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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