CHEM 2040U-W2011- ASSIGNMENT #1 DUE: FEBRUARY 2nd (Lecture Class) INSTRUCTORS: Dr. Liliana Trevani / Mr. Shumail Kamal Problem #1 A mixture of hydrogen and ammonia has a volume of 153.2 cm3 at 0.00 oC and 1 atm. The mixture is cooled to the temperature of
Kinetic theory
Ideal gas motion and pressure
[16.1]
Ideal gas approximation - a gas of many particles which
1. are much smaller than distances between them
2. have kinetic energy (move by the Newtons laws)
3. have no potential energy (of interaction betwe
Fundamental concepts
Basics
[1.3]
System an object of study, part of the world with definite boundaries.
Example: You with your skin
Surroundings everything outside the system.
Universe = system + surroundings.
Surroundings
System
Surroundings
Open system
Real gases
Equation of state
[7.2]
van der Waals equation of state - for a non-ideal gas:
[ P + a(n/V)2 ] [ V nb ] = nRT (P - measured)
[ P + a/Vm2] [ Vm b ] = RT, Vm = V/n = molar volume,
a, b = van der Waals constants (fitted to experiments)
b > 0 - red
Fundamental concepts
Gas laws
[1.4]
Boyles law (17th century):
P
for a fixed amount of gas and fixed T
T2 > T1
P ~ 1/V, or PV = const [P] = 1 Pa = 1 N/m2
1 atm = 101325 Pa
T1
P(V) = hyperbolic plot, an isotherm (T = const):
0
V
Gay-Lussacs law (18th centu
Real gases
Equation of state
[7.2]
van der Waals equation of state - for a non-ideal gas:
[ P + a(n/V)2 ] [ V nb ] = nRT (P - measured)
[ P + a/Vm2] [ Vm b ] = RT, Vm = V/n = molar volume,
a, b = van der Waals constants (fitted to experiments)
b > 0 - red
The 1st law of Thermodynamics
Reversible and irreversible processes
Internal equilibrium state:
P and T are uniform throughout the gas
Pex
1
Very (infinitely) slow increase of Pex by small increments
gradually compresses the gas, driving it through
a seri
The 1st law of Thermodynamics
Work
[2.2]
Mechanics: Work = force distance (in the direction of the force)
dw = Fx dx
w = Fx dx
x2
(Fx = F projection on x)
x1
[w] = J
For motion at an angle to the force:
dw = F dr
w = F dr
2
F dr = F dx cos
1
For F=const:
Properties of gases
Molecular collisions
[16.6]
Molecule = rigid sphere of diameter d
d = collision diameter = sum of radii
= distance between centres for collision
to occur: 1
d = r1 + r2
2
d
Freeze in space all molecules but one:
In time t, it moves f
Kinetic theory
Maxwell distribution
[11.6]
A particle has mass m and (vector) velocity v = (vx, vy, vz)
Probability for the speed component along x to be between vx and vx+dvx
(i.e. fraction of molecules with such speeds out of total number N total):
dPx