How PRESSURE, TEMPERATURE AND VOLUME RULE THE WORLD GAS LAWS How PRESSURE, TEMPERATURE AND VOLUME RULE THE WORLD

Kinetic Molecular Theory A. gas particles are in constant, random motion B. assume no volume or attractive forces C. move in straight lines D. Movement directly proportional to temperature 1. Temperature must be in Kelvin Kelvin = °C + 273 Celsius = K - 273

2. Absolute zero – the lowest temperature theoretically possible. 0K II. Gas Pressure -measured as the force and quantity of impacts of a gas on the walls of a container -vacuum-absence of collisions and/or particles -atmospheric pressure decreases as altitude increases due to fewer gas particles 1 atm = 101.3kPa = 760mmHg

III. Gas Laws A. 4 variables that interact 1. Pressure (P) – kPa, atm, mmHg 2. Volume (V) – mL or L 3. Temperature (T) – K 4. Moles (n) - moles B. Quantity of Gas 1. as number of particles increase, so does possibility of collisions, increasing pressure

C. Volume 1. Decreasing the size of a container gives particles less distance to travel, increasing the number of potential wall collisions and increasing pressure D. Temperature 1. increasing the temperature increases the kinetic energy (thus amount of movement) in a substance. Faster moving = more collisions and increase force of collisions, increasing pressure

E. Boyles Law – Pressure/Volume Relationship 1. Inversely proportional relationship a. When pressure goes up, volume goes down P1V1 = P2V2 Ex. What is the pressure of a balloon that starts out at 678mmHg and 45mL, when the volume increases to 123mL?

P1V1 = P2V2 (678mmHg)(45mL) = P2(123mL) P2 = 248.05mmHg *because both final and initial volumes were given in mL, there was no need to convert F. Charles Law – Volume/Temperature Relationship 1. Directly proportional relationship a. When temperature goes up, volume goes up as well

V1/T1 = V2/T2 Ex. A container with a volume of 5.4L at 23°C is heated to 283°C. What is the final volume? 23ºC + 273 = 296K 283ºC +273 = 556K 5.4L/296K = V2/556K V2 = 10.1L

G. Gay-Lussac’s Law – Pressure/Temperature Relationship 1. Directly proportional relationship a. When temperature increases, so does pressure P1/T1 = P2/T2

Ex. What will the final temperature (in ºC)of a gas be if it began at 13ºC at 100.9kPa and was compressed until it was 23.4kPa? H. These 3 laws can be combined into the Combined Gas Law **can memorize just this law, and eliminate any variable that doesn’t change to get the law you need P1V1 = P2V2 T1 T2

Ex. A hot air balloon has a volume of 124L at STP Ex. A hot air balloon has a volume of 124L at STP. What will the volume be when it ascends to an altitude with a pressure of .25atm and a temperature of -15ºC? P1V1/T1 = P2V2/T2 (1atm)(124L) = (.25atm)(V2) 273K 258K = 470L

I. Ideal Gas Law - relates the 3 variables you have I. Ideal Gas Law - relates the 3 variables you have already seen to number of particles (moles) -an ideal gas cannot be liquified or solidified PV=nRT P = pressure – must be in atm V = volume – must be in L n= moles – must be in moles R = gas law constant (.0821 L atm/mol K) T = temperature – must be in K

Ex. You fill a rigid steel cylinder that has a volume of 20 Ex. You fill a rigid steel cylinder that has a volume of 20.0L with nitrogen gas (N2) to a final pressure of 2.00x104kPa at 28.0C. How many moles of N2 does the cylinder contain? PV=nRT 2.00x104kPa = 197.4atm 28C+273 = 301K 197.4atm)(20.0L) = n(0.0821L atm/mol K) (301K) (197.4)(20.0) = n (0.0821)(301) n = 160 mol N2

a. 2 factors can influence results: attractions and volume 1. turns out we have not been telling you the truth. Gases have properties that affect the outcome of an expected value -You will not have to calculate the impact, but you will need to describe the effect. a. 2 factors can influence results: attractions and volume

1. gases can have attractions which draws 1. gases can have attractions which draws them closer than would be expected. This occurs at lower temperatures. a. Decreasing temperature slows the molecules down, allowing attractions to form. Low pressure allows molecules to spread out. This means the volume of the gas molecule is negligible compared to the overall volume.

2. the actual volume of gas molecules 2. the actual volume of gas molecules contributes to create a volume greater than expected a. At high pressure, the particles are compressed creating a situation where the volume of the molecule becomes important. At high temperatures, the particles move fast enough to negate attractions.

Ptotal = 79.10 + .040kPa + .94kPa + 21.22kPa = 101.30kPa J. Avogadro’s Law – equal numbers of molecules of gas occupy the same volume, regardless of the size of the molecules (MOLE!) K. Dalton’s Law – the partial pressure of each gas in a mixture adds up to the total pressure of the mixture. Ptotal = P1 + P2 + P3 +…. Ex. What is the pressure of air, which is composed of 79.10kPa for N2, .040kPa CO2, .94kPa other gases and 21.22kPa O2. Ptotal = 79.10 + .040kPa + .94kPa + 21.22kPa = 101.30kPa

L. Graham’s Law – gases with lower molecular mass L. Graham’s Law – gases with lower molecular mass effuse at a faster rate than heavier molecules 1. diffusion – tendency of molecules to move towards areas of lower concentration to reach equilibrium 2. effusion – the process in which a gas escapes though a small hole in a container RateA = molar massB RateB = molar massA