GAS LAWS
Pressure can be measured in different
units. For our calculations, we need
Pressure to be expressed in kPa.
1 atm = 760. mmHg = 101.3 kPa
“R” is the Universal Gas Constant.
Take note of the units:
R = 8.31 kPa L
moles K
To convert oC to Kelvin
degrees, you must
add 273 to the oC
STP : “standard”
temperature and
pressure 0oC = 273 K
101.3 kPa
RTP : “room”
temperature and
pressure 25oC = 298 K
101.3 kPa
Dalton's Law of Partial Pressures:
-the total pressure exerted by the mixture of non-reactive gases is equal to the
sum of the partial pressures of individual gases
PT = Pa + Pb + Pc + ... +Pz
If the individual pressures of gases are given, and these gases are all mixed
together, the new total pressure is equal to their individual pressures added
together.
⇒ A hot air balloon will float on air…Why?
⇒ Why does air become less dense as it is heated?
Charles proved this in an experiment:
Charles' Law:
-when the pressure and the number of moles of a gas are held constant, the
volume of a gas is directly proportional to the Kelvin temperature.
V1
T1
= V2
T2
Charles Law EXAMPLES:
1. A 250 mL sample of gas exists at 25 oC.
What volume will the gas occupy at 50. oC if pressure remains constant?
2. Nitrogen gas occupies 400. mL at 100 oC.
At what temperature would the gas occupy 200. mL?
Boyle's Law:
-when the temperature and the number of moles of a gas are held constant,
the volume of a gas is inversely proportional to the pressure applied on the
gas.
V1P1 = V2P2
Boyles Law EXAMPLES:
1. A sample of gas occupies 10.L at 105 kPa. At what pressure will it occupy 13.4 L?
(Assume constant temperature).
2. A sample of gas occupies 9.8 L under a pressure of 101.3 kPa. What will its
volume be at 108 kPa?
T vs P (no name for this relationship):
-the pressure of a gas, at constant volume, is directly proportional to the
absolute temperature.
P1
T1
= P2
T2
EXAMPLE:
1. At constant volume, a gas exerts 500. kPa of pressure on a container's walls at
250. K. What will the pressure be at 350. K?
Ideal gas law:
PV = nRT
Where P is the pressure in kPa, V is the volume in litres, n is the number of moles of gas,
R is the ideal gas constant, and T is the temperature in Kelvin degrees.
Note:
R = 8.31 kPa L
moles K
IDEAL GAS:
a state of matter above its boiling point but below its plasma point AND meets the following
criteria:
IDEAL GAS
vs.
REAL GAS
no attractive forces between
neighbouring molecules
liquids and solids result from
attractions between gas molecules
all molecules are perfect spheres
consider H2O and CH4 as two examples.
Their VSEPR geometry shows that
they are not perfect spheres!
molecules occupy zero volume
(don't occupy any space)
mass and volume are essential
properties of matter
molecule collisions are perfectly elastic
energy loss during collisions
causes chemical reactions
HOWEVER, despite the inadequate nature of each assumption, the combination of these allows a good model,
providing the gas is not near it condensing point.
i.e. We can use the Ideal gas equation that makes these assumptions about gases since it doesn’t really change our answer.
Ideal Gas Law EXAMPLES:
1. What volume will 480 g of ammonia gas occupy at 125 oC and 180 kPa?
2. What pressure is exerted by 54.0 g of Xenon in a 1.00 L flask at 20 oC?
Combined gas law:
memory hint: write the letters in alpha order for this calculation "tool"
P
T
V
▲
Consider the ideal gas equation, PV = nRT.
Now consider a certain number of moles of gas:
n = PV
RT
If we want to compare this number of moles of a certain gas at two sets of
conditions, we could say that :
V1P1 = V2P2, since both of sides of this equation must equal “n”, the number of moles
RT1
RT2
We can also into consideration, that “R” is a constant, and can therefore be
eliminated from both sides of the equation:
V1P1 = V2P2,
T1
T2
EXAMPLES:
1. A sample of neon occupies 100.L at 27.0oC at 133 kPa.
What volume would it occupy at standard conditions?
V1 =
V2 =
T1 =
T2 =
P1 =
P2 =
2. A meteorological balloon occupies 140 litres at 39oC and 95 kPa.
What volume will it occupy at 85oC and 121 kPa?
V1 =
V2 =
T1 =
T2 =
P1 =
P2 =
CLEARLY SHOW ALL WORK FOR EACH OF THESE QUESTIONS.
BE SURE TO HIGHLIGHT THE FORMULA YOU ARE USING IN EACH CASE.
Sig Figs Count!
1. The highest pressure ever produced in a laboratory setting was about
2.0 x 106 atm. If we have a 1.0 x 10-5 liter sample of a gas at that pressure, then
release the pressure until it is equal to 0.275 atm, what would the new volume of
that gas be?
2. If I have an unknown quantity of a gas at a pressure of 0.50 atm, a volume
of 25 liters, and a temperature of 300. K, how many moles of gas do I have?
3. Imagine a thermometer that measures temperature by the compressing and
expanding of gas in a piston. If it is measured that at 100oC the volume of the
piston is 21 L. What is the temperature outside if the piston has a volume
of 15 L? What would be appropriate clothing for the weather?
4. A tank is originally filled up at 120 K to a pressure rating of 4600 mmHg.
The tank is stored in an area that raises its temperature to 450 K.
Has the pressure of the tank increased or decreased?
Why does this (increase or decrease) make sense?
5. A 2.79 g sample of gas occupies a space of 735 ml at 1.78 atm and -21 oC.
What is the molar mass of the gas? What gas might it be?
6. Based on the postulates of the kinetic molecular theory, give the conditions of
temperature and pressure that you believe would cause a real gas to best simulate
an ideal gas. Explain your answer.