Chemistry chapter 10 & 11: KMT and Gases

The kinetic molecular theory is a group of ideas used to explain the interaction of matter and energy due to particle motion. It is the study of the effect of temperature, pressure, and volume on an amount of matter. KMT assumes that ¹⁾all matter is composed of small particles in constant, random, straight-line motion, ²⁾collisions between these particles are perfectly elastic, and ³⁾the kinetic energy of these particles is directly proportional to the Kelvin temperature. In an elastic collision there is no change in the total kinetic energy of the two particles before and after the collision.

The pressure of gas is caused by the force of the particles colliding with the wall of the container and the number of these collision. Pressure is a measure of force per unit area. Standard air pressure is the average pressure of air at sea level under normal conditions. In science, standard pressure needs to be reproducible in a laboratory, it must be measurable so a quantitative value is given to the definition. Standard pressure is the pressure that is able to support a column of mercury 760 mm tall, this pressure is defined as 1.00 atmosphere or 101.325 kPa. (1 mmHg = 1 torr) A manometer is an instrument used to measure pressure. There are two kinds of manometers: open and closed. A closed manometer is sealed at one end and has a vacuum above the liquid while the other end is open to the gas sample. A barometer is a closed manometer used to measure air pressure. (Air pressure is also referred to as atomospheric pressure or barometric pressure.) An open manometer is open at both ends, one end is open to the air and the other end is open to the gas sample. A technique used to determine the pressure of gas inside a container that is open to the air on one end is to equalize the pressure. If the level of the liquid inside the container is raised or lowered so that it is even with the level of the liquid outside the container then the pressure inside the container is the same as the pressure outside the container.

Kinetic energy is the energy of motion. Temperature is a measure of the average kinetic energy of the particles in the sample. The average speed of gas particles depends on the temperature and the mass of the particles. K.E. = 1/2 mv², where m is the mass of the particle and v is the velocity of the particle. If particles are at the same temperature then they would have the same average kinetic energy. It follows that when gas particles are at the same temperature: the higher the mass of the particles the slower they would move and the lighter the mass of the particles the faster they would move; and the higher the temperature increases the faster they move and the lower the temperature decreases the slower they move. Absolute zero is the theoretical point where all molecular motion stops, 0 K = 273.15 ºC. Standard temperature is defined as 0 ºC or 273 K.

Gas is made up of particles that move about at random and are not held by any forces to any fixed place. Gases particles occupy the entire space of the container they are in, they diffuse throughout the container until they become evenly distributed. The size of individual gas particles is extremely small compared to the volume of space they occupy and the distance between them. They are considered point masses, having mass but negligible volume. This defines an ideal (imaginary) gas: point masses with no mutual attraction forces. Real gases have volume and attraction forces, but real gases approach the behavior of ideal gases at low pressures and high temperatures. The behavior of a gas depends upon: the amount, the temperature, the pressure and the volume.

Boyle's Law: if temperature and amount of gas are held constant, the pressure of a gas varies inversely with its volume.

Charles' Law: if pressure and amount of gas are held constant, the volume of a gas varies directly with the absolute (Kelvin) temperature.

Gay-Lussac's Law: if volume and amount of gas are held constant, the pressure of a gas varies directly with the absolute (Kelvin) temperature.

Combined Gas Law: combination of the above, if the amount of gas is held constant, the volume of the gas will vary inversely with the pressure and directly with the absolute (Kelvin) temperature.

Avogadro's Principle: if pressure and temperature of gas are held constant, the volume of a gas varies directly with the amount of gas.

Dalton's Law of Partial Pressure: the total pressure of gases in a mixture is the sum of the pressures of the gasses in the container. Each gas in a mixture acts as if it is occupying the container all by itself. The pressure of each gas in the mixture is it's partial pressure.

Dalton's Law is especially useful when a gas is collected over water. The gas collected in this way is saturated with water vapor. The total pressure in the container is the pressure of the dry gas and the pressure of the water vapor. Water vapor pressure is temperature dependent: the higher the temperature the more water vapor the air can hold (humid hot summer versus dry cold winter).

Density and gases: (density is mass per unit volume) if the amount of gas remains constant, an increase in pressure will decrease the volume and therefore increase the density and an increase in temperature will increase the volume and therefore decrease the density.

Graham's Law: if pressure and temperature of gas are held constant, the rates gases effuse varies inversely as the square root of their molar masses.

Joule-Thomson effect: as highly compressed gas is allowed to escape through a small opening in a container (an aerosol can), the temperature will decrease.

Avogadro's Hypothesis: equal volumes of gas at the same temperature and pressure contain the same number of particles. It has been determined that at STP one mole of any gas contains 6.02 x 10²³ particles and occupies a volume of 22.4 Liters. This is called molar volume.

Ideal Gas Law: a law that connects the four physical variables (amount, temperature, pressure and volume) that affect ideal gas behavior into one equation.