Gas Laws

NM Standards 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. Gases consist of tiny particles that are far apart relative to their size. Collisions between gas particles and between particles and the walls of the container are elastic collisions No kinetic energy is lost in elastic collisions

Ideal Gases Ideal Gases (continued) Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion There are no forces of attraction between gas particles 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

Deviations from Ideal Behavior 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

Boyles Law Pressure is inversely proportional to volume when temperature is held constant.

Boyles laws Animation

A Graph of Boyles Law

Charless Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. (P = constant) Temperature MUST be in KELVINS!

Charles Law Animation

A Graph of Charles Law

Gay Lussacs Law The pressure and temperature of a gas are directly related, provided that the volume remains constant. Temperature MUST be in KELVINS!

Gay - Lussacs

A Graph of Gay-Lussacs Law

The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

Combined Gas Law The good news is that you dont have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! P 1 V 1 P 2 V 2 = T 1 T 2 No, its not related to R2D2

Combined Gas Law If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! = P1P1 V1V1 T1T1 P2P2 V2V2 T2T2 Boyles Law Charles Law Gay-Lussacs Law

Combined Gas Law Problem A sample of helium gas has a volume of L, a pressure of atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm? Set up Data Table P 1 = atm V 1 = 180 mL T 1 = 302 K P 2 = 3.20 atm V 2 = 90 mL T 2 = ??

Calculation P 1 = atm V 1 = 180 mL T 1 = 302 K P 2 = 3.20 atm V 2 = 90 mL T 2 = ?? P 1 V 1 P 2 V 2 = P 1 V 1 T 2 = P 2 V 2 T 1 T 1 T 2 T 2 = P 2 V 2 T 1 P 1 V 1 T 2 = 3.20 atm x 90.0 mL x 302 K atm x mL T 2 = 604 K = 331 °C = 604 K

Learning Check A gas has a volume of 675 mL at 35°C and atm pressure. What is the temperature in °C when the gas has a volume of L and a pressure of 802 mm Hg?

Solution T 1 = 308 KT 2 = ? V 1 = 675 mLV 2 = L = 315 mL P 1 = atm P 2 = 802 mm Hg = 646 mm Hg T 2 = 308 K x 802 mm Hg x 315 mL 646 mm Hg 675 mL = 178 K = - 95°C

One More Practice Problem A balloon has a volume of 785 mL on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

Solution Complete the following setup: Initial conditionsFinal conditions V 1 = 785 mLV 2 = ? T 1 = 21°C = 294 KT 2 = 0°C = 273 K Since P is constant, P cancels out of the equation. V 1 V 2 V 1 T 2 = V 1 T 2 = T 1 V 2 = V 2 T 1 T 2 T 1 = 728 mL Check your answer: If temperature decreases, V should decrease.

And now, we pause for this commercial message from STP OK, so its really not THIS kind of STP… STP in chemistry stands for Standard Temperature and Pressure Standard Pressure = 1 atm (or an equivalent) Sea Level Standard Temperature = 0 deg C (273 K) freezing temp of water STP allows us to compare amounts of gases between different pressures and temperatures

Try This One A sample of neon gas used in a neon sign has a volume of 15 L at STP. What is the volume (L) of the neon gas at 2.0 atm and –25°C? P 1 = 1.0 atm V 1 = 15 L T 1 = 273 K P 2 = 2.0 atm V 2 = ?? T 2 = 248 K V 2 = 15 L x 1.0 atm x 248 K = 6.8 L 2.0 atm 273 K

Avogadros Hypothesis Equal volumes of gases at the same T and P have the same number of molecules. V = n (RT/P) = kn V and n are directly related. twice as many molecules

Avogadros Hypothesis and Kinetic Molecular Theory P proportional to n The gases in this experiment are all measured at the same T and V.

STP and Volume AT STP one mole of gas has a volume of 22.4 Liters Standard temperature: 0°C = K Standard pressure = 1 atmosphere = 760 mmHg = kPa Standard volume of 1 mole of an ideal gas at STP: 22.4 liters

Daltons 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.

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