1. Gas laws Relationships between variables in the behaviour of gases

2. Learning objectives  Describe physical basis for pressure in a gas  Describe the basic features of the kinetic theory  Distinguish among and convert common units of pressure  Apply gas laws to simple problems in predicting conditions of a gas  Apply ideal gas law to simple stoichiometry problems in gases

3. Gas: no interactions  Not rigid  Completely fills container  Compressible  Low density  Energetic molecules

4. Kinetic theory and car tires – a case for atoms  Molecules have energy  Energy increases with T  Pressure is caused by energetic molecules striking tire wall  Pumping up tire increases number of molecules  More molecules – higher pressure  Higher temperature – higher pressure

5. Kinetic theory of gases  Gases consist of small atoms or molecules in constant random motion  Volume occupied by molecules is negligible  Molecules are independent of each other – no interactions  Collisions are perfectly elastic (no energy loss)  Average energy is proportional to the temperature

6. Under pressure: the atmosphere  Gases exert pressure by virtue of motion  Gravity makes the air density higher near the earth’s surface  Pressure decreases with elevation

7. Atmospheric pressure  Pressure is force per unit area  The weight of the air supports a column of mercury 760 mm high  Barometer is used for measuring atmospheric pressure  Atmospheric pressure changes with the weather

8. The atmosphere is layered  Troposphere  Where the weather happens  Stratosphere  Where the ozone is  Mesosphere  Ionosphere  The brutal strength of solar radiation ionizes all the components – permits transmission of radio signals around the earth without need of mirrors

9. Units of pressure  Atmosphere  Atmospheric pressure = 1 atm  mm (or cm, or in) of mercury  Atmospheric pressure = 760 mm (76 cm/29.9 in) Hg  Pascal is SI unit for pressure  Atmospheric pressure = 101 000 Pa (N/m 2 )  Pounds/square inch  Atmospheric pressure = 14.7 lb/in 2  Torr  Atmospheric pressure = 760 torr  Bar  Atmospheric pressure = 1.01 bar

10. Standard temperature and pressure (STP)  Standard conditions allow direct comparison of properties of different substances  Standard temperature is 273 K (0ºC)  Standard pressure is 760 mm Hg or 1 atmosphere  At STP, 1 mole of any ideal gas occupies 22.414 L

11. Pressure changes (units)  Convert 0.50 atm into a) mm Hg b) Pa

12. Gas laws: experience in math form  The properties of gases can be described by a number of simple laws  The laws establish quantitative relationships between different variables  They are largely intuitively obvious and familiar

13. The four variables  Pressure (P)  Volume (V)  Temperature (T in Kelvin)  Number of molecules (n in moles)

14. Variables and constants  In the elementary gas laws two of the four variables are kept constant  Each law describes how one variable reacts to changes in another variable  All the simple laws can be integrated into one combined gas law

15. Boyle’s law  The first experimental gas law  Pressure increases, volume decreases (T, n constant)

16. Boyle’s law problems  Initial conditions: P 1 and V 1  Final conditions: P 2 and V 2  Four variables: three given, one unknown  Rearrange equation:  Units are not important provided same on both sides

17. Tank contains 12 L of gas at 4,500 mm Hg. What is volume when pressure = 750 mm Hg?

18. Charles’ Law  As temperature increases, volume increases (P, n constant)  Temperature must be measured in Kelvin

19. Absolute zero  Gay-Lussac observed V changed by 1/273 of value at 0ºC  Plotted as V = kT (T = ºC + 273):  V = 0 at T = 0  Does the gas actually occupy zero volume?  No, at lower T the law is not followed

20. Do’s and don’ts with Charles’ law

21. Combined gas law  Fold together Boyle and Charles:  Given five of the variables, find the sixth  Units must be consistent  Temperature in Kelvin

22. Example of combined gas law  Gas at 27ºC and 2 atm pressure occupies 2 L. What is new volume if pressure becomes 4 atm and temperature is raised to 127ºC?

23. Gay-Lussac and law of combining volumes  When gases react at constant temperature and pressure, they combine in volumes that are related to each other as ratios of small whole numbers  His experiments with hydrogen and oxygen had implications for the understanding of the atom and the structures of simple molecules

24. Avogadro’s Law  As the number of moles of gas increases, so does the volume (P, T constant)

25. Dalton’s law of partial pressures  A mixture of gases exerts a pressure as if all the gases were independent of one another  Total pressure is the sum of the pressures exerted by each one  P = p 1 + p 2 + p 3 + …

26. Calculations with partial pressures

27. Molar gas volume  The molar volume of a gas is the volume occupied by 1 mole. At STP (standard temperature 273 K, and pressure 1 atm) one mole of gas occupies 22.4 L  Gas density is easily obtained from the molar mass and molar volume – d = m/V

28. Ideal Gas Law  The particles of an ideal gas have mass but no volume - a fair approximation at low pressures  Collisions between the gas molecules are perfectly “elastic” – like superhard billiard balls. Reasonable for smaller molecules or noble gases  R is the ideal gas constant = 0.0821 L-atmK -1 mol -1  Gases deviate from ideal behaviour as  pressure increases – closer proximity of molecules  molecules are more polar – stronger interactions

29. Calculations with the ideal gas law

30. Chemical equations with gases  Reactions with solids involve masses  Reactions with gases involve volumes

31. Stoichiometry with the ideal gas law

32. Gas laws and crash safety  The airbag represents a fascinating study of chemistry applied in a very practical area  Airbags have reduced serious injuries and fatalities by a significant margin compared with seat belts only  Chemistry plays a crucial role in the performance of the airbag

33. Timing is everything  The airbag must deploy within about 40 ms of the impact  The airbag must not deploy unless there is an impact  Inflation depends upon a rapid chemical reaction generating a quantity of gas  The bag, once inflated, must then deflate at the point of impact with the driver to prevent injury

34. Chemistry is involved at many points  Chemical reaction to produce gas (nitrogen)  Strong N≡N bond provides driving force  Reaction kinetics determine rate – must be fast  Gas laws provide inflation – P proportional to T