Chapter 12 Gas Laws and Behavior of Gases

CA Standards 4c. Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases.

Ideal Gases Ideal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory. 1.Gases consist of tiny particles that are far apart relative to their size. Therefore, gases are compressible. 2.There are no forces of attraction or repulsion between gas particles, so gas can expand and take the shape and volume of the container. 3.Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion. Collisions between gas particles and between particles and the walls of the container are elastic collisions. No kinetic energy is lost in elastic collisions. The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.

Real Gases Do Not Behave Ideally Real gases DO experience inter-molecular attractions Real gases DO have volume Real gases DO NOT have elastic collisions Likely to behave nearly ideally Gases at high temperature and low pressure Small non-polar gas molecules Likely not to behave ideally Gases at low temperature and high pressure Large, polar gas molecules

Compressibility Compressibility is a measure of how much the volume of a gas decreases under pressure. The molecules of a gas are far apart so that is why it can be compressed. The energy of a gas increases when it is compressed because the molecules absorb the energy (work) that is put into doing the compression. Example: air bags in cars absorb energy when the driver hits the bag and compresses it. So the gas increases in energy and the human has that much less energy due to the collision (less injury).

Variables that Describe a Gas Gas variables P Pressure in kPa kilopascals VVolume in liters TTemperature in Kelvin nNumber of moles of gas Ideal Gas Law: PV = nRT

Section 12.2 Factors Affecting Gas Pressure Let’s say you are pumping up your bicycle tire because it is flat. Do you agree that by pumping you are adding more air molecules to the tire? As you pump, the air pressure in the tire increases because you are putting more air molecules into a fixed volume (of the tire). When you increase the number of molecules, that increases the number of collisions, which explains why the pressure increases, because P=F/A (pressure = force/area) and there is a small force every time a molecule collides with the wall of the tire. If the temperature stays the same (e.g. you pump slowly), then 2X the # particles = 2X the pressure.

Behavior of Gases When a sealed container of gas under pressure is opened, gas always moves from an area of high pressure to an area of low pressure (just as heat always moves from high T to low T). An aerosol can works because there is higher pressure inside the can. When the button is pushed, the higher pressure gas escapes to the lower pressure region outside the can.

Volume How could you increase pressure in a closed container without adding more gas? You could decrease the volume, keeping the same amount of gas inside. An example is a piston, like in your car. If you cut the volume in half, that will double the pressure (as long as temperature stays constant). Or, if you double the volume, that will cut the pressure in half.

Temperature What is the effect of temperature on gas pressure for a sealed container? The speed, and therefore the kinetic energy (KE = ½mv 2 ) of the gas particles increases when the particles absorb thermal energy. The faster particles now impact the walls of the container with more energy, creating more force per unit area (that’s pressure). If the average KE of the gas doubles due to heat being added, then the average Kelvin temperature doubles and the pressure of the gas also doubles. Note that when working with gas laws we always use Kelvin temperature and not Celsius.

12.3 The Gas Laws Boyle’s Law – Pressure/Volume relationship Consider a gas with P 1 in volume V 1. If we change the pressure to P 2, but keep the temperature constant, what happens to volume V 2 ? Boyle’s Law: P 1 V 1 = P 2 V 2 (the product is constant)

Boyle’s Law

A Graph of Boyle’s Law Anything that is inversely proportional has a graph shaped like this. Inversely proportional means that when the x-axis variable increases, the y-axis variable decreases. Note that at any point on the P-V curve to the right, the product of P · V is constant.

Sample Problem 12-1 (Boyle’s Law)

Boyle’s Law - now you try one: The pressure on 2.50 L of anesthetic gas changes from 105 kPa to 40.5 kPa. What will be the new volume if the temperature remains constant?

PhET Simulator – University of Colorado, Boulder Gas Laws Simulation from PhET.jar

Charles’s Law: Temperature – Volume Relationship 1787 – Jacques Charles investigated the effect of temperature on the volume of a gas (pressure stayed constant at 1 atm). The limitation of his experiments, of course, is that all substances must remain in the gas phase. When temperature then volume (at const. P)

Charles’s Law From his experiments Charles determined that a Temperature vs. Volume plot would be linear. Each gas’s line was different, but he noticed they all extrapolated to volume = 0 at T = -273 o C = 0 K Note that this graph expresses temperature in Celsius.

Charles’s Law Animation

Charles’s Law

Sample problem 12-2 (Charles’s Law)

Charles Law: Your turn 5.00 L of air at o C is warmed to 100 o C. What is the new volume if the pressure remains constant? (Don’t forget to convert to Kelvin)

PhET Simulator Gas Laws Simulation from PhET.jar

Gay Lussac’s Law – The Temperature-Pressure relationship Temperature must be in KELVIN!

Gay-Lussac’s Law Volume is constant

Gay-Lussac Law – try a problem: The pressure in an automobile tire is 198 kPa at 27 o C. At the end of the trip the pressure has risen to 225 kPa. What is the temperature of the air in the tire? (assumes volume is constant)

The Combined Gas Law

Sample Prob. 12-4: Combined Gas Law

Section 12-4: Ideal Gas Law

Ideal Gas Law – Ideal Gas Constant, R

Finally, the Ideal Gas Law

Sample problem 12-5: Ideal Gas Law

Sample problem 12-6: Ideal Gas Law

Ideal gas law – you try one: A child has a lung capacity of 2.20 L. How many grams of air do her lungs hold at a pressure of 102 kPa and a body temperature of 37 o C (310 K)? (Assume the molar mass of air is 29 g/mol). First use ideal gas law to find moles Then convert moles to grams of air using molar mass

Dalton’s Law of Partial Pressures For a mixture of gases in a container, P Total = P 1 + P 2 + P This is particularly useful in calculating the pressure of gases collected over water.

What is held constant?Graph for Boyle’s Law Equation for Boyle’s LawInverse or direct? Temperature must be in Kelvin (Hint: good slide to put on study buddy) Boyle’s Law Temperature

What is held constant?Graph for Charles’s Law Equation for Charles’ LawInverse or direct? Temperature must be in Kelvin (Hint: good slide to put on study buddy) Charles’ Law pressure

What is held constant?Graph for Gay-Lussac’s Law Equation for Gay Lussac’s LawInverse or direct? Temperature must be in Kelvin (Hint: good slide to put on study buddy) Gay Lussac’s Law volume

Temperature must be in Kelvin. Remember  STP = 1 atm and 0 o C Ideal Gas Law PV = nRT Hmmm, good for Study buddy