2. Gas Laws Problems Boyle’s Law Charle’s Law Gay-Lussac’s Law

3. Review Kinetic Molecular Theory Gases consist of large numbers of tiny particles that are far apart relative to their size Collisions between gas particles and between particles and container walls are elastic collisions. Gas particles are in continuous rapid, random motion. They therefore posses kinetic energy, which is the energy of motion. There are no forces of attraction or repulsions between gas particles. The average kinetic energy of gas particles depends on the temperature of the gas

4. Volume The amount of space something occupies For gas molecules, the space that the gas molecules are allowed to move around in SI unit for volume is L or m 3

5. Pressure Pressure is the force exerted over an area (P = F/A) Pressure of a gas comes from the force of the moving gas molecules hitting a certain area of the container they are inside SI units for pressure –Pa or kPa Other units include –Atm, torr, and mm of Hg

6. Temperature Temperature relates to the Kinetic energy of the gas molecules Higher temperatures have higher kinetic energies Si unit is Celsius Other units include –Farenheit and Kelvin

7. Temperature in Gas Laws When using the gas laws, we cannot use temperature in the units of Celsius For all gas laws, we must use the temperature unit Kelvin Kelvin = Celsius + 273 –All temperatures used in the gas law equations must be in Kelvin

8. Boyle’s Law Relationship between –Pressure and Volume If the volume is decreased, then the gas molecules have less space to move and will hit the container walls more frequently so pressure will increase If the volume is increased, then the gas molecules will have more space to move and will hit the container walls less frequently so pressure will decrease

9. Boyle’s Law The relationship between volume and pressure is inversely proportion –Meaning that when one increases, the other decreases Mathematically, this is expressed as –Pressure initial x Volume initial = Pressure final x Volume final –Or P I x V I = P F x V F Note: it is always a good idea to conceptually check what should happen to a variable before solving the equation

10. Boyle’s Law Example If the volume of a gas is changed from 0.5L to 1.3L and the initial pressure was 0.4 atm, what will the final pressure be? First, do we expect the final pressure to be less than or greater than the initial pressure? At the end of the problem, we need to go back and check to see that our numbers match with what we expect to happen Next, match the numbers in the problem to the variables in the equation –P I = 0.4 atm –V I = 0.5L –P F = ? –V F = 1.3L Then, write down the equation to be used: –P I x V I = P F x V F

11. Boyle’s Law Example If the volume of a gas is changed from 0.5L to 1.3L and the initial pressure was 0.4 atm, what will the final pressure be? After we write down the equation to be used, identify the unknown variable –P I x V I = P F x V F Rearrange the equation to solve for the unknown variable – (P F x V F ) ÷ V F = ( P I x V I ) ÷ V F –P F = ( P I x V I ) ÷ V F Plug in the numbers to get a final answer –P I = 0.4 atm –V I = 0.5L –P F = ? –V F = 1.3L –P F = ( P I x V I ) ÷ V F = (0.4 atm x 0.5 L ) ÷ 1.3 L = 0.13 atm Does this match with our prediction at the beginning?

12. Charle’s Law Relationship between –Temperature and Volume If the temperature is increased, then the molecules will be moving more rapidly and push on the walls of the container If the temperature is decreased, then the molecules will move more slowly and not hit the walls as frequently which will decrease the volume

13. Charle’s Law The relationship between temperature and volume is directly proportion –Meaning that when one increases, the other also increases Mathematically, this is expressed as –Volume initial ÷ Temperature initial = Volume final ÷ Volume final –Or V I ÷ T I = V F ÷ T F Note: it is always a good idea to conceptually check what should happen to a variable before solving the equation

14. Charle’s Law Example If the volume of a gas is changed from 1.5L to 0.9L and the final temperature was measured at 45 o C, what must the initial temperature have been? First, do we expect the initial temperature to be less than or greater than the final temperature? At the end of the problem, we need to go back and check to see that our numbers match with what we expect to happen Next, match the numbers in the problem to the variables in the equation –V I = 1.5 L –T I = ? –V F = 0.9L –T F = 45 o C + 273 = 318K –*NOTE: all temperatures must be converted to Kelvin Then, write down the equation to be used: –V I ÷ T I = V F ÷ T F

15. Charle’s Law Example If the volume of a gas is changed from 1.5L to 0.9L and the final temperature was measured at 45 o C, what must the initial temperature have been? After we write down the equation to be used, identify the unknown variable –V I ÷ T I = V F ÷ T F Rearrange the equation to solve for the unknown variable – ( V I ÷ T I ) x T I = (V F ÷ T F ) x T I – V I ÷ (V F ÷ T F ) = (V F ÷ T F ) x T I ÷ (V F ÷ T F ) –T I = V I ÷ (V F ÷ T F ) Plug in the numbers to get a final answer –V I = 1.5 L –T I = ? –V F = 0.9L –T F = 45 o C + 273 = 318K –T I = V I ÷ (V F ÷ T F )= 1.5L ÷ (0.9L ÷ 318K)= 530 K Does this match with our prediction at the beginning?

16. Gay-Lussac’s Law Relationship between –Temperature and Pressure If the temperature is increased, then the molecules will be moving more rapidly and push on the walls of the container so the pressure will increase If the temperature is decreased, then the molecules will move more slowly and not hit the walls as frequently so the pressure will decrease

17. Gay-Lussac’s Law The relationship between temperature and pressure is directly proportion –Meaning that when one increases, the other also increases Mathematically, this is expressed as –Pressure initial ÷ Temperature initial = Pressure final ÷ Volume final –Or P I ÷ T I = P F ÷ T F Note: it is always a good idea to conceptually check what should happen to a variable before solving the equation

18. Gay-Lussac’s Law Example If the pressure of a gas is changed from 145torr to 450torr and the initial temperature was measured at 23 o C, what must the final temperature be? First, do we expect the final temperature to be less than or greater than the initial temperature? At the end of the problem, we need to go back and check to see that our numbers match with what we expect to happen Next, match the numbers in the problem to the variables in the equation –P I = 145 torr –T I = 23 o C + 273 = 296K –P F = 450 torr –T F = ? –*NOTE: all temperatures must be converted to Kelvin Then, write down the equation to be used: –P I ÷ T I = P F ÷ T F

19. Gay-Lussac’s Law Example If the pressure of a gas is changed from 145torr to 450torr and the initial temperature was measured at 23 o C, what must the final temperature be? After we write down the equation to be used, identify the unknown variable –P I ÷ T I = P F ÷ T F Rearrange the equation to solve for the unknown variable –(P I ÷ T I ) x T F = P F ÷ T F x T F –(P I ÷ T I ) x T F ÷ (P I ÷ T I ) = P F ÷ (P I ÷ T I ) –T F = P F ÷ (P I ÷ T I ) Plug in the numbers to get a final answer –P I = 145 torr –T I = 23 o C + 273 = 296K –P F = 450 torr –T F = ? –T F = P F ÷ (P I ÷ T I ) = 450 torr ÷ (145torr ÷ 296K) = 918 Does this match with our prediction at the beginning?

20. Steps For Solving Gas Law Problems: Predict whether the variable will increase or decrease Label all known and identify unknown –Change all temperatures to Kelvin Write the equation to be used Identify the unknown in the equation Rearrange equation to solve for unkown Plug in numbers and solve equation Check that number matches prediction

21. Distinguishing Laws Identify which two variable change, then match that to the law Pressure and Volume => Boyle’s Law Temperature and Volume => Charle’s Law Temperature and Pressure => Gay-Lussac’s Law

22. Temperature Volume Pressure DEcINC INCINC INCINC DECDEC DECDEC Temperature, Pressure, and Volume changes

23. Temp Pressure Volume mols