The Ideal Gas equation
The pressure law (P/T = constant) helps us find
out what happens to the pressure and temperature of a gas when one or other of these
quantities changes.
Charles' law (V/T = constant) helps us find out what happens to its
volume and temperature when either one of these quantities changes and finally Boyle's Law
(PV = constant) helps us find out what happens to the pressure and volume of a gas when
one or other of these quantities changes.
If we combine the two equations we get
another equation involving all three – pressure, volume and temperature.
This
equation is called the gas equation or more properly the Ideal Gas Equation.
Ideal Gas Equation
PV/T = constant = R (for one mole of the gas)
or
P1V1/T1 = P2V2/T2 (for any fixed mass of gas)
The quantity R is a constant
called the universal gas constant and its value is 8.3 J/mol K.
Remember that in all these
gas calculations the temperature must be in Kelvin (
oC +
273)
Example problems
1. What is the volume of 1 mole of air at 27oC if its pressure is 50 000 Pa?
T = 300 K
Volume (V) = RT/P = 8.3x300/50000= 0.05 m3.
2. If a fixed mass of gas has a volume of 2 m3 at 27oC and is heated to 227oC and at the same time the pressure of the gas changes from 100 000 Pa to 180 000 Pa, what is its final volume?
T1=300K T2=500K
Using P1V1/T1 = P2V2/T2 [100 000x2]/300 = [180 000xV2]/500
Final volume (V2) = 1.85 m3.
3. When measured in early morning in the cool (19oC) a car tyre has a pressure
of 180 000 Pa above atmospheric pressure.
If the volume of the air in the tyre
stays constant, what will the pressure in the tyre become if it stands in the sun
for some time so that its temperature rises to 35 oC?
Atmospheric pressure = 100 000 Pa.
Original pressure = 180 000 + 100 000 = 280 000 Pa.
Final pressure = P2 =280 000x292/308 = 265 454 Pa = 265 000 Pa
Standard
temperature and pressure
In some chemical experiments you need to know the volume
that a gas would occupy at 0
°C and 760 mm Hg pressure. These values of
temperature and pressure are known as standard temperature and pressure or STP.
The
pressure exerted by a 760 mm high column of mercury is 101 396 Pa. This number is often called
one atmosphere and simplified to 100 000 Pa.
One useful fact is that one mole of any
gas at STP occupies a volume of 22.4 litres or 22.4x10
-3 m
3.
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