Ch. 12
Behavior of Gases
Gases
• Gases expand to fill its container, unlike solids
or liquids
• Easily compressible: measure of how much
the volume of matter decreases under
pressure
Variables that describe a gas
• Pressure (P)
– Measured in kilopascals, kPa
– Pressure and number of molecules are directly
related
 increase molecules = increase pressure
– Gases naturally move from areas of high pressure
to low pressure, due to the available space to
move into
Variables that describe a gas
• Volume (V)
– Measured in Liters, L
– Volume and pressure are inversely related
• As volume decreases, the pressure increases
• Smaller container = less room for movement, therefore
molecules hit sides of container more often
Variables that describe a gas
• Temperature (T)
– Measured in Kelvin, K
– The temperature and pressure are directly related
• Increase in temp = increase in pressure
• Volume must be held constant
• Molecules hit the walls harder (due to increase in K.E.)
and more frequently.
Think about a tire in hot weather…
Variables that describe a gas
• Amount
– Measured in moles, mol
– Moles and pressure are directly related
• Increase in # of moles = increase in pressure
Ex: Inflating a balloon is adding more molecules.
• Temperature must remain constant
Gas Laws
• Describe how gases behave
• Change can be calculated
• Know the math and the theory!!
Boyle’s Law (1662)
• Gas pressure is inversely related to volume
(as volume increases, pressure decreases)
• Temperature is constant
P1V1= P2V2
Ex: The pressure of a 2.5L of gas
changes from 105 kPa to 40.5 kPa.
What will be the new volume?
Charles’s Law (1787)
• Volume is directly proportional to temp.
(increase volume, increase temp)
• Pressure is constant
𝑉1 𝑉2
=
𝑇1 𝑇2
Ex: A sample of Nitrogen occupies a
volume of 250 mL at 25oC. What
volume will the gas occupy at 95oC?
Gay-Lussac’s Law (1802)
• Pressure and temperature are directly related
(Increase pressure= Increase temperature)
• Volume is constant!
𝑃1
𝑇1
=
𝑃2
𝑇2
Ex: A gas has a pressure of 710 kPa at
227oC. What will the pressure be at
27oC, if the volume does not change?
Combined Gas Law
• Combines 3 gas laws: Boyle’s, Charles’, and GayLussac’s
• Used when it is difficult to hold any one variable (P,
V, or T) constant
𝑃1𝑉1
𝑇1
•
=
𝑃2𝑉2
𝑇2
Can take away any variable that is constant
– Take temp away = Boyle’s
– Take Pressure away = Charle’s
– Take Volume away = Gay-Lussac’s
Ex: 3.0 L of Hydrogen gas has a pressure of
1.5 atm at 20oC. What would the volume be
if the pressure increased to 2.5 atm at 30oC?
Ideal Gas Law
• Used for gases that behave “ideally”
• Allows you to solve for # of moles of a contained gas
when P, V, and T are known.
• Use constant
(𝐿∙𝑘𝑃𝑎)
R=8.31
(𝑚𝑜𝑙 ∙𝐾)
𝑃𝑉 = 𝑛𝑅𝑇
P(pressure)- must be in kPa
V (volume)- must be in L
n (# of moles)- muse be in moles of gas
R- gas constant
T (Temperature)- Must be in Kelvin (oC + 273= K)
Ideal Gas Law
• A gas behaves “ideally” if it conforms to the gas laws
– Gases do not usually do this
– Real gases only behave this way at:
1. High temps (molecules move fast)
2. Low pressure (molecules are far apart)
• This is because gases will stay a gas under these conditions
– Molecules are not next to each other very long so attractive forces can’t
play a role b/c molecules are moving too fast
– Ideal Gases do no exist because:
1.
2.
Molecules do take up space
There are attractive forces between molecules otherwise no
liquid would form.
(Molecules slow down to become liquids)
Ex: What volume will 2.0 mol of N2
occupy at 720 torr and 20oC?
Dalton’s Law of Partial Pressures
• Used for mixture of gases in a container
• If you know the P exerted by each gas in a
mixture, you can calculate the total gas
pressure
• It is particularly useful in calculating pressure
of gases collected over water.
Ptotal = P1 + P2 + P3…
*P1 represents the “partial pressure” or the contribution by the gas
Ex: Helium, Nitrogen, and Oxygen exist in a container.
Calculate the total pressure of the mixture for the
following partial pressures:
He = 200 kPa N= 500 kPa O= 400 kPa
Graham’s Law of Effusion
• Rate of effusion and diffusion are inversely proportional to
the square root of the mm of molecules
– Effusion: Gas escaping through tiny holes in a container
– Diffusion: movement from area of high concentration to low
concentration (ex: perfume spreading across a room)
(Both depend of the mm of the molecule, which determines speed)
𝑅𝑎𝑡𝑒 𝐴
𝑅𝑎𝑡𝑒 𝐵
=
𝑚𝑎𝑠𝑠 𝐵
𝑚𝑎𝑠𝑠 𝐴
• Type of Molecule is important
– Gases with lower mm effuse/diffuse faster
– Ex: Helium diffuses/effuses faster than Nitrogen from a balloon b/c
Helium moves faster due to lower mm.
Big = Slow
small = Fast
Ex:
𝑅𝑎𝑡𝑒 𝐻2
𝑅𝑎𝑡𝑒 𝑁2