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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 pressureEx: 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
=
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!
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 Gay-Lussac’s
• Used when it is difficult to hold any one variable (P, V, or T) constant
=
• 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 R=8.31
P(pressure)- must be in kPaV (volume)- must be in Ln (# of moles)- muse be in moles of gasR- gas constantT (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. Molecules do take up space2. 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)
= • 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: