Day 1: KMT

Kinetic Molecular Theory

  • Kinetic molecular theory (KMT) is a model that predicts the behavior of gases under various conditions.

Four Assumptions of Kinetic Molecular Theory

  1. Constant Motion of Gas Particles

    • Gas is a collection of particles in constant straight-line motion.

    • Gas particles are always moving in straight lines until they collide with something.

    • After colliding, they bounce off and continue in another straight line until they collide again.

    • Possible collisions include:

      • Other gas particles

      • Walls of the container

    • Gas particles do not attract or repel each other and do not interact.

    • Nature of Motion: Completely random and unimpeded by attractions or repulsions.

    • Collisions:

      • Collisions between gas particles and other surfaces are elastic.

      • Elastic Collision Defined: No energy is lost or gained during the collision. Particles exit the collision with the same energy they had when entering.

  2. Negligible Particle Size

    • There is significant space between gas particles compared to their size.

    • Particle size is considered negligible for practical purposes.

    • Identity of the gas does not affect behavior; both small particles (e.g., hydrogen) and larger particles (e.g., radon) behave similarly.

  3. Kinetic Energy and Temperature

    • The average kinetic energy of gas particles is proportional to the gas temperature in Kelvin.

    • Conversion from Celsius to Kelvin:
      Kelvin = Celsius + 273

    • Use Kelvin for all gas-related calculations.

    • Kinetic energy only proportional to Kelvin temperature, not Celsius.

Properties of Gases Explained by Kinetic Molecular Theory

  • Compressibility:

    • Gases can be compressed because of the vast space between particles. Compressing a gas reduces the empty space rather than shrinking the particles.

  • Shape and Volume:

    • Gases assume the shape and volume of their containers. The particles move freely and fill the entire container.

  • Density:

    • Gases have very low densities compared to solids and liquids.

    • Example:

    • Converting 12 ounces of liquid water to water vapor at the same pressure would require approximately 1700 cans of gaseous water.

Questions and Answering Examples

  • Which statement is inconsistent with KMT assumptions?

    • Accurate: As temperature increases, gas particles move faster on average.

    • Incorrect Statement: The size of gas particles dramatically affects the properties of the gas (it does not, as their sizes are negligible).

    • Consistent Statement: Gases have lower densities than solids and liquids.

Pressure in Gases

  • Pressure Defined: Pressure is the amount of force per unit area.

  • Gas pressure arises from collisions of gas particles with the walls of the container.

  • Key insight: Collisions with other gas particles do not contribute to pressure.

  • Increasing collisions result in increased pressure, while reducing the number of collisions decreases pressure.

Example Question

  • Which sample of gas has the lowest pressure, assuming identical conditions?

    • The sample with the fewest gas particles will have the lowest pressure due to fewer collisions.

Units of Pressure

  • There are six key units of pressure:

    1. Pascal (Pa)

    2. Atmosphere (atm)

    3. Millimeters of Mercury (mmHg)

    4. Torr (Torr)

    5. Pounds per Square Inch (psi)

    6. Inches of Mercury (inHg)

  • An additional unit is:

    • kilopascal (kPa) which equals 1000 pascals.

Standard Pressure Values

  • Standard pressure at sea level is:

    • 1 ext{ atm} = 101325 ext{ Pa}

    • 760 ext{ mmHg} = 760 ext{ Torr} = 14.7 ext{ psi} = 29.92 ext{ inHg}

  • Connection Between Units: mmHg and Torr are equivalent; Torr is an older term.

Example Conversions

  • Convert 0.311 atm (Mount Everest pressure) to mmHg:

    • Using conversion factor: 1 atm = 760 mmHg

    • Calculation:
      0.311 ext{ atm} imes 760 ext{ mmHg/atm} = 236.36 ext{ mmHg}

    • Rounding to three significant figures: 236 mmHg.

  • Convert 0.997 atm (room pressure) to kPa:

    • Using conversion factor: 1 atm = 101325 Pa

    • Calculation:
      0.997 ext{ atm} imes 101325 ext{ Pa/atm} ext{ and divide by } 1000 = 101 ext{ kPa}

Conclusion

  • Kinetic molecular theory provides a framework for understanding gas behavior, highlighting the assumptions and implications of particle motion, pressure, and temperature relationships.