1. 1 IDEAL GAS LAW Brings together gas properties. Can be derived from experiment and theory. BE SURE YOU KNOW THIS EQUATION! P V = n R T

2. 2 Using PV = nRT P = Pressure V = Volume T = Temperature n = number of moles R is a constant, called the Ideal Gas Constant Instead of learning a different value for R for all the possible unit combinations, we can just memorize one value and convert the units to match R. R = 8.31 R = 8.31 L kPa mol K

3. 3 Using PV = nRT How much N 2 is required to fill a small room with a volume of 960 cubic feet (27,000 L) to 745 mm Hg at 25 o C? Solution Solution 1. Get all data into proper units V = 27,000 L V = 27,000 L T = 25 o C + 273 = 298 K T = 25 o C + 273 = 298 K P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm And we always know R, 0.0821 L atm / mol K

4. 4 Using the Ideal Gas Law At 34 o C, the pressure inside a nitrogen-filled tennis ball with a volume of 0.148 L is 212 kPa. How many moles of nitrogen gas are in the tennis ball? KNOWNS P = 212 kPa V = 0.148 L T = 34 o C R = 8.31 (L · kPa)/(K · mol) UNKNOWN n = ? mol N 2

5. 5 Convert degrees Celsius to kelvin. T = 34 o C + 273 = 307 K

6. 6 Rearrange the equation to isolate n P V = n R T P V = n R T /RT P V n R T R T P VP V = n= n =

7. 7 Substitute the known values for P, V, R, and T into the equation and solve. Calculate Solve for the unknown. n = 1.23  10 –2 mol N 2 n =n = 8.31 (L·kPa) / (K·mol)  307 K 212 kPa  0.148 L n =n = R  T P  VP  V

8. 8 Learning Check Dinitrogen monoxide (N 2 O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (in the tank in the dentist office?

9. 9 Learning Check A 5.0 L cylinder contains oxygen gas at 20.0°C and 735 mm Hg. How many grams of oxygen are in the cylinder?