Gas Laws

Properties of Gases Gases have no definite shape or volume They take the shape & volume of whatever container they are in Balloon, Can, Room, etc. Gases uniformly fill the container they are in Gases easily compress or expand

Properties of Gases All gases mix completely with any other gas Example: Air Nitrogen, Oxygen, Carbon Dioxide, Water Vapor, and others all evenly mixed in our atmosphere

Properties of Gases Gases exert pressure on their surroundings Example: Blowing up a balloon Air inside pushes against the sides of the balloon and keeps it firm Example: Puncturing a Pop Can Carbon Dioxide exerts pressure on the can – puncture allows a place for the gas to escape

Pressure Pressure = Force/Area Examples of Pressure: Carrying something heavy by the handles A cat walking on you Tire Pressure

Atmospheric pressure Atmospheric Pressure results from the mass of the air being pulled toward the center of the earth by gravity Atmospheric Pressure is also known as air pressure Changes with Altitude– higher pressure at lower altitudes Changes with weather– temperature & humidity Cold fronts (high pressure) & Warm fronts (low pressure) Change in pressure leads to storms

Barometer A device that measures atmospheric pressure is a barometer Atmospheric pressure pushes down on the mercury, pushing it up the tube. The stronger the atmospheric pressure the higher the mercury gets pushed up the tube

Units of pressure There are many units for pressure 1 atm = 760 torr = 760 mm Hg = 101,325 Pascals (Pa) = 101.325 Kilopascals (kPa) = 14.7 psi SI unit is atm – make sure all pressure problems and answers have atm as their unit! Standard atmospheric pressure is 1 atm

Cartesian Diver Group activity What happens when you squeeze the bottle? Are you increasing or decreasing the pressure in the bottle? Look closely at the dropper in the bottle, what (other than water) is in the dropper? When you squeeze the bottle what happens to the volume of the (non-water) contents of the dropper? Is it increasing or decreasing?

Boyle’s Law When the temperature and amount of gas stays the same then the pressure and volume of the gas vary inversely As pressure increases, volume decreases As pressure decreases, volume increases Did this happen with our Cartesian divers? YES! When we increased the pressure of the container the air bubble got smaller

Boyle’s LAW We should be able to predict what will happen in a problem without even seeing any numbers Example: If you have a gas and you increase the pressure what happens to the volume? Example: If you have a gas and you increase the volume what happens to the pressure?

Boyle’s Law Equation Boyle’s Law P1V1 = P2V2 P1 = Original Pressure V1 = Original Volume P2 = New Pressure V2 = New Volume Pressure is measured in atm Volume is measured in Liters (L) If P1V1 = P2V2 then P2 = P1V1 V2 = P1V1 V2 P2

Boyle’s Law Problem #1 Carbon Dioxide is in a pop can and has a pressure of 2 atm and a volume of 0.5L. If you increase the volume to 2L what is the new pressure? Does this answer make sense? P1V1 = P2V2 P2= P1V1 V2 P2= (2atm)(0.5L) 2L P2= .5 atm

Boyle’s Law problem #2 Freon-12 was once used in refrigerators but has been replaced because it destroys the ozone. If a 1.5 L sample of freon at a pressure of 0.075 atm is put under a pressure of 0.2 atm, what would the volume of the gas be? P1V1 = P2V2 V2= P1V1 P2

Boyle’s Law problem #3 A sample of neon has a volume of 2.5 L at a pressure of 0.5 atm, what is the pressure of the neon if it is compressed into a container with a volume of 1 L? Do you expect pressure to increase or decrease? Solve the problem

Charles’ Law When the pressure and the amount of gas are kept the same, the volume and temperature of gas are directly proportional As volume increases, temperature increases As volume decreases, temperature decreases Just like Boyle’s Law we can predict what will happen in a problem without even seeing any numbers If temperature increases what happens to volume?

Charles Law Equation Charles Law V1 = V2 T1 T2 V1 = Original Volume T1 = Original Temperature V2 = New Volume T2 = New Temperature Volume is measured in Liters (L) Temperature is measured in Kelvin (K) If V1 = V2 then V2 = V1T2 and T2 = V2T1 T1 T2 T1 V1

Charles’ Law and Absolute Zero Charles did an experiment to cool several different gases. Obviously there was a problem since at some temperature the gases would liquefy. However, when he extrapolated the data, all lines converged on a certain temperature (right around -273°C) Kelvin took up on this idea and decided to make a new temperature scale and start absolute zero at zero.

Absolute Zero All gas law problems must be in Kelvin!!!! Kelvin = oC + 273 Example What is the Kelvin temperature of -30oC? K= -30 + 273 = 243 Temperature = 243 K

Charles’ Law #1 A sample of gas at 288K has a volume of 2 L. The temperature is raised to 300K. What is the new volume? Does this make sense? V1 = V2 V2 = V1T2 T1 T2 T1 V2= (2L)(300K) V2= 2.08L 288K

Charles’ Law #2 A sample of gas at 300K has a volume of 1.5L and the temperature is lowered to 250K What is the new volume? V1 = V2 T1 T2 V2 = V1T2 T1

Charles’ Law Problem #3 A 2.0 Liter sample of air is collected at 298K and then cooled to 278 K. Do you expect the volume increase or decrease? What is the new volume?

Combined Gas Law Combining Boyle’s and Charles’ Laws (but keeping the amount of gas constant) you get: P1V1 = P2V2 T1 T2 Use this Law when Pressure, Volume, and temperature are all changing

Combined Gas Law P1V1 = P2V2 can be rearranged to solve for… T1 T2 P2 = P1V1T2 Pressure is in atm T1V2 V2 = P1V1T2 Volume is in Liters (L) T1P2 T2 = P2V2T1 Temperature is in Kelvin (K) P1V1

Combined Gas Law Problem #1 If a 5.0 L sample of gas at 295K and 3.0 atm pressure is cooled to 275K and the pressure is decreased to 2.0 atm, what is the new volume of the gas? V1= 5 P1= 3 T1= 295 P2= 2 T2=275 V2 = P1V1T2 V2 = (3)(5)(275) V=6.99L T1P2 (295)(2)

Combined Gas Law Problem #2 If a 2 L sample of gas at 300K and 5.0 atm pressure is cooled to 250K and the volume is decreased to 1 L, what is the new pressure of the gas? V1= P1= T1= V2= T2= P2 = P1V1T2 T1V2

Combined Gas Law Problem #3 A 8 L sample of gas at 295K and 3.0 atm gets its volume decreased to 3 L and the pressure increased to 5 atm, what is the new temperature?

PV = nRT Ideal Gas Law P = Pressure in atm V = Volume in Liters (L) T = Temperature in Kelvin (K) n = the number of moles of gas R = Universal Gas Constant = 0.0821 L·atm mol·K Notice the units for R, all Ideal Gas Law problems must be in these units!!!

Ideal Gas Law PV = nRT P = nRT V = nRT V P n = RT T = PV PV nR

Ideal Gas Law Problem #1 A sample of Hydrogen gas has a volume of 8.5 L at a temperature of 275K and a pressure of 1.5 atm. How many moles of gas are present? R= 0.0821 T=275 P=1.5 V=8.5 n = RT n = (0.0821)(275) 1.77 moles PV (1.5)(8.5)

Ideal Gas Law Problem #2 2.5 moles of Carbon Dioxide has a volume of 3L and a temperature of 300K. What is the pressure of the gas? R= 0.0821 n= T= V= P = nRT V

Ideal Gas Law Problem #3 What volume is occupied by 10 moles of Carbon Monoxide at 295K and 0.5 atm? R= 0.0821 n= T= P=

Ideal Gas Law Problem #4 What temperature is 5 moles of Oxygen that has a volume of 6 L and a pressure of 0.2 atm?

STP Sometimes there’s a shortcut! STP stands for “Standard Temperature and Pressure” STP is 1 atm and 273K At STP, 1 mole of any gas has a volume of 22.4L

Ideal Gas Law Problem #5 How many moles of Nitrogen are present in 1.0L of gas at STP?

Dalton’s Law of Partial Pressure Remember that gases mix evenly The pressure of the mixture is equal to the pressure of each individual gas added up Pressure (total) = Pgas1 + Pgas2 + Pgas3 +…

Dalton’s Law Problem #1 Mixtures of Helium and Oxygen are used in the “air” tanks of underwater divers. If 12L of O2 and 46L of Helium are in a 5.0L tank at 295K and 1.0atm, what is the partial pressure of each gas? P = nRT P0xygen = ( V

Dalton’s Law Problem #2 A 2.0 L flask contains a mixture of 0.05 moles nitrogen and 0.025 moles of oxygen gas at 295K. The total pressure in the container is 0.91 atm. What is the partial pressure of each gas in the container?

Dalton’s Law Problem #3 A 3L container with 1 mole of Helium and 0.20 moles of Fluorine gas at 300K. What is the partial pressure of each gas is in the container?