Unit 12 - Gases Pressure Pressure and Volume: Boyle’s Law Volume and Temperature: Charles’s Law Volume and Moles: Avogadro’s Law Ideal Gas Law Dalton’s Law of Partial Pressures Kinetic Molecular Theory of Gases Gas Stoichiometry

Unit 12 - Gases Upon completion of this unit, you should be able to do the following: Describe the effect of a change in temperature on a gas and determine the new volume or gas pressure at the new temperature. Use the combined gas law to determine the pressure, temperature or volume of a gas when experimental conditions change. Determine the molar mass, molar volume or density of a gas from experimental data. Apply the ideal gas law to determine the pressure, volume, temperature or number of moles in a gas sample. Calculate the partial pressure of a gas in a mixture given the mole ratio of the mixture. Find the number of moles present given the partial pressure ratio. Use the postulates of the kinetic molecular theory to explain the differences between the three phases of matter. Use the gas laws to solve stoichiometry problems involving gaseous reactants or products.

Pressure A gas expands to fill its container, is easily compressed and mixes completely with other gases. A gas exerts pressure on its surroundings (see balloon). The air inside the balloon pushes against the elastic sides. The gases most familiar to us form the earth’s atmosphere. The mass of air in the atmosphere is pulled toward the center of the earth by gravity resulting in a pressure exerted by the air. This is called atmospheric pressure.

Pressure One method of measuring atmospheric pressure is to use a mercury barometer. The weight of the atmosphere will support a column of about 760 mm Hg.

Pressure

Pressure The unit “mm Hg” is also called torr. It is also equal to 1 atmosphere, another unit of measure for pressure. In engineering, the unit of pounds per square inch, abbreviated as PSI, is used. 1 atm = 14.69 PSI The SI unit for pressure is called the Pascal, abbreviated as Pa. 1 atm = 101,325 Pa

Pressure Atmospheric pressure is lower at higher altitudes. At an altitude of 9600 feet, the atmospheric pressure is 520 mm Hg. Convert that pressure to atmospheres.

Pressure and Volume The first careful studies of gases were made by Robert Boyle in the late 1600’s.

Pressure and Volume

Pressure and Volume Note that the temperature and moles of gas remained constant. As volume decreases, pressure increases. This is an inverse relationship. He determined that the product of pressure times volume equals a constant, or PV=k. This is know as Boyle’s Law.

Pressure and Volume Using Boyle’s Law, we can predict the new volume of a gas if the pressure changes. P1V1 = P2V2 (1 atm)(1L) = (2 atm)(x L) x = ½ L

Pressure and Volume 0.56 L

Pressure and Volume 9.7 atm

Volume and Temperature Jacques Charles showed that the volume of a gas increases as the temperature of the gas increases. The solid lines are actual data. The dashed lines are extrapolated to a point defined as absolute zero on the Kelvin scale.

Volume and Temperature Note that the pressure and moles of gas remained constant. As volume increases, temperature increases. This is a direct relationship. He determined the direct proportionality between volume and temperature, or V=bT. This is know as Charles’s Law. The units of temperature in this equation are in degrees Kelvin.

Volume and Temperature We can also write Charles’s Law as = 1.9L

Volume and Temperature -29 oC

Volume and Moles Experiments show that when the number of moles of gas is doubled (at constant temperature and pressure), the volume doubles. The volume of a gas is directly proportional to the number of moles of the gas, V = an. This is known as Avogadro’s Law. =

Volume and Moles 8.1 L

We can rewrite this as the Ideal Gas Law Combining these laws gives the equation V = R Where R is the combined proportionality constant and is called the universal gas constant and is equal to .08206 l-atm/oK-mol. We can rewrite this as the Ideal Gas Law PV = nRT

Ideal Gas Law .57 mol

Ideal Gas Law 12.5 L

Ideal Gas Law 4.4 atm

Ideal Gas Law 3.07 L

Dalton’s Law of Partial Pressure Many important gases contain a mixture of components. One notable example is air. Scuba divers who are going deeper than 150 feet use another important mixture, helium and oxygen. Normal air is not used because the nitrogen present dissolves in blood in large quantities as a result of the high pressures experienced by the diver under several hundred feet of water. When the diver returns too quickly to the surface, the nitrogen bubbles out of the blood just as soda fizzes when it is opened, and the diver gets decompression sickness – a very painful and potentially fatal condition. Because helium gas is only slightly soluble in blood, it does not cause this problem.

Dalton’s Law of Partial Pressure Studies of gaseous mixtures show that each component behaves independently of the others. John Dalton was one of the first scientists to study mixtures of gases. He observed that the total pressure exerted is the sum of the partial pressures of the gases. The partial pressure of a gas is the pressure the gas would exert if it were alone in the container. Ptotal = P1 + P2 + P3

Dalton’s Law of Partial Pressure

Dalton’s Law of Partial Pressure

Dalton’s Law of Partial Pressure 2.59 x 10 -2 mol

Kinetic Molecular Theory

Kinetic Molecular Theory The meaning of temperature Per the KMT, the temperature of a gas reflects how rapidly its individual particles are moving. At high temperatures the particles move very fast and hit the walls of the container frequently. At low temperatures the particles move slower and collide with the walls less often. Temperature really is a measure of the motions of the gas particles. Kelvin temperature is directly proportional to the average kinetic energy of the gas particles.

Kinetic Molecular Theory The relationship between pressure and temperature As a gas is heated, the particles move faster, hitting the walls of its rigid (constant volume) container more frequently. The impacts become more forceful as the particles move faster. Pressure is due to collisions with the wall, so as temperature increases, so does pressure.

Kinetic Molecular Theory The relationship between volume and temperature As a gas is heated, the particles move faster, causing the pressure to increase. If we allow a volume change so that pressure can be held constant, the gas will expand to maintain constant pressure. So, the KMT model predicts that the volume will increase as the temperature increases.

Kinetic Molecular Theory

Gas Stoichiometry 3.13 L

Gas Stoichiometry 7.81 x 10 -2 mol N2