Unit 8: Gases Chapter 12

Key Concepts Properties of Gases, Kinetic-Molecular Theory Barometer, Manometer Units of Pressure (mmHg, atm) Units of Temperature (K) Standard Temperature Pressure (STP) Boyle’s Law, Charles’ Law, Gay-Lussac’s Law Combined Gas Law Ideal Gas Law Dalton’s Law, Graham’s Law

Properties of Gases Kinetic-Molecular Theory: Gas particles are far apart Fluidity and compressibility- gas particles can easily move around one another or move closer together because they are farther apart than liquid or solid particles Gas particles are in constant motion They collide with each other and the walls of their container, and those collisions cause pressure.

Properties of Gases More space to move around Less space to move around Less collisions = less pressure More collisions = more pressure

Measuring Pressure Barometer: measures atmospheric pressure Atmospheric pressure pushes down on the mercury. The mercury is pushed up the glass tube. Atmospheric pressure pushes down on the mercury, the mercury is pushed up the glass tube. The more atmospheric pressure, the higher the mercury moves up the glass tube. 760 mmHg mmHg is a measurement of atmospheric pressure 760 mmHg is the atmospheric pressure at sea level

Measuring Pressure Manometer: measures the difference between atmospheric pressure and the gas pressure in a container h Patm Pgas < Patm Pgas = Patm - h h Patm Pgas > Patm Pgas = Patm + h Atmospheric pressure pushes down on the mercury. Gas pressure pushes down on the mercury. The height is the difference between the atmosphere and gas pressures Pressure of the atmosphere is pushing down on the mercury on the right side, and the pressure of the gas is pushing down on the left side. The height is the difference in pressure between the atmosphere and the gas.

Measuring Pressure Units of Pressure torr pounds per square inch (psi) pascals (Pa) millimeters mercury (mmHg) atmospheres (atm) Standard pressure at sea level is 760 mmHg or 1 atm

Measuring Temperature Units of Temperature fahrenheit (°F) celsius (°C) kelvin (K) Standard temperature is 0°C or 273K

STP STP: standard temperature & pressure Standard Pressure: 1atm = 760mmHg Standard Temperature: 0°C = 273K ____ °C + 273 = K We use Kelvins instead of Celsius for temperature because Kelvins start at absolute zero (lowest temp possible), so there is never a negative measurement of heat.

PhET Simulation Follow along with the PhET gas properties simulation Fill out the worksheet

Gas Lab Trash Bag Egg in Flask Crushing Cans Soap in Microwave

Gas Laws Boyle’s Law Gay-Lussac’s Law Charles’ Law Combined Gas Law Ideal Gas Law Dalton’s Law Graham’s Law

Boyle’s Law P1V1 = P2V2 Boyle’s Law: pressure and volume Inversely proportional relationship (opposite): if volume decreases, pressure increases P1V1 = P2V2

Boyle’s Law Ex. A balloon has a volume of 1.2L and a pressure of 760mmHg. If the pressure increases to 800mmHg, what is the new volume? P1V1 = P2V2 V2 = (P1V1)/P2 = (760mmHg x 1.2L) / (800mmHg) = 1.14L

Gay-Lussac’s Law P1 = P2 T1 T2 Gay-Lussac’s Law: pressure and temperature Directly proportional relationship (same): if temperature increases, pressure increases P1 = P2 T1 T2

Gay-Lussac’s Law Ex. A container has gas with a pressure of 760mmHg at a temperature of 20°C, and the temperature increases to 40°C. What is the new pressure? Hint: use kelvin! P1/T1 = P2/T2 P2 = T2 x (P1/T1) = (40°C+273) x (760mmHg/(20°C+273)) = 812mmHg

Charles’ Law V1 = V2 T1 T2 Charles’ Law: temperature and volume Directly proportional relationship (same): if temperature increases, volume increases V1 = V2 T1 T2

Charles’ Law Ex. A 5L balloon at 10°C is heated to a temperature of 70°C. What is the new volume? Hint: use kelvin! V1/T1 = V2/T2 V2 = T2 x V1/T1 = (70°C+273) x (5L/(10°C+273)) = 6.06L

Combine the gas laws… P1V1 = P2V2 V1 = V2 P1 = P2 T1 T2 T1 T2 Boyle’s Put the three equations together to form the combined gas law Gay-Lussac’s Charles’

Boyle’s Law, Gay-Lussac’s Law, & Charles’ Law Combined Gas Law Combined Gas Law: pressure, volume, and temperature Boyle’s Law, Gay-Lussac’s Law, & Charles’ Law P1V1 = P2V2 T1 T2

Combined Gas Law Ex. A 10L balloon at sea level with a pressure of 1atm and a temperature of 30°C is taken to the top of Mauna Kea, where the pressure is 0.6atm and the temperature is 15°C. What is the new volume of the balloon? (P1V2)/T1 = (P2V2)/T2 V2 = (P1V1T2)/(T1P2) = (1atm x 10L x (15°C+273)) / ((30°C+273) x 0.6atm) = 15.8L

Ideal Gas Law PV = nRT Ideal Gas Law: equation for an “ideal gas” Pressure (P), volume (V), temperature (T), moles (n), and the gas constant (R) PV = nRT Ideal Gas: follows all of the gas laws perfectly Use the gas constant (R) that matches the unit of pressure (mmHg or atm) *NOTE: the gas constant (R)’s unit of volume is L, so you must convert ml to L R = 62.4 LmmHg/molK or R = 0.0821 Latm/molK Use the gas constant (R) that matches the unit of pressure (mmHg or atm)

Ideal Gas Law Ex. What is the volume of 2mol of gas at 0.8atm and 20°C? PV = nRT V = nRT/P = [(2mol)(0.0821Latm/molK)(293K)] / (0.8atm) = 60.1L R = 62.4 LmmHg/molK or R = 0.0821 Latm/molK Use the gas constant (R) that matches the unit of pressure (mmHg or atm)

Ideal Gas Law Ex. A sample of gas occupies 5L at a pressure of 740mmHg and a temperature of 25°C. How many moles are in the sample of gas? PV = nRT n = PV/RT = [(740mmHg)(5L)] / [(62.4LmmHg/molK)(298K)] = 0.2 mol R = 62.4 LmmHg/molK or R = 0.0821 Latm/molK Use the gas constant (R) that matches the unit of pressure (mmHg or atm)

Dalton’s Law Ptotal = P1 + P2 + P3 + … Dalton’s Law: pressure of a mixture of gases Pressure depends on the number of gas particles Add all the pressures together to get the total Ptotal = P1 + P2 + P3 + …

Dalton’s Law Ex. A sample of gas contains oxygen, nitrogen, and helium gas. The oxygen exerts a pressure of 300mmHg, the nitrogen exerts a pressure of 450mmHg, and the helium exerts a pressure of 100mmHg. What is the total pressure? Ptotal = P1 + P2 + P3 Ptotal = 300mmHg + 450mmHg + 100mmHg = 850mmHg

Graham’s Law Graham’s Law: speed of gases at the same temperature… Heavy molecules move slower Light molecules move faster *Compare atomic masses from the periodic table

Graham’s Law Ex. A sample of helium and a sample of argon have a temperature of 25°C, which gas is moving faster? He= 4 g/mol, Ar=40 g/mol. Helium is lighter so it moves faster. If the gases are at different temperatures, the hotter one moves faster and the colder one moves slower.