chapter 14 the ideal gas law and kinetic theory. hydrogen oxygen carbon sodium every element has an...
TRANSCRIPT
HydrogenOxygen Carbon
Sodium
Every element has an atomic mass
(1 u = 1.6605 x 10-27 kg)
Measured in atomic mass units (u)
………
Molecules – combinations of atoms
Ex: Water 2 Hydrogens
1 OxygenH2O
= 2 (1.00794 u) + 1 (15.9994 u)
Molecular mass = 2 (mH) + 1 (mO)
= 18.0153 u
Objects contain billions of particles
1 mole of particles = 6.022 x 1023 particles = NA
Avogadro’s Number
Ex: Calculate the mass in grams of 1 mole of hydrogen atoms.
(The SI unit for quantity of a substance)
One mole of a substance
has the same mass in grams (g)
that one particle has in
atomic mass units (u).
The Ideal Gas Law
Web Link: Ideal Gas
PV=nRT
P = Pressure
V = Volume
n = # of moles
R = 8.31 J/mol K
T = Temp. (Kelvins)If N = # of particles
PV=NkT
k = Boltzmann’s Constant = 1.38 x 10-23 J/K = R/NA
Ideal Gas at Constant Temperature
Isothermic
PV=nRT
constant
PV=constant
PiVi= PfVf
or Boyle’s Law
Since Pressure and Volume are inversely proportional:
P
V
Use the ideal gas law to decide which answer best reflects the number of moles of particles in an
automobile tire:
a) .0025 mol b) .025 mol c) 2.5 mol d) 2500 mol
We haven’t yet calculated the speeds of the molecules in an ideal gas……
Web Link: Gas Temperature
Ideal Gas
This molecule has an average speed
This one has a different average speed
What about the Kinetic Energy of a gas molecule?
m
vKE = ½mv2
What about the average Kinetic Energy of a group of gas molecules?
KE = ½mvrms2
Recall: Higher temperature
Greater average molecule speed
More Kinetic Energy KE Temp
K E kT32 Average KE of an
ideal gas molecule
(k = Boltzmann’s constant = 1.38 x 10-23 J/K)
Kelvin temperature
12 rm s
2 32m v kT
So now we can relate the mass, speed, and temperature of molecules in an ideal gas:
A single molecule has no temperature since temperature is an averaging effect.
Temperature is simply a measure of the average Kinetic Energy of the molecules of a substance.
Notes:
Web Link: Molecules in Motion
Two containers of different ideal gases have the same temperature. Do the molecules of both gases
have the same vrms ?
A. Yes B. No
Internal Energy (U) – the sum of all types of energies of the molecules of a substance
For a Monatomic Ideal Gas:
one-atom
U = (# atoms)(½mvrms2)
Why isn’t this true for a Diatomic (2-atom)gas?
Web Link: Diatomic Molecule
U nRT32
Internal Energy of n moles of a monatomic, ideal gas at temp T
(Example:Neon)
(U T for any ideal gas)
Diffusion – when molecules move from a region of higher concentration to a region of lower concentration
perfume in air
Solute – the substance that is diffusing
Solvent – what it’s diffusing into
Web Link: Diffusion
Examples:
cream in coffee
Remember heat conduction?
The equation for diffusion is similar. Just replace the conduction quantities with the diffusion quantities:
A
L
Q mass (m)
Qk A T t
L
m
D A C t
L
Fick’s Law of Diffusion
T concentration diff. (C)
k diffusion constant (D)
Thermodynamics
Heat (Q) Chapters 12,13,14
Work (W) Chapter 6
Ex:
Rub hands together
W Q
Car engine
Q W
Ex:
SurroundingsSystem
Walls can be either:
Diathermal - heat can flow through
or Adiabatic – heat can’t flow through
In Thermodynamics we talk about the state of the system:
Pressure, Volume & Temperature
4 Laws of Thermodynamics(0th, 1st, 2nd, 3rd)
0th Law of Thermodynamics
Consider 3 objects and their temperatures:
T1 T2 T3
If T1 = T2 and T2 = T3
then T1 = T3
Duuuu
Recall:
Forces do Work (W)
Can change Kinetic Energy (KE)
Can change Potential Energy (PE)
Heat (Q)Can change
Internal Energy (U)
also
In any of the above cases,
Total Energy is conserved
which brings us to…………
1st Law of Thermodynamics
U = Uf – Ui = Q - W
U = Change in internal energy of a system
Q = Heat added to the system
W = Work done by the system
- (Work done on the system)
Ex:
a) If 600 J of heat is added to a system as 200 Joules of work is done on the system, what is the change in its internal energy?
b) If 300 J of heat is added to a system as 300 joules of work is done by the system, what is the change in its internal energy?