Gas Variables and Kinetic Molecular Theory


  • Absolute zero is defined as 0 K (Kelvin), which corresponds to approximately -273.15°C (Celsius).

  • At absolute zero, the motion of particles theoretically comes to a complete stop, and they possess minimum energy.

Conversions:

  • To convert from Celsius to Kelvin, add 273.15 to the Celsius value.

  • To convert from Kelvin to Celsius, subtract 273.15 from the Kelvin value.

Conversion Factors

  • Conversions:

    • 1 atm = 760 mmHg (torr) = 101.3 kPa

    • Note: kPa is a rounded number & affects significant figures; atm & mmHg are exact conversions.

Conversions:

  • 760 mmHg & torr= 1atm= 101.3 kPa

The theory assumes that gas particles are in constant random forces traveling in straight lines until they hit another particle or the container wall.

b. The particles themselves are so small compared to the large amount of empty space

between them that their individual volume is considered to be negligible.

c. There are no attractive or repulsive forces between the particles, meaning

they do not stick together or push each other apart.

d. When particles do collide with each other or the container, the collisions are called

elastic, which means no kinetic energy is lost during the collision.

  1. Gases consist of tiny particles (atoms or molecules) that are in constant, random, and rapid motion. These particles move in straight lines until they collide with other particles or the walls of the container.

  2. The volume of individual gas particles is negligible compared to the total volume of the container they occupy. Most of the volume occupied by a gas is empty space.

  3. Gas particles exert no attractive or repulsive forces on each other. Intermolecular forces are considered to be non-existent in an ideal gas.

  4. Collisions between gas particles and with the container walls are elastic, meaning that no kinetic energy is lost during collisions. The total kinetic energy of the gas system remains constant.

  5. The average kinetic energy of gas particles is directly proportional to the absolute temperature (in Kelvin). As temperature increases, the average speed and kinetic energy of the particles increase. At any given temperature, all gas particles have the same average kinetic energy.

Maxwell-Boltzmann Distribution Curves

The Maxwell-Boltzmann distribution describes the distribution of molecular speeds for a sample of gas particles at a particular temperature, showing a range of speeds rather than a single speed.

Characteristics of the Curve

  • Characteristic Speeds:

    • Most Probable Speed (vpvp​): The speed possessed by the largest number of molecules (at the peak of the curve).

    • Average Speed (vavgvavg​): The arithmetic mean of all molecular speeds.

    • Root-Mean-Square Speed (vrmsvrms): A measure of the average speed related to particle mass and temperature, defined as vrms=3RTMvrms=M3RT​​, where RR is the ideal gas constant, TT is the absolute temperature, and MM is the molar mass.

Effects on the Curve

  • Effect of Temperature:

    • Higher temperatures shift the curve to the right, increasing the most probable and average speeds.

    • The peak flattens and broadens, indicating a wider distribution of speeds and a greater fraction of particles at higher speeds.

  • Effect of Molar Mass:

    • At a given temperature, gases with lower molar masses (lighter particles) have a Maxwell-Boltzmann curve shifted to the right and a broader distribution compared to heavier gases.

    • Lighter particles move faster on average to maintain the same average kinetic energy.

Relationship with Gas Laws

The Kinetic Molecular Theory provides the theoretical foundation for empirical gas laws:

  • Boyle's Law (P1V1=P2V2P1V1=P2V2):

    • At constant temperature, decreasing volume increases particle collision frequency with walls, thus increasing pressure.

  • Charles's Law (V1T1=V2T2T1V1​=T2V2​):

    • At constant pressure, increasing temperature auses particles to move faster and collide more forcefully. Volume must increase to maintain constant pressure.

  • Gay-Lussac's Law (P1T1=P2T2T1P1​=T2P2​):

    • At constant volume, increasing temperature causes particles to move faster, colliding more forcefully and frequently, thus increasing pressure.

  • Avogadro's Law (V1n1=V2n2n1V1​=n2V2​):

    • At constant temperature and pressure, an increase in the number of moles (nn) of gas requires an increase in volume to maintain constant collision frequency and force.

  • Ideal Gas Law (PV=nRTPV=nRT):

    • Combines all individual gas laws and is a direct consequence of KMT postulates and the kinetic energy-temperature relationship.