Post on 23-Feb-2016
description
4.3.4 Ideal Gases
Stow
mar
ket P
hysi
cs Boyle’s Law
Gas has four properties: Pressure (Pa) Temperature (°C or K) Volume (m3) Mass (kg, but more usually in moles)
The Gas Laws relate different properties
Boyle’s Law relates pressure p and volume v
Stow
mar
ket P
hysi
cs Boyle’s Law
If a gas is compressed, its pressure increases and its volume decreases
Pressure and volume are inversely related
The pressure exerted by a fixed mass of gas is inversely proportional to its volume, provided the temperature of the gas remains constant
pV = constant p 1 V
Stow
mar
ket P
hysi
cs Boyle’s Law
More usefully, the formula can be written:
p1V1 = p2V2
Attempt SAQ 4 on page 93
Stow
mar
ket P
hysi
cs Charles’ Law
-273 0 +100
V/m3
θ /°C
0 300 T/K
This graph shows the result of cooling a fixed mass of gas at a constant pressure
Stow
mar
ket P
hysi
cs Charles’ Law
The relationship between volume V and thermodynamic temperature T is:
V T
or V = constant
T
Stow
mar
ket P
hysi
cs Charles’ Law
“The volume of a fixed mass of gas is directly proportional to its absolute temperature, provided its pressure remains constant”
Stow
mar
ket P
hysi
cs Combine the Gas Laws
pV = constant T
or
p1V1 = p2V2
T1 T2
Stow
mar
ket P
hysi
cs Questions
Now do SAQ’s 5 to 8 on page 94
Objective
(c) state the basic assumptions of the kinetic theory of gases
Stow
mar
ket P
hysi
cs Kinetic Theory of Gases
A gas contains a very large number of spherical particles
The forces between particles are negligible, except during collisions
The volume of the particles is negligible compared to the volume occupied by the gas
Stow
mar
ket P
hysi
cs Kinetic Theory of Gases
Most of the time, a particle moves in a straight line at a constant velocity. The time of collision with each other or with the container walls is negligible compared with the time between collisions
The collisions of particles with each other and with the container are perfectly elastic, so that no kinetic energy is lost
Stow
mar
ket P
hysi
cs Measuring Gases
One mole of any substance contains 6.02 x 1023 particles
6.02 x 1023 mol-1 is the Avogadro constant NA
Stow
mar
ket P
hysi
cs Questions
Now do SAQ’s 1 and 2 on pages 91 and 92
Stow
mar
ket P
hysi
cs Ideal Gas Equation
Calculating the number n of moles
number of moles (n) = mass (g) molar mass (g mol-1)
Stow
mar
ket P
hysi
cs Ideal Gas Equation
For a gas consisting of N particles:
pV = NkT
where k = 1.38 x 10-23 JK-1
N = number of particles
Stow
mar
ket P
hysi
cs Ideal Gas Equation
For n moles of an ideal gas:
pV = nRT
where R = 8.31 J mol-1 K-1
p = pressure (Pa)V = volume (m3)n = number of moles of gasT = temperature (K)
Stow
mar
ket P
hysi
cs Questions
Now do SAQ’s 9 to 14 on page 98
Objective
(f) explain that the mean translational kinetic energy of an atom of an ideal gas is directly proportional to the temperature
of the gas in kelvin
Stow
mar
ket P
hysi
cs Mean Translational Kinetic Energy
‘Mean’Either: add up all the KE’s of each individual
molecules, then calculate the average
or watch one molecule over a period of time and
calculate the average KE over that time
Stow
mar
ket P
hysi
cs Mean Translational Kinetic Energy
‘Translational’
energy due to the molecule moving along, as opposed to energy due to the molecule spinning around (‘rotational’)
Stow
mar
ket P
hysi
cs Mean Translational Kinetic Energy gas molecules rush around, colliding place a thermometer in the gas, and the
molecules will collide with it energy from the molecules will be shared with
the thermometer eventually, gas and bulb are at the same
temperature (thermal equilibrium) more energy, higher temperature height of the liquid in the thermometer is related
to the energy of the molecules
Stow
mar
ket P
hysi
cs Mean Translational Kinetic Energy
therefore:
‘The Mean Translational Kinetic Energy of a molecule of an ideal gas is proportional to the temperature of the gas in kelvin’
Objective
(g) select and apply the equationE = 3/2 kT
for the mean translational kinetic energy of atoms
Stow
mar
ket P
hysi
cs Mean Translational Kinetic Energy
total kinetic energy of gas T
total internal energy of gas T
therefore:
Stow
mar
ket P
hysi
cs Mean Translational Kinetic Energy
E = 3/2 kT
where:
E = mean translational KE of an atom in a gask = Boltzmann constant (1.38 x 10-23 JK-1)T = temperature (K)
Stow
mar
ket P
hysi
cs Questions
Now do SAQ’s 15 to 19 on page 100
and
End of Chapter Questions on pages 101 - 102