The ideal gas Law
Where does this come from?
Robert Boyle found
That is, the product of the pressure of a gas times the volume ofa gas is a constant for a given sample of gas. In Boyle's experimentsthe Temperature (T) did not change, nor did the number of moles (n)of gas present. So Boyle found
but did not explore the effect the temperature, or the number ofmoles would have on pressure and volume.
Jaques Charles found
That is, the volume of a given sample of gas increases linearlywith the temperature if the pressure (P) and the amount of the gas(n) is kept constant. So Charles found
Avagadro's Postulate
At the same temperature and pressure equal volumes of all gassescontain the same number of molecules.
V = n (RT/P)
Guy Lussac found that 1 volume of Cl2 combined with 1volume of H2 to make 2 volumes of HCl. The equation forthe reaction is
With this example we can clearly see the relationship between thenumber of moles of a gas, and the volume of a gas.
At constant temperature and pressure the volume of a gas is directly proportional to the number of moles of gas.
Not so coincidentally if V is constant instead of P then
At constant temperature and volume the pressure of a gas is directly proportional to the number of moles of gas.
You could remember all the different gas laws,
P1/T1 = P2/T2
V1/T1 = V2/T2
and so on...
Or you could think about the problem a bit and use PV=nRT.
N2O is placed in a piston. Initially the volume of thepiston is 3.0 L, and the pressure of the gas is 5.0 atm. The pistonis used to compress the gas to a volume of 1.5 L; determine thepressure of the N2O.
well, before the compression
or
after expansion
since n, R, and T do not change
substituting
P = 1.0 x 10 L
See, if you forget all those different relationships you can justuse PV=nRT.
A PV = nRT problem
What is the volume of 1 mole of an ideal gas at STP (StandardTemperature and Pressure = 0 °C, 1 atm)?
(1) V = 1(0.08206)(273.15)
V = 22.41 L
So, the volume of an ideal gas is 22.41 L/mol at STP.
This, 22.4 L, is probably the most remembered andleast useful number in chemistry.
Another exampleWhat is the volume of 5.0 g NH3 at 25 °C and 1 atm. ofpressure?
Well we just found that the volume of 1 mole of an ideal gas is 22.41 L so we can use this as a conversion factor...right?
Everyone remembers that 1 mol of an ideal gas occupies a volume of 22.4 L, but this is probably the least useful number in chemistry. Alot of people forget that this relationship is only true at STP (0 °C and 1 atm.).
So, use
To use PV=nRT we need to have moles of NH3.
It is not practical to use PV=nRT as a conversionin a factor label problem so we will just solve for V.
V = 7.18 = 7.2 LNH3
Seltzer water is made by dissolving CO2 in water.Seltzer can be made at home using small containers of pressurizedCO2. If one of the cartridges contains 20.00 mLCO2 at 55.00 atm at 23.0 °C and it expands into anempty seltzer bottle with a volume of 1.000 L and the resultingpressure is 1.000 atm what is the temperature of the gas.
Before the gas expands...
and
after the gas expands...
or
since R has not changed (it is called the universal gasCONSTANT for a reason) and we have notchanged the number of moles of CO2...
or...
What will the pressure be when the gas warms to 23.0 °C?
before expansion and warming...after expansion and warming to room temp
once again R and n have not changed, and now not even T has notchanged so...
solve for P