The Property of Gases – Kinetic Molecular Theory And Pressure

Kinetic Molecular Theory of Gases The word kinetic refers to motion. Kinetic energy is the energy an object has because of its motion. Kinetic Molecular Theory makes assumptions about: Size Motion Energy of gas particles

Kinetic Molecular Theory Part 1 According to the KMT all matter consists of tiny particles that are in constant, random motion Move in a straight line until they collide with other particles or with the walls of the container.

Kinetic Molecular Theory Part 2 2. Gas particles are much smaller than the distances between them. Most of a gas consists of empty space. Gas consists of small particles that are separated from one another by empty space Most of the volume of a gas consists of empty space Because they are so far apart, there are no attractive or repulsive forces between the gas molecules The motion of one particle is independent of the motion of other particles

Kinetic Molecular Theory Part 3 No kinetic energy is lost when gas particles collide with each other or with the walls of the container (elastic collision) Undergoes elastic collision – no kinetic energy is lost when particles collide. The total amount of kinetic energy remains constant.

Kinetic Molecular Theory Part 4 All gases have the same average kinetic energy at a given temperature Temperature is a measure of average kinetic energy of particle in a sample of matter. Kinetic energy and temperature are directly related The higher the temperature, the greater the kinetic energy The Kelvin temperature of a substance is directly proportional to the average kinetic energy of the particles of the substance. 273 + _____oC = _______Kelvin There is no temperature lower than 0 Kelvin (Absolute Zero). Kinetic Energy = ½ mv2; where m = mass and v = velocity

Absolute Zero The greater the atomic and molecular motion, the greater the temperature is of a substance. If all atomic and molecular motion would stop, the temperature would be at absolute zero (0 Kelvin or -273 oC)

Introduction to Diffusion and Effusion When we first open a container of ammonia, it takes time for the odor to travel from the container to all parts of a room. This shows the motion of gases through other gases. In this case, ammonia gas, NH3, moves through air. This is an example of diffusion and effusion.

Diffusion and Effusion Diffusion is the tendency of a gas to move toward areas of lower density. Ammonia moving throughout a room. Effusion is the escape of a gas from a container from a small hole. Air escaping from a car tire. The heavier the molecule, the slower it will effuse or diffuse.

Diffusion and Effusion

Graham’s Law The practical effect of Graham’s Law is that small molecules travel faster than larger molecules. This is true for both diffusion and effusion.

Graham’s Law ra = rate at which substance a travels rb = rate at which substance b travels ma = mass of substance a mb = mass of substance b

ta = ma tb mb Graham’s Law Since rate is distance over time, this equation can also be rearranged as follows: ta = ma tb mb

Graham’s Law Practice Problem For example: A sample of an unknown gas flows through the wall of a porous cup in 39.9 min. An equal volume of gaseous hydrogen, measured at the same temperature and pressure, flows through in 9.75 min. What is the molar mass of the unknown gas?

Graham’s Law Practice Problem We need the equation using time. ta = ma tb mb

Graham’s Law Practice Problem What do we know? ta = 39.9 min tb = 9.75 min ma = x amu mb = 2 amu

Graham’s Law Practice Problem Plug into the equation: 39.9 = x 9.75 2

Graham’s Law Practice Problem Cross multiply and solve for x 39.9(2) = 9.75(x) 56.43 = 9.75(x) 5.78 = (x) 5.782 = x 33.49 = x

Pressure Pressure is the force per unit area Gas pressure is the force exerted by a gas per unit surface area of an object. Gas pressure is the result of billions of collisions of billions of gas molecules with an object Atmospheric pressure (air pressure) results from the collisions of air molecules with objects. The air pressure at higher altitudes is slightly lower than at sea level because the density of the Earth’s atmosphere decreases as elevation increases. Vacuum - Empty space with no particles and no pressure

Measuring Pressure Barometer – an instrument used to measure atmospheric pressure

Measuring Pressure Manometer – an instrument used to measure gas pressure in a closed container

Units of Pressure and STP Average atmospheric pressure is 1 atm 1atm = 760 torr = 760 mmHg = 101.3 kPa STP (Standard Temperature and Pressure) 1 atm and 0oC or 1 atm and 273 K Like using the our system of measuring versus the metric system; means the same thing but different units

Conversion Factors for Pressure 1 atm = 760 torr = 760 mmHg = 101.3 kPa

Example 1 Convert 2.5 atm into torr, mmHg, kPa 2.5 atm 760 torr 1 atm 2.5 atm 760 mmHg 1 atm = 1900 mmHg 2.5 atm 101.3 kPa 1 atm = 250 kPa

Example 2 Convert 215 kPa into torr, mmHg, atm 215 atm 760 torr 215 atm 760 mmHg 101.3 kPa = 1610 mmHg 215 atm 1 atm 101.3 kPa = 2.12 atm