Chapter 14 The Behavior of Gases

The measure of how much the volume of matter decreases Compressibility The measure of how much the volume of matter decreases under pressure.

Properties of a Gas They are easy to compress. They expand to fill their containers. They occupy far more space than the liquids or solids from which they form.

Variables that describe a Gas The four variables and their common units: 1. pressure (P) in kilopascals(kPa) 2. volume (V) in Liters(L) 3. temperature (T) in Kelvin(K) 4. number of moles (n) (mol)

Amount of Gas When we inflate a balloon, we are adding gas molecules. Increasing the number of gas particles increases the number of collisions thus, the pressure increases If temp. is constant- doubling the number of particles doubles pressure

Pressure and the number of molecules are directly related More molecules means more collisions. Fewer molecules means fewer collisions.

Common use? Aerosol (spray) cans gas moves from higher pressure to lower pressure a propellant forces the product out whipped cream, hair spray, paint

2. Volume of Gas In a smaller container, molecules have less room to move. Hit the sides of the container more often. As volume decreases, pressure increases. (think of a syringe)

3. Temperature of Gas Raising the temperature of a gas increases the pressure, if the volume is held constant. The molecules hit the walls harder, and more frequently! The only way to increase the temperature at constant pressure is to increase the volume.

Homework Section: 14.1 Practice Problems Review Due: 3/17/06

The Gas Laws These will describe HOW gases behave. Can be predicted by the theory. Amount of change can be calculated with mathematical equations.

Boyle’s Law At a constant temperature, gas pressure and volume are inversely related. As one goes up the other goes down P1 x V1= P2 x V2

A balloon is filled with 25 L of air at 1. 0 atm pressure A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm what is the new volume?

P1 = 1 atm V1 = 25 L P2 = 1.5atm V2 = ? L

P1 x V1= P2 x V2 P1 x V1 P2 = V2 1atm x 25L 1.5atm = V2 16.7 L = V2

A balloon is filled with 73 L of air at 1.3atm pressure. What pressure is needed to change the volume to 43L?

P1 = 1.3atm V1 = 73 L P2 = ? atm V2 = 43 L

P1 x V1= P2 x V2 P1 x V1 V2 = P2 1.3atm x 73L 43 L = P2 16.7 L = V2

Charles’s Law The volume of a gas is directly proportional to the Kelvin temperature, if the pressure is held constant. V1 V2 T1 T2 =

What is the temperature of a gas expanded from 2. 5 L at 25 ºC to 4 What is the temperature of a gas expanded from 2.5 L at 25 ºC to 4.1L at constant pressure? V1 = 2.5L T1 = 25ºC + 273 = 298K V2 = 4.1L T2 = ?ºC

V1 V2 T1 T2 = T2 T1 x V2 V1 = T2 298K x 4.1L 2.5L = T2 = 488K = 216°C

V1 = 8.3L T1 = 17ºC + 273 = 290K T2 = 96°C + 273 = 369K V2 = ?ºC What is the final volume of a gas that starts at 8.3 L and 17ºC, and is heated to 96ºC? V1 = 8.3L T1 = 17ºC + 273 = 290K T2 = 96°C + 273 = 369K V2 = ?ºC

V1 V2 T1 T2 = V1 x T2 V2 T1 = 8.3L x 369K V2 290K = V2 = 10.6L

P1 P2 T1 T2 = Gay-Lussac’s Law The temperature and the pressure of a gas are directly related, at constant volume. P1 P2 T1 T2 =

P1 = 1.2atm T1 = 25ºC + 273 = 298K T2 = 100ºC + 273 = 373K P2 = ? atm What is the pressure inside a 0.250 L can of deodorant that starts at 25 ºC and 1.2 atm if the temperature is raised to 100 ºC? P1 = 1.2atm T1 = 25ºC + 273 = 298K T2 = 100ºC + 273 = 373K P2 = ? atm

P1 P2 T1 T2 = P2 T2 P1 T1 = P2 (373K)(1.2atm) 298K = P2 = 1.5 atm

Combined Gas Law The Combined Gas Law deals with the situation where only the number of molecules stays constant. Formula: (P1 x V1)/T1= (P2 x V2)/T2 This lets us figure out one thing when two of the others change.

P1 = 4.8 atm V1 = 15 L T1 = 25ºC + 273 = 298K P2 = 17 atm V2 = ? L A 15 L cylinder of gas at 4.8 atm pressure and 25 ºC is heated to 75 ºC and compressed to 17 atm. What is the new volume? P1 = 4.8 atm V1 = 15 L T1 = 25ºC + 273 = 298K P2 = 17 atm V2 = ? L T2 = 75ºC + 273 = 348K

= = = P1 V1 P2 V2 T1 T2 V2 P1 V1T2 P2 T1 V1 (4.8 atm)(15L)(348K) (17 atm)( 298K) = V1 = 4.9 L

Examples A 15 L cylinder of gas at 4.8 atm pressure and 25 ºC is heated to 75 ºC and compressed to 17 atm. What is the new volume? If 6.2 L of gas at 723 mm Hg and 21 ºC is compressed to 2.2 L at 4117 mm Hg, what is the final temperature of the gas?

Boyle’s Law The combined gas law contains all the other gas laws! If the temperature remains constant... P1 V1 T1 x = P2 V2 T2 Boyle’s Law

Charles’s Law P1 V1 T1 x = P2 V2 T2 The combined gas law contains all the other gas laws! If the pressure remains constant... P1 V1 T1 x = P2 V2 T2 Charles’s Law

The combined gas law contains all the other gas laws! If the volume remains constant... P1 V1 T1 x = P2 V2 T2 Gay-Lussac’s Law

Homework Section: 14.2 Practice Problems Review Due: 3/21/06

Ideal Gases We are going to assume the gases behave “ideally”- obeys the Gas Laws under all temp. and pres.

Particles have no volume. No attractive forces. Ideal Gases An ideal gas does not really exist, but it makes the math easier and is a close approximation. Particles have no volume. No attractive forces.

Ideal Gases There are no gases for which this is true; however, Real gases behave this way at high temperature and low pressure.

The Ideal Gas Law #1 Equation: P x V = n x R x T Pressure times Volume equals the number of moles times the Ideal Gas Constant (R) times the temperature in Kelvin. This time R does not depend on anything, it is really constant R = 8.31 (L x kPa) / (mol x K)

The Ideal Gas Law We now have a new way to count moles (amount of matter), by measuring T, P, and V. We aren’t restricted to STP conditions P x V R x T n =

Examples How many moles of air are there in a 2.0 L bottle at 19 ºC and 747 mm Hg? What is the pressure exerted by 1.8 g of H2 gas in a 4.3 L balloon at 27 ºC? Samples 12-5, 12-6 on pages 342 and 343

6. Ideal Gas Law #2 P x V = m x R x T M Allows LOTS of calculations! m = mass, in grams M = molar mass, in g/mol Molar mass = m R T P V

Density Density is mass divided by volume m V so, m M P V R T D = D =

Ideal Gases don’t exist Molecules do take up space There are attractive forces Otherwise there would be no liquids formed

Real Gases behave like Ideal Gases. When the molecules are far apart The molecules do not take up as big a percentage of the space We can ignore their volume. This is at low pressure

Real Gases behave like Ideal gases when... When molecules are moving fast = high temperature Collisions are harder and faster. Molecules are not next to each other very long. Attractive forces can’t play a role.

Avogadro’s Hypothesis Avogadro’s Hypothesis: Equal volumes of gases at the same temp. and pressure contain equal numbers of particles. Saying that two rooms of the same size could be filled with the same number of objects, whether they were marbles or baseballs.

Dalton’s Law of Partial Pressures The total pressure inside a container is equal to the partial pressure due to each gas. The partial pressure is the contribution by that gas. PTotal = P1 + P2 + P3

We can find out the pressure in the fourth container. By adding up the pressure in the first 3. 2 atm 1 atm 3 atm = 6 atm + +

Examples What is the total pressure in a balloon filled with air if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg? In a second balloon the total pressure is 1.3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mm Hg?

Diffusion Molecules moving from areas of high concentration to low concentration. Example: perfume molecules spreading across the room. Effusion: Gas escaping through a tiny hole in a container. Depends on the speed of the molecule.

Graham’s Law RateA  MassB RateB  MassA = The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. Kinetic energy = 1/2 mv2 m is the mass v is the velocity.

Graham’s Law Heavier molecules move slower at the same temp. (by Square root) Heavier molecules effuse and diffuse slower Helium effuses and diffuses faster than air - escapes from balloon.