Gas Properties and Gas Laws Chapters 10-11

Kinetic Molecular Theory of Gases An ideal gas is one that fits all the assumptions of this theory: 1) Gases consist of a large number of particles that are relatively far apart for their size. 2) Collisions between gas particles and walls of a container are elastic collisions. Elastic collisions are those that have no net loss of kinetic energy. 3) Gas particles are in continuous, rapid motion. 4) There are no attractive or repulsive forces between gases (IMFs!!!). 5) The average kinetic energy of gases depends on the temperature.

Real Gases Real gases do not behave strictly according to the principles of the kinetic molecular theory. This is because real gases occupy space and exert attractive forces on each other (IMFs!). This is most noticeable for gases at low temperatures and high pressures. Why? Because the gas molecules are closer together so IMF become more important!

Major Components that Describe Gases 1) Quantity of gas (n)- measured in moles 2) Pressure of gas (P)- measured in atmospheres (atm) 3) Temperature of gas (T)- measured in K Conversion from C to K= C + 273=K 4) Volume of gas (V)- measured in L Other characteristics of gases- Mix completely with other gases Fill their entire container Are easily compressed

Pressure Pressure is defined as the force per unit of area on a surface. All gases exert pressure on the surfaces with which they collide. The atmosphere exerts pressure. Pressure is measured using a barometer. A barometer is a tube filled with mercury that changes height with response to atmospheric pressure. Why mercury?

Units of Pressure Atmospheric pressure= 1 atm, 760 mmHg, 760 torr, 101,325 Pa Atm= atmosphere mmHg= millimeters of mercury Torr= from Torricelli, who invented the barometer Pa=pascal Standard Temperature and Pressure (STP)= defined as 1 atmosphere of pressure and 0 degrees Celsius. Conversions: 1) Convert 754 mmHg to atm. 2) Convert 1.25 atm to torr. 3) Convert atm to Pa.

Gas Laws Gas Laws are mathematical relationships between pressure, volume, temperature and amount of gas. Boyle’s Law = the volume of gas varies inversely with the pressure at a constant temperature P 1 V 1 =P 2 V 2 Example: A sample of oxygen gas has a volume of 150. mL when its pressure is atm. What will the volume of the gas be at a pressure of atm if the temperature remains constant?

Charles’ Law Charles’ Law- the volumes of a gas varies directly with its temperature at a constant pressure V 1 = V 2 T 1 T 2 You know this to be true because this is why the volume of a gas increases as the temperature increases. So helium balloon expand slightly on a hot day and contract on a colder day. Example: A sample of neon gas occupies a volume of 752 mL at 25° C. What volume will the gas occupy at 50° C if the pressure remains constant?

Gay-Lussac’s Law As you might be able to figure out based on Boyle’s and Charles’ laws…the relationship between pressure and temperature is also a direct relationship. So, at constant volume, the pressure of a gas varies directly with temperature: P 1 = P 2 T 1 T 2 Graphically the relationship between pressure and temperature is as follows:

The Combined Gas Law The combined gas law combines Boyle’s and Charles’ law. P 1 V 1 = P 2 V 2 T 1 T 2 Example: A helium-filled balloon has a volume of 50.0 L at 25° C and 1.08 atm. What volume will it have at atm and 10.°C? Combined gas law practice

Dalton’s Law of Partial Pressures Yes…this is John Dalton, the man who developed the first atomic theory. He found that in the absence of a chemical reaction, a pressure of a mixture of gases was equivalent to the sum of the pressures of each individual gas. Partial pressure is the pressure exerted by one component of the mixture of gases. Thus, the sum of the partial pressures equals the total pressure. P tot =P 1 +P 2 +P 3 +… This becomes an important factor for people working at high altitudes. Example: Calculate the partial pressure in mmHg of the following gases in air at 760 mmHg, nitrogen, oxygen, argon and carbon dioxide. Their abundance by volume is 78.08%, 20.95%, 0.934% and 0.035% respectively.

The Mole Fraction Mole Fractions (χ)- just how they sound…it is the fraction of each gas. To find mole fraction: Moles of gas(x) Total moles of gas in mixture The number you get should be a decimal that is less than 1! You can also find partial pressure of a gas by using the total pressure multiplied by the mole fraction. P gas =χ gas P tot

Gases Collected by Water Displacement Often times gases in the lab are collected by displacing water from a tube called a eudiometer. The gas produced by a reaction will bubble up through the tube and be collected at the end. This occurs because the gas is less dense than water. However, a gas collected by this method is not pure because it is mixed with water vapor. Therefore, the pressure of the dry and pure gas can be obtained using Dalton’s law of partial pressures. P tot = P gas + P H2O The vapor pressure of water (P H2O ) varies with temperature but can be looked up in a textbook or online. So, you would measure the total pressure of the room using a barometer…then subtract the vapor pressure of water at that temperature to get the vapor pressure of the pure gas collected.

Practice problem Oxygen gas from the decomposition of potassium chlorate was collected by water displacement. The barometric pressure and the temperature during the experiment were torr and 20.0 °C, respectively. What was the partial pressure of the oxygen gas collected? 1) Where do you start? 2) Do you need any additional information not listed?

How do gases react with one another? Gay-Lussac discovered that at constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers. This became known as Gay-Lussac’s law of combining volumes. Avogadro’s law went further, stating that equal volumes of gases at the same temp and pressure contain equal numbers of molecules. Let’s consider the following reaction: 2 H 2 + O 2  2 H 2 O Avogadro’s law further stated that the gas volume is directly proportional to the amount of gas in moles (n).

Molar Volume of Gases The molar volume of a gas is the volume of a gas occupied by 1 mole of that gas. At STP, this volume is 22.4 L. This is why we can use the conversion 1 mol = 22.4 L at STP. Example: A chemical reaction produces mol of oxygen gas. What volume in L is occupied by this gas at STP?

The Ideal Gas Law PV=nRT This is the ideal gas law, and the single most important equation for determining the relationship between the variables of pressure, volume, number of moles and temperature. R is the gas constant. It is equivalent to L  atm mol  K Since the units of R include Kelvin and atm, you MUST convert units to these units before you use the ideal gas law!!!!!

Practice Using the Ideal Gas Law What is the pressure in atmospheres exerted by a mol sample of nitrogen gas in a 10.0 L container at 298K? n=0.500 mol V=10.0 L T=298 K R= L  atm/mol  K P=? Equation: PV=nRT Rearrange to solve for P!

More Practice 1) What is the volume in L of a mol sample of oxygen gas at 20.0°C and atm? 2) What mass of chlorine gas, Cl 2, in grams, is contained in a 10.0 L tank at 27°C and 3.50 atm? 3) A sample of CO 2 with a mass of 0.30 g was placed in a 250 mL container at 400 K. What is the pressure exerted by the gas?

Finding Molar Mass of gases The ideal gas equation can be rearranged with density in mind to solve for the molar mass (MM) of a compound. MM=dRT P *Remember all good kitty cats put dirt (dRT) over their pee (P). Example: At 28°C and atm, 1.00 L of gas has a mass of 5.16 g. What is the molar mass of this gas?

Another example: What is the density of ammonia gas if the pressure is atm and the temperature is 63.0°C?

Diffusion and Effusion Diffusion refers to the spontaneous mixing of particles due to random motion. Particles move from areas of high concentration to areas of low concentration until equilibrium is established.