Chapter 14 The behavior of gases

Reviewing what we know about gases… What do we know about… Kinetic energy? Distance between molecules? Density? Compressibility? Compressibility: how much the volume of matter decreases under pressure.

Pressure Based on: The number and magnitude of the collisions with the container walls How do you increase pressure? Amount of gas Volume of container Temperature

When this goes up, pressure goes… When this goes down, pressure goes … Assignment: using the reading on pages 414-417 fill in the following chart… Definition Units When this goes up, pressure goes… When this goes down, pressure goes … Amount of gas Number of atoms or molecules in a given amount of space Mole Down– less atoms means less collisions, thus less pressure Volume of container Amount of space available for the gas (there are 3) Up– less space means more collisions and more pressure Temperature K

Gas Laws -mathematical relationships (__________) between Volume, Temp, Pressure and quantity of gas (i.e. # of moles = n) Note: x  y __________________________________ x  1/y ___________________________________

Boyle's Law States that the ________ of a gas _______________ with the ___________ at constant Temperature. i.e. P  1/V => PV  1 => PV = k k is different for each gas under different circumstances. But for the same gas: if you change P, V changes, such that __________________________________

P1V1 = k P2V2 = k P3V3 = k …. so _________Boyle’s Law Units: ANY, as long as you’re consistent.

Boyle’s Law problems:

Charles’s Law Jacques Charles (1787) noticed that as you ________ the _______ of a gas, the _______ also increases proportionately. (why?) i.e. V  T If you cool a gas enough, then according to Kinetic Theory, an ideal gas should reach zero volume (theoretically), but not for real gases. Gas particles condense close enough to become liquid, then solid, with a finite Volume.

Graph of Volume vs Temperature: Note that when you extend the graph for any gas, they all terminate at a Temp. of _______ for zero Volume. This is ____________________________________! Lord ______ took advantage of this knowledge and decided to start a third Temperature scale with this as the starting point.

The lowest possible temperature is known as ________________ = -273oC (~ -460oF) We use Absolute Zero as the starting point of the new temperature scale called the Kelvin scale. (K) So _____________ and ______________ Which leads to: K = oC + 273

Charles Law: the __________ of a gas at constant pressure ___________with the ___________ (in Kelvin) http://physics.gac.edu/~mellema/Aapt2001/Charles'%20Law.htm

So, let’s plot V vs T(K) and see what we get. The slope… rise over run… is V/T… is a constant k i.e. V  T => V  1 => V = k(constant) T T So Charles Law

Charles Laws Problems:

Gay-Lussac's Law Joseph Gay-Lussac (1802) noticed that as you _________________of a fixed Volume of a gas, the ____________________. Gay-Lussac’s Law: “the Pressure of a fixed mass of a gas, held at constant Volume, varies directly (proportionately) with the Kelvin Temperature.”

i.e. P  T  P  1  P = k T T So: Gay-Lussac’s Law

Gay-Lussac’s Problems:

Combined gas law: Summary of Eqns: Boyle’s Law P1V1 = P2V2 Charles’s V1 = V2 T1 T2 Gay-Lussac’s P1 = P2 T1 T2

All 3 eqns are connected to each other & we can combine them all into 1 eqn. (=?) We get a combination of all 3 eqns called the: Combined gas law. Anything that is held constant, simply gets cancelled out of the eqn.

Ideal Gas Law So far, we have formulas that tell us what happens to a gas when you change certain factors:- P, V & T (n is constant) Now lets look at a gas in absolute terms where no variables are changing. Ideal Gas Law: the mathematical relationship between _____________________AND the ________________ of a gas. * Based on the concept of an ideal gas… which is not a real gas… remember?

So, Ideal Gas Law is: PV = nRT where T is in K, V is in L REMEMBER there are several different values of R, depending on what units of Pressure you use

Instead of using k, there is a special constant called the Ideal Gas Constant (R) If P is in kPa, R = 8.314 L.kPa/mol.K atm, R = 0.0821 L.atm/mol.K

Examples At 34.0˚C, the pressure inside a nitrogen-filled tennis ball with a volume of 148mL is 212kPa. How many moles of gas are inside the ball?

A helium filled balloon contains 0 A helium filled balloon contains 0.16 mol He at 101kPa and a temperature of 23 ˚C. What is the volume of the gas in the balloon?

Exceptions to Ideal gas law Real Gases: act like Ideal gases in most circumstances, except.. Consider a gas at high pressure, or at low T, what happens to Volume? Real gases stop acting like ideal gases… so the ideal gas law does NOT apply iff the gas is at a very low temperature (near 0 K) or very high pressure (near 60,000 kPa)

Dalton’s Law of Partial Pressures The # of gas molecules directly affects the pressure of the gas. ____________________________________________________________________________________________ In a mixture of gases that is confined in a fixed volume, each gas provides its own pressure contributing to the total. Each individual gas’s pressure is known as their “Partial Pressure”

Two separate gases, (O2 & N2 ) each in separate containers, have an individual pressure of 0.12 atm’s They are transferred to a third container. The new pressure of the gases when combined is ____________.

Dalton’s Law of Partial Pressures states that: “the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.” i.e. PT = P1 + P2 + P3 +… e.g. PATM = PO2 + PN2 + PCO2 +... = 101.3 kPa ∴ To get the total pressure of a gas mixture, solve for the individual pressures then add them

Effusion & Diffusion Diffusion: the gradual mixing of 2 gases due to their spontaneous random motion.

Effusion Effusion: process where the molecules of a gas confined in a container, randomly pass through a tiny opening in the container.

Recall that KE = ½ mv2 and that 2 gases at the same Temp Recall that KE = ½ mv2 and that 2 gases at the same Temp. have the same Kinetic Energy. So Gas A Gas B @ same T. KE(A) = KE(B) If gas B is a lighter molecule (mB is lower) then vB must be higher for KE to remain the same. The whole point: Lighter, less dense gases travel faster at the same Temperatures.

Graham’s Law of Effusion __________________________________________ ____________________________________________ Graham’s Law of Effusion “states that the rates of effusion (r or v) of gases (at same T & P ) are inversely proportional to the square root of their Molar Masses” We could prove it, but lets not  Graham’s Law… rate of effusion of Gas 2 (v2) =  M1 rate of effusion of Gas 1 (v1)  M2

Gases e Finito !