Equal volumes of gases at the Equal volumes of gases at the same T and P have the same T and P have the same number of molecules.same number of molecules.

V = knV = kn

V and n are directly related.V and n are directly related.

twice as many twice as many moleculesmolecules

MOLEY…MOLEY…MOLEY…MOLEY…MOLEY!!!MOLEY!!!

V1 = V2n1 n2

STP Values

PV=kPV=k

V/T=kV/T=k

P/T=kP/T=k

V/n=kV/n=k

=k=kPVPV

nTnTthenthen

k is given the variable R, and is called the Ideal Gas Constant

So…

Brings together gas properties.

Can be derived from experiment and theory.

BE SURE YOU KNOW THIS EQUATION!

P V = n R TP V = n R T

P = PressureV = VolumeT = TemperatureN = number of moles

R is a constant, called the Ideal Gas Ideal Gas ConstantConstant

Instead of learning a different value for R for all the possible unit combinations, we can just memorizememorize oneone value and convert the units to match R.convert the units to match R.

R = 0.08206R = 0.08206

L • atm mol • K

How much N2 is required to fill a small room with a volume of 960 cubic feet (27,000 L) to 745 mm Hg at 250 C?

Solution1. Get all data into proper units V = 27,000 L T = 250 C + 273 = 298 K P = 745 mm Hg (1 atm/760 mm Hg)

= 0.980 atmAnd we always know R, 0.08206 L atm /

mol K

How much N2 is req’d to fill a small room with a volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at 250 C?

SolutionSolution2. Now plug in those values and solve for

the unknown.

PV = PV = nnRTRT

n = 1.1 x 10 -3 mol

RT RTRT RT

n = (0.980 atm) (27,000 L) _ (0.08206) (298 K)

Dinitrogen monoxide (N2O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (mm Hg) in the tank in the dentist office?

P(20.0 L) = (2.86moles)(0.08206)(296K)P = 3.47 atmP = 3.47 x 760 mmHg 1 atmP = 2640 mmHg

A 5.0 L cylinder contains oxygen gas at 20.0°C and 735 mm Hg. How many grams of oxygen are in the cylinder?

(.97atm)(5.0L)=n(0.08206)(293K)4.85 = 24.04n.20 moles = n.20 moles O2 x 32.00 g O2

1 mole= 6.4 grams O2