Ideal Gas Law PV = NkT http://phet.colorado.edu/en/simulation/gas-properties phet http://www.walter-fendt.de/ph14e/gaslaw.htm all three

Boyles’ law P a 1/V Pressure / N m-2 Gradient = NKT 1/Volume / m-3 http://www.grc.nasa.gov/WWW/K-12/airplane/boyle.html

Charles’ law V a T Volume / m3 Gradient = NK/P Temperature / °C Absolute zero = -273 °C Where the volume shrinks to zero. http://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html

Pressure law P a T Pressure / N m-2 temperature / K Gradient = NK/V

Applying the Ideal Gas Law A child’s helium-filed balloon escapes at sea level and 20.0 ° C. When it reaches an altitude of 3300 m where the temperature is 4.40°C and the pressure is only 0.710 atm, how will its volume compare to that at sea level? P1V1 = NkT1  V1 = NkT1/P1 (at sea level) P2V2 = NkT2  V2 = NkT2/P2 (at 3300 m) V2/V1 = (NkT2/P2)/(NkT1/P1) = (T2 /T1 ) x (P1 /P2) V2/V1 = (T2 /T1 ) x (P1 /P2) = ( 277.4 K/293 K) x ( 1 atm/ 0.71 atm) = 1.33

Ideal Gas Law Standard Temperature and Pressure (STP). STP is 273.15 K and P = 1.013 x 105 N/m2 Avogadro’s Number NA = 6.02 x 1023 (molecules/mole) Alternative forms of ideal gas law: PV = nRT or PV = mrT

Ideal Gas Facts 1 mole of an ideal gas at STP: Consists of 6.02 x 1023 molecules Has a volume of 0.0224 m3

PV = NkT N = PV/(kT) N = 12.5 x 1.013 x 105 x 0.00195 A scuba tank has a volume of 3900 cm3. For very deep dives, the tank is filled with 50% (by volume) pure oxygen and 50% pure helium. How many oxygen molecules are there in the tank if it is filled at 20°C to a gauge pressure of 12.5 atm? PV = NkT N = PV/(kT) N = 12.5 x 1.013 x 105 x 0.00195 1.38 x 10-23 x293 N = 6.60 x 1023

Questions 1 atms = 101 kN m-2 1 litre = 0.001 m3 Boltzmann constant = 1.38 x 10-23 J k-1 Avogadro number = 6.022 x 1023 Q.1 If I have 4 moles of a gas at a pressure of 5.6 atm and a volume of 12 liters, what is the temperature? 205 K Q.2 If I have 17 moles of gas at a temperature of 67 0C, and a volume of 89 liters, what is the pressure of the gas? 5.34 Atms 540 KN/m2 Q.3 My car has an internal volume of 2600 liters. If the sun heats my car from a temperature of 200 C to a temperature of 550 C, what will the pressure inside my car be? Assume the pressure was initially 101 KN/m2. 113 KN/m2 Q.4 How many molecules and how many moles of gas are in my car in problem 3 6.5 x 1025 molecules and 108 moles

Q.5 A toy balloon filled with air has an internal pressure of 1.25 atm, a volume of 2.50 L and is at a temperature of 295 K. If I take the balloon to the bottom of the ocean where the pressure is 95 atmospheres and temperature is 273 k, what will the new volume of the balloon be? How many moles of gas does the balloon hold? 0.030 m3 0.129 mol Q.5 The temperature inside my refrigerator is about 40 Celsius. If I place a balloon in my fridge that initially has a temperature of 220 C and a volume of 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator? Assume constant pressure. 0.47 L Q.6 How hot will a 2.3 L balloon have to get to expand to a volume of 400 L? Assume that the initial temperature of the balloon is 25 0C. Assume constant pressure. 51 800 K

Q.7 On hot days, you may have noticed that potato chip bags seem to “inflate”, even though they have not been opened. If I have a 250 mL bag at a temperature of 19 0C, and I leave it in my car which has a temperature of 600 C, what will the new volume of the bag be? 285 mL Q.8 In a thermonuclear device, the pressure of 0.050 liters of gas within the bomb casing reaches 4.0 x 106 atm. When the bomb casing is destroyed by the explosion, the gas is released into the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after the explosion? 2.0 x 105 L Q.9 Divers get “the bends” if they come up too fast because gas in their blood expands, forming bubbles in their blood. If a diver has 0.05 L of gas in his blood under a pressure of 250 atm, then rises instantaneously to a depth where his blood has a pressure of 50.0 atm, what will the volume of gas in his blood be? Do you think this will harm the diver? V = 0.25 L yes each bubble expands by a factor of 5