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# ideal_gas_equation

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• pg 1
```									Ideal gas equation

Combining the equations PV = constant, P/T = constant and V/T = constant gives:

PV /T = constant

If we use 1 mole of gas the constant is known as the molar gas constant (R).
So for one mole of the ideal gas equation is:

Ideal Gas equation (one mole):                   PV = RT

Example problem
3                                                      o        o
0.3 m of an ideal gas are heated at constant pressure from 27 C to 127 C. What is the new volume
of the gas?
3
V2 = [V1T2]/T1 = [0.3 x 400]/300 = 0.4 m
(Notice that the temperatures used are always in Kelvin!)

Now the volume of one mole of an ideal gas at Standard Temperature and Pressure (STP)
5                            3
(1.014x10 Pa and 273.15 K) is 0.0224m and so

1.014x105 x 0.0224 = 1 x R x 273.15           and therefore R = 8.314 JK-1mol-1.

For n moles this equation becomes:

Ideal Gas equation (n moles): PV = nRT

For a change from P1, V1 and T1 to P2, V2 and T2 the equation can be written:

P1V1 = P2V2
T1     T2

Example problem
5                       3
If 600g of argon have a pressure of 1.5 x 10 Pa and a volume of 0.3m what is the temperature of the
gas?
Molar mass of argon = 40g and so we have 15 moles.
Therefore:
5                  o
T = PV = 1.5 x 10 x 0.3 = 361 K = 88 C
nR 15 x 8.31

We have of course assumed that argon behaves as an ideal gas.

1
Example problem
o
A petrol - air mixture in the piston of a car engine initially has volume of 50cc, a temperature of 27 C
5
and is at a pressure of 2 x 10 Pa. When it is ignited by the spark plug the volume increases to 450cc
4
and the pressure drops to 8 x 10 Pa. What is the final temperature of the mixture. (assume that it
behaves as an ideal gas!)
5                4
2 x 10 x 50 = 8 x 10 x 450
300                T2
4                         o
Therefore final temperature (T2) = 8 x 10 x 450 x 300 = 1080 K = 807 C
5
2 x 10 x 50

The equation of state for 1 kg of the gas is:

PV = [R/M]T = rT

where M is the molar mass in kg (2 x 10-3 for hydrogen and 32 x 10-3 for oxygen, for
example) and r is a further constant depends on the gas under consideration. Therefore for
m kg of the gas we have:

PV= mRT/M       = mrT

For a fixed mass of gas whose conditions are changed from P1, V1 and T, to P2, V2 and T2
the equation of state can be written:

P1V1/T1 = P2V2/T1

Note that the temperature must always be measured in kelvins.

PV (J)

20

10

200
Temperature (K)

2

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