Gay-Lussac’s Law
(And a few
other topics.)
Gay-Lussac was a balloonist.
Gay-Lussac (1778-1850)
In 1802 he went up to 23,000 feet in a
balloon – a record for 50 years.
Wanted to investigate the composition of
the atmosphere as a function of altitude.
Gay-Lussac
Examined relationship betw P & T at
constant V and moles
If T , the gas molecules will move faster,
colliding with the walls more frequently &
more energetically.
Pressure results from collisions between
gas molecules & walls of container. So, if
T , we expect P .
Gay-Lussac
Tiger Graphic
Which
temperature
scale has a
direct
relationship to
molecular
velocity?
Kelvin
Typical data from a Gay-Lussac type experiment.
What kind of relationship is illustrated in this graph?
T (K)
Gay-Lussac’s Law
Describes relationship between pressure &
temperature at constant volume & amount.
P = kT or P/T = k
What kind of relationship is this?
Straight line with y-intercept of zero. It’s
direct.
Gay-Lussac: Verbal
The pressure exerted by a confined gas is
directly related to the Kelvin temperature
at constant volume.
When temperature decreases, the
pressure of a gas (decreases, increases,
stays the same). Decreases
When temperature increases, the pressure
of a gas (decreases, increases, stays the
same). Increases
Gay-Lussac’s Law
P1 = P2
T1
T2
Useful problem-solving format.
Combined Gas Law
Putting it all together:
P1V1 = P2V2
T
T2
1
For a fixed amount of gas.
Combined Gas Law
Given 5 of the 6 variables, you can identify
the 6th.
Do problems when more than 1 variable
changes.
If a variable is constant, just ignore it.
Avogadro’s Hypothesis
Equal volumes of gases at the
same temperature and pressure
contain equal numbers of
particles.
3 containers – same size, same temperature,
same pressure.
Box A
He
Box B
N2
Box C
CH4
What can you say about the number of
molecules in each box? It’s the same.
What can you say about the number of
atoms in each box? B = 2 X A & C = 5 X A
Molar Volume
1 mole of any gas at STP occupies 22.4 L
Diffusion
At the same temperature, light molecules
move faster than heavy molecules.
At 25C, which gas molecules will move
the fastest from the following:
H2, He, N2, CO2, Xe
Which will move the slowest?
Dalton’s Law of Partial Pressure
The total pressure of a mixture of gases =
the sum of the pressures of all the gases
in the mixture.
The portion contributed by each gas is
called the partial pressure of that gas.
Ptot = P1 + P2 + P3 + P4 + … Pn
Dalton’s Law Problems
Given a mixture of 200 torr of He, 500 torr
of N2, and 150 torr of Ne, what is the total
pressure?
Dalton’s Law Problems
A mixture of O2, CO2, and N2 has a total
pressure of 1800 torr. The partial pressure
of the O2 is 380 torr and the partial
pressure of the CO2 is 960 torr. What is
the partial pressure of the N2?
Ptot = P02 + PCO2 + PN2
Rearrange: PN2 = Ptot – PO2 – PCO2
PN2 = 1800 – 380 – 960 = 460 torr