Ideal gases Assumptions: 1.There are a huge number N of molecules, each of mass m, moving in random directions at various speeds. 2.On average, the molecules are large distances from each other. --> The average separation is much greater than the size 3.The molecules only interact when they collide. 4.Collisions with each other and the wall are perfectly elastic, like perfectly elastic pool balls.

These assumptions are usually valid when a gas is at: 1.low density; and 2.relatively higher temps (away from condensation point)

Monatomic vs. Diatomic Gases: Where are the monatomics?

Ideal gas law: PV = nRT (memorize) Usually, P = pressure in Pa = Nm -2 V = volume in m 3 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 0 C 2. Pressure = 1 atm = 1.01 x 10 5 N m -2 (Pa)

Review: What is a mole (mol)? 1 mol = the amount of substance that contains as many atoms or molecules as there are in 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 g of He gas?

Ex 3. What is the mass of 1 mole of O 2 gas? Ex 4. How many moles are in 12.8 g of oxygen gas?

Note: 1 mol contains Avagadro’s number N A of particles N A = 6.02 x particles per mole (given) = 6.02 x mol -1

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

Ex 7. What is the volume occupied by 5.60 g of nitrogen (molecular mass = 14.0) gas is at a temperature of C and a pressure of atm? T = _______ K; P = _________ Pa; n = _______moles Use: P V = n R T How many liters is this? (1000 L = 1 m 3 )

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 P 1 V 1 /nR= P 2 V 2 /nR P 1 V 1 = P 2 V 2 (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 P 2 :

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.

Ex. 9. Heat is added to a gas initially at a temp of 37 0 C and a pressure of 1.33 atm at constant volume. What will be the new pressure (in atm) if the temperature rises to 57 0 C? Constant V: PV = nRT Solve for: V = nRT/P = constant before = after nRT 1 /P 1 = nRT 2 /P 2 T 1 /P 1 = T 2 /P 2 (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:

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:

Ex. 10. A gas occupies a volume of 2.00 liters at a temp of of 25 0 C. What will be its new volume (in liters) when it is at a new temp of C at constant pressure? Constant P: PV = nRT --> solve for P = nRT/V = constant before = after nRT 1 /V 1 = nRT 2 /V 2 T 1 /V 1 = T 2 /V 2 (n constant) Make sure T is in kelvins, Then substitute values in:

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?