Chapter 10: Physical Characteristics of Gases

The Kinetic-Molecular Theory of Matter The kinetic-molecular theory is based on the idea that particles of matter are always in motion.

The Kinetic-Molecular Theory of Gases The theory provides a model of what is called an ideal gas. An ideal gas is an imaginary gas that perfectly fits all the assumptions of the kinetic-molecular theory.

The Kinetic-Molecular Theory of Gases The kinetic-molecular theory of gases is based on the following five assumptions:

Assumption #1 “Gases consist of large numbers of tiny particles that are far apart relative to their size.” Molecules of gases are much farther apart than those of liquids or solids. Most of the volume occupied by a gas is empty space. This is why their density is much less and why they can be compressed so much easier.

Assumption #2 “Collisions between gas particles and between particles and container walls are elastic.” An elastic collision is one in which there is no net loss of kinetic energy.

Assumption #3 “Gas particles are in continuous, rapid, random motion. Therefore, they possess kinetic energy, which is energy of motion.” Gas particles move in all directions. The kinetic energy of the particles overcomes the attractive forces between them.

Assumption #4 “There are no forces of attraction or repulsion between gas particles.” You can think of ideal gas molecules as behaving like small billiard balls. When they collide, they do not stick together but immediately bounce apart.

Assumption #5 “The average kinetic energy of gas particles depends on the temperature of the gas.” The kinetic energy of any moving object, including a particle, is given by the following equation: KE = ½mv2 M = mass V = speed All gases at the same temperature have the same average kinetic energy. Small molecules (small mass, m) have higher average speeds.

The Kinetic-Molecular Theory and the Nature of Gases The kinetic-molecular theory applies only to ideal gases. Although ideal gases do not actually exist, many gases behave nearly ideally if pressure is low or temperature is high.

Expansion Gases do not have a definite shape or volume. Gases take the shape of their containers. Gases evenly distribute themselves within a container.

Fluidity Gas particles easily flow past one another.

Low Density The density of a substance in the gaseous state is about 1/1000 the density of the same substance in the liquid or solid state.

Compressibility Gases can be compressed, decreasing the distance between particles, and decreasing the volume occupied by the gas.

Diffusion Spontaneous mixing of particles of two substances caused by their random motion. Rate of diffusion is dependent upon: Speed of particles Diameter of particles Attractive forces between particles

Effusion Process by which particles under pressure pass through a tiny opening Rate of effusion is dependent upon: Speed of particles (small molecules have greater speed than large molecules at the same temperature, so they effuse more rapidly)

Deviations of Real Gases from Ideal Behavior When their particles are far enough apart and have enough kinetic energy, most gases behave ideally. However, all real gases deviate to some degree from ideal-gas behavior. A real gas is a gas that does not behave completely according to the assumptions of the kinetic-molecular theory.

Deviations of Real Gases from Ideal Behavior Real gases occupy space and exert attractive forces on one another. Likely to behave nearly ideally: Gases at high temperature and low pressure Small non-polar gas molecules Likely not to behave ideally: Gases at low temperature and high pressure Large, polar gas molecules

Pressure  

Composition of the Dry Atmosphere 78% Nitrogen (N2) 21% Oxygen (O2) 1% Other gases

Measuring Pressure Barometer The mercury barometer was invented by Evangelista Torricelli in the 1600’s

Units of Pressure Table 10-1 Units of Pressure Unit Symbol Definition/Relationship Pascal Pa SI pressure unit 1 Pa = 1N/m2 Millimeter of mercury mm Hg Pressure that supports a 1 mm column of mercury in a barometer Atmosphere Atm Average atmospheric pressure at sea level and 0oC 1 atm = 760 mm Hg = 760 torr = 1.01325 x 105 Pa = 101.325 kPa = 760 torr Torr torr 1 torr = 1 mm Hg

Standard Temperature and Pressure (STP) Standard Temperature = 0oC Standard Pressure = 1 atm = 760 mm Hg (torr) = 101.3 kPa

The Gas Laws Gas laws – simple mathematical relationships between the volume, temperature, pressure, and quantity of a gas

Boyle’s Law Pressure-Volume Relationship The volume of a fixed mass of gas varies inversely with the pressure at constant temperature Volume increases as pressure decreases Volume decreases as pressure increases

Boyle’s Law  

Boyle’s Law

Boyle’s Law Practice Problem A sample of gas has a volume of 6.20 L at 20oC and 0.980 atm pressure. What is its volume at the same temperature and at a pressure of 1.11 atm?

Charles’s Law Volume-Temperature Relationships Jacques Charles – Volumes of any gas at constant pressure would change by 1/273 of the original volume for every Celsius degree the temperature rose or fell from 0oC

Kelvin Temperature Scale (Absolute Scale) K = 273 + ___oC oC = K – 273 0 K = absolute zero Gas volume and Kelvin temperature are directly proportional Standard temperature = 0oC = 273 K

Charles’s Law The volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature

Charles’s Law  

Charles’s Law

Charles’s Law Practice Problem The volume of a gas sample is 746 mL at 20oC. What is its volume at body temperature (37oC)? Assume the pressure remains constant.

Gay Lussac’s Law The pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature

Gay Lussac’s Law  

Gay Lussac’s Law

Gay Lussac’s Law Practice Problem A gas has a pressure of 0.370 atm at 50.0oC. What is the pressure at standard temperature?

The Combined Gas Law A mathematical expression of the relationship between pressure, volume, and temperature of a fixed amount of gas (constant mass) In real life experiments, pressure, volume, and temperature may all change

Combined Gas Law  

Combined Gas Law Practice Problem A gas sample originally occupies a volume of 0.546L at 745 mm Hg and 95oC. What pressure will be needed to contain the sample in 155 mL at 25oC?

Dalton’s Law of Partial Pressures Partial Pressure – the pressure exerted by each gas in a mixture Dalton’s Law – The total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases PT = P1 + P2 + P3 + P4 +…

Dalton’s Law Gases Collected by Water Displacement

Dalton’s Law Practice Problem A container with two gases, helium and argon, is 30.0% by volume helium. Calculate the partial pressure of helium and argon if total pressure inside the container is 4 atm.