Gases & Atmospheric Chemistry The Ideal Gas Law Unit 5

Gas Laws Summary  T(K) = t (ºC)  Boyle’s Law: p 1 v 1 = p 2 v 2  Charles’s Law: v 1 /T 1 = v 2 /T 2  Gay-Lussac’s Law: p 1 /T 1 = p 2 /T 2  Combined Gas Law: p 1 v 1 /T 1 = p 2 v 2 /T 2

No change?  What happens if you don't change the conditions of a gas, but just want to find out what a gas is like when it's sitting in a container, not doing much?  The gas laws we’ve looked at so far won't help you much, because they are equations which depend on making a change and comparing the conditions before the change and after the change to make determinations about what the gas is like.

The Ideal Gas Law  The ideal gas law is an equation of state, which means that:  you can use the basic properties of the gas to find out more about it without having to change it in any way.  Because it's an equation of state, it allows us to not only find out what the pressure, volume, and temperature are, but also to find out how much gas is present in the first place

Real Gas Behaviour  There are several assumptions in the kinetic molecular theory that describe an ideal gas  Gas molecules have zero volume  Forces of attraction/repulsion are zero  Molecules move in straight lines  Collisions are completely elastic  An imaginary model of a gas that obeys all the gas laws perfectly under all conditions  However, at high pressure and low temperature there are problems with these assumptions  In very small volumes there will be many more interactions and collisions  The volumes of the gas molecules is now a significant fraction of the container

Real GasIdeal Gas In some cases (polar molecules), mild attractions exist between particles (volume is mildly decreased) No attractions exist between particles (no IMF) Gas particles occupy spaceGas particles have no volume Some gases do condense at low temperature and high pressure Ideal gases will NOT condense into liquid “Mostly” obey the gas lawsObey gas laws perfectly Constant RANDOM motion Motion of particles is always in straight lines

The Ideal Gas  We make these assumptions because:  a) They make the equations a whole lot simpler than they would be otherwise, and  b) Because these assumptions don’t cause too much deviation from the ways that actual gases behave

The Ideal Gas Law  Ideal Gas Law = the product of the pressure and volume of a gas is directly proportional to the amount and the Kelvin temperature of the gas

The Ideal Gas Law  P = pressure in kPa  V = volume in Liters  n = number of moles of gas  R = gas constant  Depends on the units of P, T and V  T = temperature in Kelvin

Pv = nRT  R = Gas constant = the constant of variation, R, that relates the pressure in kilopascals volume in liters, amount in moles and temperature in Kelvins of an ideal gas R= kPaL/molK R = atm L /mol K

The Ideal Gas Law  Remember…  At STP, 1mol of an ideal gas would occupy a volume of 22.4 L

Summary: Properties of an Ideal Gas  V-T and P-T graphs are perfectly straight lines  Gas does not condense to a liquid when cooled  Gas volume = 0 at absolute zero  PV = nRT  Gas particles are point size (volume of particle = 0 )  Gas particles do not attract each other

Let’s Practice  Examples: 1. Calculate the molar volume of ammonia gas at SATP. (ans: 24.8 L) 2. The pressure gauge on a 15.0 L cylinder of oxygen gas has a reading of 2.70x10 3 kPa and a temperature of C. What is the mass of oxygen in the cylinder? (ans: 528 g)

Try These… 3. Use the ideal gas law to calculate the molar volume of a gas at STP. 4. A cylinder of laughing gas (N 2 O) has a diameter of 23.0 cm and a height of 140 cm. The pressure is 108 kPa at a temperature of 294 K. How many grams of laughing gas are in the cylinder? Hint: V cylinder =  r 2 h