.0821 L·atm/(mol·K)

  • P = Pressure in atm

  • V = Volume in L

  • n = moles of gas

  • T = Temperature in K

Dalton’s Law of Partial Pressures

• Definition: The total pressure of a gas mixture is the sum of the partial pressures of all individual gases within the mixture

• Equation:
  $P<em>t = P</em>1 + P<em>2 + … + P</em>n$

Applications and Examples

• Example calculating the partial pressure of oxygen in a gas mixture given total pressure and partial pressure of cyclopropane.

Additional Video and Website Links

• Resources for further learning:

  • Videos on rearranging gas law equations, selecting gas law equations, and extra help for gas laws.

  • Interactive simulation on gas laws.