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Ideal gases Assumptions: There are a huge number N of molecules, each of

Ideal gases Assumptions: There are a huge number N of molecules, each of mass m, moving in random directions at various speeds. On average, the molecules are large distances from each other. --> The average separation is much greater than the size

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Ideal gases Assumptions: There are a huge number N of molecules, each of

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  1. Ideal gases • Assumptions: • There are a huge number N of molecules, each of • mass m, moving in random directions at various speeds. • On average, the molecules are large distances from each other. • --> The average separation is much greater than the size • The molecules only interact when they collide. • Collisions with each other and the wall are perfectly elastic, • like perfectly elastic pool balls.

  2. These assumptions are usually valid when a gas is at: • low density; and • relatively higher temps (away from condensation point)

  3. Monatomic vs. Diatomic Gases: Where are the monatomics?

  4. Ideal gas law: PV = nRT (memorize) Usually, P = pressure in Pa = Nm-2 V = volume in m3 n = the number of moles of gas R = the universal gas constant =8.31 J mol-1 K-1 (given) T = the absolute (kelvin) temperature Also useful to know: Standard temperature and pressure (STP): 1. T = 273 K = 0 0C 2. Pressure = 1 atm = 1.01 x 105 N m-2 (Pa)

  5. Review: What is a mole (mol)? 1 mol = the amount of substance that contains as many atoms or molecules as there are in 12.00 g of carbon-12 1 mol= the number of grams of a substance numerically equal to the atomic (or molecular) mass --> The “grams per mol” is called its “molar mass” Ex 1. What is the mass in grams (g) of 1 mol of He gas? Ex 2. How many moles are in 0.700 g of He gas?

  6. Ex 3. What is the mass of 1 mole of O2 gas? Ex 4. How many moles are in 12.8 g of oxygen gas?

  7. Note: 1 mol contains Avagadro’s number NA of particles NA = 6.02 x 1023 particles per mole (given) = 6.02 x 1023 mol-1

  8. Ex 5. How many atoms are in 0.700 g of helium gas? Ex 6. How many molecules are in 12.8 g of oxygen gas?

  9. Ex 7. What is the volume occupied by 5.60 g of nitrogen (molecular mass = 14.0) gas is at a temperature of 40.0 0C and a pressure of 0.860 atm? T = _______ K; P = _________ Pa; n = _______moles Use: P V = n R T How many liters is this? (1000 L = 1 m3)

  10. Ex. 8. A gas occupies a volume of 5.0 liters at a pressure of • 2.0 atm. If the gas compressed to a volume of 3.0 liters • at constant temperature, what is its new pressure (in atm)? • Constant T: PV = nRT --> solve for T = PV/nR = constant • before = after • P1V1/nR = P2V2/nR • P1V1 = P2V2 (n also constant) • With the equation in this form, any P and V units are OK • as long as you are consistent. So substitute values in the last • equation and solve for P2:

  11. The previous example uses Boyle’s Law: PV = nRT = constant b/c T is constant This is like: xy = constant --> P and V are inversely proportional Graph: P V Explain Boyle’s law using particle collisions.

  12. Ex. 9. Heat is added to a gas initially at a temp of 37 0C and • a pressure of 1.33 atm at constant volume. What will be the • new pressure (in atm) if the temperature rises to 57 0C? • Constant V: PV = nRT • Solve for: V = nRT/P = constant • before = after • nRT1/P1 = nRT2/P2 • T1/P1 = T2/P2 (n is constant) • With the equation in this form, any P units are OK as long • as you are consistent, but T must be in kelvins. Substitute in:

  13. This is an example of Guy Lussac’s Law: PV = nRT --> V = nRT/P = constant --> T/P = constant --> T = constant x P --> T and P are directly proportional Graph: P T Explain Guy-Lussac’s law using particle collisions:

  14. Ex. 10. A gas occupies a volume of 2.00 liters at a temp of of 25 0C. What will be its new volume (in liters) when it is at a new temp of 50. 0C at constant pressure? Constant P: PV = nRT --> solve for P = nRT/V = constant before = after nRT1/V1 = nRT2/V2 T1/V1 = T2/V2 (n constant) Make sure T is in kelvins, Then substitute values in:

  15. This is an example of Charles’ Law: PV = nRT --> P = nRT/V = constant --> T/V = constant --> T = constant x V --> T and V are directly proportional Graph: V T Explain Charles’ law using particle collisions. Especially, how can pressure remain constant when T increases?

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