Gases: Chapter 12 and 13

Objective: Describe the postulates of The Kinetic Molecular Theory

Characteristics of Gases

• Unlike liquids and solids:

– gases expand to fill their containers.

– gases are highly compressible.

– gases have extremely low densities.

– BECAUSE GASES HAVE SPACE BETWEEN THEIR PARTICLES. THEY HAVE A LARGE VOLUME COMPARED TO THEIR MASS.

– gases follow the KINETIC MOLECULAR THEORY.

Kinetic Molecular Theory

• Gas particles do not attract or repel each other. (They are free to move in their container.)

• Gas particles are much smaller than the distance between them. (The volume of a gas is the space between the particles, the particles themselves have virtually no volume.)

• Gas particle are in constant, RANDOM motion. (Particle move in a straight line until they collide.)

• Kinetic energy is not lost during these collisions.

• All gases have the same average kinetic energy at a given temperature.

Ideal Gases

• Gases that follow all of the postulates of the KMT are IDEAL GASES.

• Other gases are called REAL GASES.

• The ideal gas law relates the volume, temperature, number of moles, and pressure of gases.

•PV=nRT• R is the Universal Gas Constant

• R = 0.0821 L atm/mol K

Practice Problem

• What is the volume of 5.6 grams of helium gas at a pressure of 2.2 atmospheres and a temperature of 303 Kelvins?

Gas Laws

Objective: describe and calculate the relations between volume, pressure, number of moles, and temperature for an ideal gas as described by Boyle’s law, Charles’ law, Avogadro’s law, Dalton’s law of particle pressure, and the ideal gas law.

Pressure• Pressure is exerted when

gas particles collide with anything.

• Force per unit area.

• P = F/A

• Units of pressure:– Pascal = N/m2

– Atmospheres = atm

– Torr

– mm of Hg (same as Torr)

– PSI

– 1 atm = 101 kPa = 760 Torr = 760 mm Hg

• http://lake-link.com/info/barometric_pressure.cfm

• The first barometer was invented by Evangelista Torricelli. It measures atmospheric pressure.

Boyle’s Law

• The volume of a given amount of gas, held at a constant temperature, varies inversely with pressure.

• The higher the pressure, the smaller the volume.

•P1V1 = P2V2• http://eculator.com/formula/calculator.do?equation

=Pressure-of-gas-(Boyle's-law)&id=57

Boyle’s Law Problem

• If 2.5 liters of hydrogen gas has a pressure change from 2.0 atm to 2,200 Torr, what is the new volume?

Temperature• Temperature is the average

kinetic energy of the particles.• At the same temperature all

gases have the same kinetic energy.

• KE = ½mv2

• Speed depends on mass.• So smaller particles move faster.• When working with gases KELVIN

TEMPERATUERS must ALWAYS BE USED.

• K = °C + 273• °C = K – 273• Absolute zero (0 K) is lowest

possible temperature.• http://www.visionlearning.com/library/modules/mid48/Ima

ge/VLObject-318-021121021101.gif

Charles’ Law

• The volume of a given mass of gas is directly proportional to its Kelvin temperature at constant pressure.

• V1T2 = V2T1

• Temperatures must be in Kelvins. • http://scienceuniverse101.blogspot.com/2012/

02/charless-law-and-hydrogen-balloons.html

Charles’ Law Problem

• If 5.0 liters of helium gas has its temperature raised from 25°C to 100.°C, what will be the new volume?

Other gas relationships.

Combined Gas Law

• If both temperature and pressure changes than Boyle’s and Charles’ Laws are combined.

• P1V1T2 = P2V2T1

Gay-Lussac’s Law

• A direct relationship exist between temperature and pressure if volume is held constant.

• P1T2 = P2T1

Practice Problems

Combined Gas Law

• What is the new volume of a gas if 2.4 liters of nitrogen at 36⁰ Celsius and a pressure of 2.0 atm is heated to 75⁰ C and the pressure is dropped to 1.5 atm?

Gay-Lussac’s Law

• A 750 mL aerosol can is thrown into a fire. What will the new pressure be if the temperature is increased from 25⁰C to 425⁰C? The original pressure was 2.85 atm.

Sage – N – Scribe The Sage gives the Scribe step – by – step instructions how to solve the problem.

The Scribe records the Sage’s solution step – by – step in writing.If the Sage is correct, the Scribe praises the Sage. Otherwise, the Scribe coaches, then praises.

Students switch roles for the next problem.

EXAMPLE:What is the volume of a sample of gas originally at 27⁰C and at 5.0 atm pressure in a volume of

4.0 L if the pressure is changed to 2.5 atm with the temperature remaining constant?

Initial (#1) Final (#2)

Pressure

Volume

Temperature

Avogadro’s Law

• Equal volumes of gas at the same temperature and pressure contain equal numbers of particles.

• V1n2 = V2n1

• 1 mole of any gas at STP = 22.4 liters of volume.

• STP = Standard Temperature and Pressure

• 0.00⁰C (273 K) and 1.00 atmosphere

• What volume does 3.4 moles of neon gas occupy if 5.7 moles occupies 128 liters?

Dalton’s Law of Partial Pressure

• The total pressure of a gas mixture is equal to the sum of the partial pressures of the gases in the mixture.

• PT = P1 + P2 + P3 + …• Pair = Pnitrogen + Poxygen

Expansion and Contraction

• Date:

• Partners:

• Problem: Can the volume of a gas be predicted when pressure or temperature is changed?

• Hypothesis:

Procedures • Balloon in the vacuum.• Heating a balloon.• Heating a “coke” can.• Cartesian Diver• Bicycle Pump and Syringe• Blowing Up a PEEP.

• RESULTS: Describe, in detail, each reaction.• CONCLUSIONS: Which gas law is being

demonstrated with each reaction?

IDEAL GAS LAW

• Can also be used to calculate density.

• D = m/V

• PV = nRT SO n/V = P/RT

• n = m/M (M = molar mass)

• D = m/V = PM/RT

• What is the density of a helium balloon in this classroom? Temperature = 25⁰C and Pressure = 665 mm of Hg.

Gas Stoichiometry

Objective: perform stoichiometric calculations, including determination of mass and volume relationships between reactants and products for reactions involving gases.

Stoichiometry

• One mole of any gas at STP has a volume of

(22.4 L).• Standard Temperature and Pressure

• 1.00 atm and 0.00⁰C (273K)

• What volume hydrogen gas is produced at STP when 4.59 grams of aluminum is added to excess hydrochloric acid and allowed to react completely?

Example• What is the volume of hydrogen gas produced,

at STP, if 2.5 grams of zinc reacts completely with excess hydrochloric acid?

NOT AT STP

• What is the volume of gas produced when 6.20 grams of potassium chlorate decomposes to produce potassium chloride and oxygen? The temperature is 25°C and the pressure is 0.891 atmospheres.

Stoichiometry

• Because of Avogadro’s Law gas stoichiometry problems can use the balanced chemical equation as both mole and volume relationships.

• At the same temperature and pressure, equal volumes of gases contain equal numbers of particles.

• 2 C2H6(g) + 7 O2(g) → 4 CO2(g) + 6 H2O(g)

• 2 moles of ethane = 7 moles of oxygen = etc.

• 2 liters of ethane = 7 liters of oxygen = etc.

What is the volume of ammonia produced if 3.42 liters of hydrogen reacts with 2.42 liters of nitrogen?

Review

Gas Law Variables Constants Equation

BOYLE’S

CHARLES’S

COMBINED

GAY-LUSSAC

AVOGADRO’S

Sample Problems

• A sample of a gas in a RIGIDcontainer (the volume of the gas can not change) at 25.0°C and 1.00 atm has its temperature increased to 100.0°C. What will be the new pressure?

• What is the new pressure of 250. mL of a gas that is compressed to 100. mL when the original pressure was 4.0 atm and the temperature is held constant?

Sample Problems

• The volume of a sample of oxygen is 100.0 mL when the pressure is 2.000 atm and the temperature is 45.0 oC. What is the new temperature if the volume increases to 200.0 mL and the pressure decreases to 1.000 atm?

• The volume of a gas is 30.0 mL at 100.0 K. What will be the new temperature if the gas is compressed to 10.0 mL under constant pressure?

Ideal Gas Law

• Relationship ONLY

• Values not Changing.

• PV = nRT

• What is the volume of 15.0 grams of nitrogen gas at a temperature of 24.0 degrees Celsius and a pressure of 0.911 atmospheres?

Kinetic Molecular Theory

• Molecules do not attract or repel.

• Particles are very small compared to the space between the particles.

• Constant RANDOM motion.

• No loss in Kinetic Energy after collisions.

• Temperature is Average Kinetic Energy so smaller particles move faster.

Stoichiometry• 10.0 grams of aluminum reacts with excess hydrochloric acid

at a temperature of 25.0°C and a pressure of 665 mm of Hg.

• Write the reaction:

• Calculate Molar Volume at these conditions:

• Calculate the volume of hydrogen produced in the reaction: