Ideal Gas Law

PV = nRT

re-arrange nV

= PRT

n =molar mass (g/mol)

mol gas = mass gas (g)

mass of sampleV x molar mass

= PRT

= densitymassV

density = P x molar mass

RT

density = x molar mass

RT

P

A colorless liquid is isolated as a product in a reaction.

It might be cyclohexane, C6H12.

volume of flask = 213 mL

T = 100.0oC P = 754 torr

mass of flask = 77.834 g

0.582 g

0.213 L

= 0.992 atm x molar mass

0.08206 x 373.15

molar mass = 84.4 g/mol

mass of flask + gas = 78.416 g

Dalton’s Law of Partial PressuresPtotal = Pdry air + Pwater vapor

Ptotal = P1 + P2 + P3+ …

In a mix of two gases, A and B

PA =

V

nA RT PB =

V

nB RT

partial pressures

PT =

V

nA RT

V

nB RT+

PT = RT (nA + nB)V

PA

PT

= nA

nA + nB

= XA mol fraction

Pi = Xi PT

Kinetic Molecular Theory of Gases1. Gases consist of a large number of molecules.

Vmolecules

Ideal gases have mass, but no volume

<< Vcontainer

2. Gas molecules are in constant, random motion.

collisions with wall = Pressure

3. Attractive and repulsive forces negligible.

4. Energy transferred during collisions.

5. Average KE is proportional to temperature (K)

all gases have same average KE at same T

average KE does not change, at fixed T

Kinetic Molecular Theory of Gases

5. Average KE is proportional to temperature (K)

all gases have same average KE at same T

average KE same for all particles at T

distribution of molecular velocity, u

most probable u increases with T

Boyle’s Law

V 1/P

Charles’ Law

V T

Avogadro’s Law

V n

Dalton’s Law

Ptotal= P1+ P2+ P3+ …

Dalton’s Law

Ptotal= P1+ P2+ P3+ …

= UF6

= H2 (2.01 g/mol)

(352 g/mol)

KE = ½ mu2 m = massu = average velocity

root mean square velocity urmsurms = 3RT/M

M = molar mass (kg)

R= 8.314 J/K mol

urms =

urms = 145 m/s

1926 m/s

Graham’s Law of Effusion

escape of gases through a small hole

rate1 = rate2

M2 / M1

diffusion mixing of gases

mean free path

1 atm 6 x 10-9 mspace 3 x 1010 m

Real Gasesn

RT

1. Gases consist of a large number of molecules. Vmolecules

Ideal gases have mass, but no volume

<< Vcontainer

need to correct V for Vgas

= PV

3. Attractive and repulsive forces negligible.

Real Gasesn = PV

RT

need to correct V for Vgas

need to correct P for interactions

P + n2aV2

V - nb = nRT

P + n2aV2

V - nb = nRT

van der Waals Equation

a related to Intermolecular Forcesmolecular complexity

b related to molecular volume

a, b experimental

Pi = Xi PT

acetylene (C2H2) produced in reaction

CaC2 (s) + 2H2O (l) C2H2 (g) + Ca(OH)2 (aq)

gas collected over water PT = 738 torrV = 523 mLT = 23oCHow many grams of C2H2

Pwater at 23oC = 21 torr

PT = Pwater + Pacetylene 738 = 21 + Pacetylene

Pacetylene = 717 torr = .943 atm

nacetylene = .943 x 0.523 L0.0821 x 296

= 0.0202

0.0202 mol x 26.04 g/mol= 0.529 g