1. 1 Chapter 12 : Day 2 IDEAL GAS LAWIDEAL GAS LAW

2. 2 Using KMT to Understand Gas Laws Recall that KMT assumptions are Gases consist of molecules in constant, random motion. P arises from collisions with container walls. No attractive or repulsive forces between molecules. Collisions elastic. Volume of molecules is negligible.

3. 3 Properties of Gases Gas properties can be modeled using math. Model depends on— V = volume of the gas (L) T = temperature (K) n = amount (moles) P = pressure (atmospheres)

4. 4 IDEAL GAS LAW IDEAL GAS LAW Brings together gas properties. Can be derived from experiment and theory. P V = n R T

5. 5 Using PV = nRT How much N 2 is req’d to fill a small room with a volume of 27,000 L to P = 745 mm Hg at 25 o C? R = 0.082057 Latm/Kmol Solution 1. Get all data into proper UNITS V = 27,000 L T = 25 o C + 273 = 298 K P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm

6. 6 Using PV = nRT R = 0.082057 Latm/Kmol Solution 2. Now calc. n = PV / RT n = 1.1 x 10 3 mol (or about 30 kg of gas)

7. 7 Deviations from Ideal Gas Law Real molecules have volume. There are intermolecular forces. –Otherwise a gas could not become a liquid. Fig. 12.20

8. 8 Deviations from Ideal Gas Law Account for volume of molecules and intermolecular forces with VAN DER WAAL’S EQUATION. Measured V = V(ideal) Measured P intermol. forces vol. correction J. van der Waals, 1837-1923, Professor of Physics, Amsterdam. Nobel Prize 1910. nRT V - nb V 2 n 2 a P + ----- )(

9. 9 Deviations from Ideal Gas Law Cl 2 gas has a = 6.49, b = 0.0562 For 8.0 mol Cl 2 in a 4.0 L tank at 27 o C. P (ideal) = nRT/V = 49.3 atm P (van der Waals) = 29.5 atm

10. 10 Gases are most ideal when: 1. higher temperatures = more motion  T 2. lower pressures = fewer hits  P 3 larger volumes = more space between  V 4. less gas in space = fewer number  n

11. 11 IDEAL GAS LAW Brings together gas properties. Can be derived from experiment and theory. P V = n R T

12. 12

13. 13 Chapter 12 : Day 3 GAS DENSITY

14. 14 Highdensity Low density density = mass/ volume d = g/V

15. 15 IDEAL GAS LAW Brings together gas properties. Can be used to determine molar mass of a gas or determine the density of a gas P V = n R T

16. 16 Molar Conversions moles = mass/ molar mass n = g/  

17. 17 GAS DENSITY PV = nRT or d and proportional d and  proportional n = P_ V RT g = P where g is the mass  V RT where  is the molar mass d = g = P  V RT

18. 18 USING GAS DENSITY The density of air at 15 o C and 1.00 atm is 1.23 g/L. What is the molar mass of air? 1. Calc. moles of air. V = 1.00 LP = 1.00 atmT = 288 K V = 1.00 LP = 1.00 atmT = 288 K n = PV/RT = 0.0423 mol n = PV/RT = 0.0423 mol 2. 2. Calc. molar mass mass/mol = 1.23 g/0.0423 mol = 29.1 g/mol