PV = nRT
Gas Laws
What happens when?
• You squeeze more air into an object?
(T,P,V)
• You make the volume larger or smaller?
(T,P)
• Heat up or cool down a gas? (P,V)
• To get to the Ideal Gas Law you have to
start at the basics:
•
•
•
•
•
Avogadro’s Hypothesis
Dalton’s Law of Partial Pressures
Boyle’s Law - PV
Gay-Lussac’s Law - PT
Charles’ Law - TV
Avogadro’s Hypothesis
Equal Volumes of gases (at the same temperature and
pressure) contain Equal Numbers of Molecules
So, a Liter of Nitrogen gas has the same
number of molecules as a Liter of
Hydrogen gas
N2
H2
Dalton’s Law of Partial Pressures
Many gases (air) are Mixtures.
At the same temperature, they
have the same average kinetic
energy. So:
At constant volume and temperature, the
total pressure exerted by a mixture of
gases is equal to the sum of the partial
pressures
Boyle’s Law - PV
PxV=k
Pressure x Volume = constant
What if you are comparing?
P1 x V 1 = P 2 x V 2
What is the volume if the initial pressure
is 5atm and volume is 10 liters, and the
pressure is increased to 10atm?
What if it goes to 79atm?
SIDE TOPIC
Jacques-Ives Cousteau
With a partner,
invented the aqualung – 1943 (there were
earlier systems)
Gay-Lussac’s Law - PT
PαT
P/T =k
Pressure / Temperature = constant
Gay-Lussac’s Law II
Changing Pressure
Changing Temperature
Kelvin
K = C° + 273
C° = K – 273
Kelvin is the Unit - Not Degrees Kelvin
Temperature has to be
measured in Kelvin,
which is based on a
Celcius degree and
starts at Absolute Zero,
or 0K
There was another
temperature scale
called Rankine,
used in the USA
for a short time – it
was a Fahrenheit
version of Kelvin.
You only see it in
a few textbooks
from the 1950’s
and in very early
NASA documents.
BP H2O = 671.64°R
FP H2O = 491.67 °R
Absolute 0 = 0 °R
Before and after (Gay-Lussac+Kelvin)
P1 / T1 = P2 / T2
OK – What if the initial pressure is
1atm and temperature is 310K, if
we get the temperature to 373K,
what’s the new pressure?
Absolute Zero - COLD!!!
• Absolute Zero = 0K, -273.15C, -459.67F, 0R
• The current world record was set in 1999 at 100 picokelvins
(pK), or 0.000 000 000 1K
• February 2003, the Boomerang Nebula was observed to have
been releasing gases at a speed of 500,000 km/h for the last
1,500 years. This has cooled it down to ~1 K, which is the
lowest natural temperature ever recorded.
• Korea: Since the country began meteorological observation, the
lowest recorded temperature was minus 32.6 degrees in
Yangpyeong, Gyeonggi Province, on Jan. 5, 1981.
• Korea this year: -24.3 C, the lowest temperature in the country,
in Cheorwon – Jan 3, 2013
Charles’ Law
1st Hydrogen Balloon –
attacked by villagers!
BTW – Gay-Lussac wrote up Charles’ Law and said he’d gotten it from Charles –
Charles never wrote it up himself – so some people call it Charles / Gay-Lussac Law
Charles Law Volume and
Temperature
Before and after (Charles)
V1 / T1 = V2 / T2
OK – What if the initial volume is 10
liters and temperature is 293K, if
we get the temperature to 500K,
what’s the new volume?
PUT IT ALL TOGETHER
• And you get the Ideal Gas Law…
• Drat – “Ideal” vs. “Real” – I knew I left something
out… Reality vs. what is a nice formula…
• Real Gasses don’t get to 0 volume and 0 pressure
at Absolute Zero – in fact, you can’t (quite) get to
0K (pretty close though!).
• Most gases are near Ideal at normal Temperatures
and Pressures – so, it works out!
Mnemonic:
PerVerts
Are =
Not
Really
Terrible
(yes they are, but
this is just to
memorize the
formula!)
R = PV / nT
Units
Pressure – mm Hg, atm, Torr, Pascal, Barr
Volume – mL, Liter
Number of moles – moles
R – Gas Constant – see Next slide!!!
Temperature - Kelvin
R
PV = nRT
• How many moles do you have when:
• The Pressure is 1 atm, the Volume is 22.4
Liters, and the temperature is 273 K.
(Welcome to STP!!!)
How high up can a
pump based on
sucking water
move the water?