Gases

Ê A Gas is composed of particles ä usually molecules or atoms ä Considered to be hard spheres far enough apart that we can ignore their volume. ä Between the molecules is empty space. The Kinetic Theory of Gases Makes three assumptions about gases:

Ë The particles are in constant random motion. ä Move in straight lines until they bounce off each other or the walls. Ì All collisions are perfectly elastic

The Average speed of an oxygen molecule is 1660 km/hr at 20ºC The molecules don’t travel very far without hitting each other, so they move in random directions.

Gas Pressure Pressure is the result of collisions of the molecules with the sides of a container A vacuum is completely empty space - no particles, no pressure! Pressure measured in units of atmospheres (atm) (SI = pascal) Measuring device = barometer

Mercury barometer At one atmosphere pressure, a column of mercury = 760 mm high. Dish of Mercury Column of Mercury 1 atm Pressure

Mercury Barometer At one atmosphere pressure, a column of mercury = 760 mm high. Thus, another unit of pressure is mm Hg 1 atm = 760 mm Hg and also = kPa 760 mm 1 atm Pressure

Kinetic Energy and Temperature Temperature is a measure of the average kinetic energy (K.E.) of the molecules of a substance. Higher temperature = faster molecule movement At absolute zero (0 K), all molecular motion would theoretically stop.

The average kinetic energy is directly proportional to the temperature, in Kelvin If you double the temperature (in Kelvin) you double the average kinetic energy. If you change the temperature from 300 K to 600 K, the kinetic energy doubles. Temperature

If you change the temperature from 300 ºC to 600 ºC the kinetic energy doesn’t double. –Because 873 K is not twice 573 K

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

1. 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. Gases naturally move from areas of high pressure to low pressure because there is empty space to move in - spray can is example.

1. 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)

2. 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.

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

1. Boyle’s Law At a constant temperature, gas pressure and volume are inversely related. –As one goes up the other goes down Formula to use: P 1 x V 1 = P 2 x V 2

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

2. Charles’s Law The volume of a gas is directly proportional to the Kelvin temperature, if the pressure is held constant. Formula to use: V 1 /T 1 = V 2 /T 2

Examples What is the temperature of a gas expanded from 2.5 L at 25 ºC to 4.1L at constant pressure? What is the final volume of a gas that starts at 8.3 L and 17 ºC, and is heated to 96 ºC?

3. Gay-Lussac’s Law The temperature and the pressure of a gas are directly related, at constant volume. Formula to use: P 1 /T 1 = P 2 /T 2

Examples What is the pressure inside a L can of deodorant that starts at 25 ºC and 1.2 atm if the temperature is raised to 100 ºC? At what temperature will the can above have a pressure of 2.2 atm?

4. Combined Gas Law The Combined Gas Law deals with the situation where only the number of molecules stays constant. Formula: (P 1 x V 1 )/T 1 = (P 2 x V 2 )/T 2 This lets us figure out one thing when two of the others change.

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?

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

5. The Ideal Gas Law #1 Equation: PV = nR 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)

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 PV RT The Ideal Gas Law n =

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.

7. 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. P Total = P 1 + P 2 + P 3

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

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

8. Graham’s Law The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. Kinetic energy = 1/2 mv 2 m is the mass v is the velocity. Rate A  Mass B Rate B  Mass A =

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. Graham’s Law