The Behavior of Gases

Kinetic-Molecular Theory of Gases, Gas Laws, Ideal Gases,

Partial Pressures, and

Graham’s Law of Effusion

Bell Work

How would you describe solids vs. liquids vs. gases?

• The kinetic molecular theory is based on the idea that particles of matter are always in motion.• Use it to explain the properties

of gases in terms of the energy of particles and forces that act between them .

Kinetic-Molecular Theory

Kinetic-Molecular Theory of Gases• A gas is composed of particles

(molecules or atoms).• Gas particles are considered to be

small, hard spheres (billiard balls).• Particles have insignificant volume

compared to total volume occupied by the gas.

• Particles are far apart from each other.

• Between the particles is empty space.

• No attractive or repulsive forces exist between particles.

• Particles move rapidly in constant random motion.

• Movement is independent; particles travel in straight paths until a collision.

• Collisions between gas particles are perfectly elastic.

Kinetic-Molecular Theory of Gases

Kinetic-Molecular Theory of Gases

• The temperature of a gas depends on the average kinetic energy of the particles of the gas.

• Average kinetic energy (KE) of a gas molecule is proportional to the absolute temperature. • KE increases with increasing

temperature

• At any given temperature, all gases have the same average KE.

Kinetic-Molecular Theory of Gases

Nature of Gases

• Expansion:• Gases do not have a definite

shape or a definite volume

• Fluidity:• Because the attractive forces

between gas particles are insignificant, gas particles glide easily past one another

Nature of Gases

• Low Density:• About 1/1000 the density of the

same substance in liquid or gas phase

• Particles farther apart

• Compressibility:• Volume of a gas can be greatly

decreased

Kinetic-Molecular Theory of Gases

• An ideal gas is a hypothetical gas that perfectly fits all the assumptions of the kinetic-molecular theory.• KMT only applies to ideal gases

• PROBLEM!• Ideal gases do not actually

exist

• SOLUTION!• A real gas can behave

ideally at low P and high T

Kinetic Molecular

Theory“The Opposite”

Real Gases• A real gas is a gas that does

not behave completely according to the assumptions of the KMT.

• KMT holds true when particles have little attraction for each other• Non polar gases

What Do You Observe?

Pressure

• Gas pressure: the force exerted by a gas per unit area of an object.

• Gas pressure is the result of simultaneous collisions of billions of rapidly-moving particles with an object.

• Vacuum: no gas particles, no pressure

Atmospheric Pressure: the collision of air molecules with objects.

Units of Pressure

• SI Unit is the pascal (Pa); kPa is used more frequently.

• Other units include: mmHg, bar, torr, psi, atmosphere (atm)

• 1 atm = 760 mmHg = 760 torr = 101.3 kPa

• A barometer measures air pressure.

Standard Atmospheric Pressure (STP)

• STP is the typical pressure at sea level

• STP is the pressure needed to support a column of mercury

760 mm high.• STP for a gas is 0°C and 1 atm.

Units of Pressure Sample Problems

1. The average atmospheric pressure in Denver, Colorado, is 0.830atm. Express this pressure in (a) mmHg and (b) kPa

2. Convert 177kPa to mmHg and to atm.

Dalton’s Law Activity

1. Take the total mass of the items in your tray.

2. Take the mass of each item individually.

3. Are both masses equal?

4. An extra item is added to your tray. You only have the new total mass for the items in your tray. How could you find the mass of just the extra item?

Dalton’s Law of Partial Pressures

• What if we have a mixture of gases?

• The total pressure of a mixture of gases equals the sum of the pressures each would exert if it were present alone.

• Ptotal = P1 + P2 + P3 +…

A Partial Pressure Calculation

• Determine the partial pressure of oxygen gas in the following mixture that contains: Ptotal = 93.4 atmPnitrogen= 46.7 atmPhelium = 26.7 atm

• 20.0 atm

Patm = Pgas + PH2O

• Oxygen gas from the decomposition of potassium chlorate, KClO3, was collected by water displacement. The barometric pressure and the temperature during the experiment were 731.0torr and 20.0°C, respectively. What was the partial pressure of the oxygen collected?

Patm = Pgas + PH2O

• Some hydrogen gas is collected over water at 20.0°C. The levels of water inside and outside the gas-collection bottle are the same. The partial pressure of hydrogen is 742.5torr. What is the barometric pressure at the time the gas is collected?

The Gas Laws

• The gas laws are simple mathematical relationships between the volume, temperature, pressure, and amount of a gas.

What Do You Observe?

Boyle’s Law, 1662

• Pressure-Volume Relationship• At constant n and T:

P 1/V or PV = constant as P, V

• For use in calculations, P1V1 = P2V2

• Examples of Boyle’s Law?

Boyle’s Law

Boyle’s Law Graph: Volume vs. Pressure

Charles Law

Charles’ Law, 1787

• Temperature-Volume relationship• At constant n and P:

T V as T, V• For use in calculations:

V1/T1 = V2/T2

• Examples of Charles’ Law?

Charles’ Law

Charles’ Law Graphs: Volume vs. Temperature

Charles’ Law and the Kelvin Scale

• We get a straight-line graph of Charles’ Law data.

• Zero volume equals -273.15C.• Lord Kelvin creates the absolute scale

where 0K = -273.15C.• WE MUST USE KELVIN SCALE

FOR CHARLES’ LAW CALCS!

Gay-Lussac’s Law

Gay-Lussac’s Law, 1802

• Temperature-Pressure relationship• At constant n and V,

TP as T, P• Temperature must be in Kelvin• For use in calculations:

P1/T1 = P2/T2

• Examples of Gay-Lussac’s Law?

Gay-Lussac’s Law

Gay-Lussac’s Law

Gas Law Formulas

Combined Gas Law

• At constant n,

P1V1/T1 = P2V2 /T2

Combined Gas Law

• A gas with a volume of 4.0 L at 90.0 kPa expands until the pressure drops to 20.0 kPa. What is the new volume if the temperature doesn’t change?

• 18 L

Combined Gas Law

• We have a fixed quantity of gas at 23.0C and a pressure of 748 torr. The gas volume is 10.3 L. If the temperature rises to 165.0C, what will the new volume be if the gas pressure remains constant?

• Volume = 15.2 L

Combined Gas Law

• A fixed quantity of gas at 23.0C has a pressure of 748 torr and occupies a volume of 10.3 L. Calculate the volume (L) if the pressure increases to 1.88 atm and the temperature remains constant.

• 5.39 L

Combined Gas Law

• A gas with a volume of 300. mL at 150.0C is heated until its volume is 600. mL. What is the new temperature of the gas if the pressure remains constant during the heating process?

• 846 K

Combined Gas Law

• The gas in a used aerosol can is at a pressure of 103 kPa at 25.0C. If David throws the can into a fire, what will the gas pressure be when the temperature reaches 928.0C?

• Pressure = 415 kPa

A Combined Gas Law Calculation

• The volume of a gas-filled balloon is 30.0 L at 313 K and 153 kPa. What would the volume be at STP?

• 39.5 L

• A sealed cylinder contains nitrogen gas at 1.00 x 103 kPa pressure and a temperature of 20.0C. When the cylinder is left in the sun, the temperature rises by thirty degrees. What is the new gas pressure in kPa?

• 1.10 x 103 kPa

Combined Gas Law

A Combined Gas Law Calculation

• A gas at 155 kPa and 25.0C has an initial volume of 1.00 L. If the pressure increases to 605 kPa and the volume decreases to 0.342 L, what is the final temperature of the gas in Kelvin?

• 398 K

Combined Gas Law

• A sample of gas at 47°C and 1.03atm occupies a volume of 2.20L. What volume would this gas occupy at 107°C and 0.789atm?

Gas Volumes

• Gay-Lussac’s Law of Combining Volumes of Gases states that at constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers.

Gas Stoichiometry

3NO2(g) + H2O(l) 2HNO3(l) + NO(g)

1. If 702L of NO2 gas reacts with water, what volume of NO gas will be produced?

2. What volume of NO2 gas was used to produce 631mL of NO gas?

*Assume the gases are measured under the same conditions before and after the reaction.

Gas Stoichiometry

C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(g)

1. What will be the volume, in liters, of oxygen required for the complete combustion of 0.350L of propane?

2. If 0.341L of oxygen combusts in this reaction, what volume of carbon dioxide will be produced?

Avogadro’s Law

• Mole-Volume relationship• At constant T and P: n V as n, V• In other words, doubling the moles

of a gas will cause V to double if P and T are held constant.

Avogadro’s Law

Molar Volume of a Gas

• Avogadro’s Hypothesis: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

• Molar Volume of a Gas: At STP, 1 mole of any gas = 22.4L

= 6.02 x 1023 particles

Gas Stoichiometry

• What volume does 0.0685mol of gas occupy at STP?

• What quantity of gas, in moles, is contained in 2.21L at STP?

Gas Stoichiometry

• At STP, what is the volume of 7.08mol of nitrogen gas?

• What is the mass of 2.00L of C2H6 (30.1g/mol) at STP?

• What is the mass of 3.11L of CH4 at STP?

Gas Stoichiometry

• What is the density of CH4 at STP?

• What is the density of C2H6 at STP?

• A 1.00L sample of gas has a mass of 1.87g at STP. What is its molar mass?

Gas Stoichiometry• A 1.0L sample of a gas has a

mass of 1.34g at STP. What is its molar mass?

Ideal Gas Law

• PV = nRT

P = pressure (various units) V = volume (L)

n = number of gas moles (mol) T = temperature (K only) R = ideal gas constant. R has many units. Most common: 8.314 L• kPa/mol•K and 0.0821 L•atm/mol•k

Ideal Gas Law

• A gas that obeys this equation is said to behave ideally.

• This law accounts for the properties of most gases under a wide variety of circumstances.

• This law works best for gases at low pressure and high temperature.

An Ideal Gas Law Calculation

• A rigid hollow sphere contains 251 mol of He gas at a temperature of 621K and a pressure of 1.89 x 103 kPa. How many liters of gas are in the sphere?

• 686 L

An Ideal Gas Law Calculation

• If 4.50 g of methane gas (CH4) are in a 2.00-L container at 35.0C, what is the pressure in the container (atm)?

• 3.55 atm

An Ideal Gas Law Calculation

• A deep underground cavern contains 2.24 x 106 L of methane gas at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many kg of CH4 does the cavern contain?

• 2.06 x 104 kg methane

Why Don’t Real Gases Behave Ideally?…Volume

• Contrary to the Kinetic-Molecular Theory, real gases do have finite volumes.

• At low pressure, gas volume is negligible compared with the container volume. Gas particles move freely.

• At higher pressures, the volume of the gas particles is a larger fraction of the total space available. Free space is more limited. Gas volumes are greater than those predicted by the Ideal Gas Law.

Why Don’t Real Gases Behave Ideally?…Attractive Forces• Contrary to the K-M Theory, real

gases particles are attracted to each other.

• At high pressure, particles experience more attraction because they are closer together.

• As temperature decreases, gas particles move slower and experience more attraction.

• More attraction = more deviation from ideal behavior.

Gas Effusion and Diffusion

Gas Effusion and Diffusion

• Effusion: the escape of gas molecules through a tiny hole. Ex: slow leakage through a balloon’s pores.

• Diffusion: the spread of a gas throughout open space. Ex: diffusion of perfume molecules in a room.

Diffusion or Effusion?

Graham’s Law of Effusion

• The effusion rate of a gas is inversely proportional to the square root of its molar mass.

• To compare the effusion rates of two gases at same T and P: r1/r2 = √(M2/M1)

• where r1= rate of first gas r2 = rate of second gas M1 = molar mass of first gas

• M2 = molar mass of second gas

How Does Effusion Work?

• At the same temperature, a lighter gas effuses faster than a heavier gas. Why?

• A gas molecule can only escape through a hole by randomly hitting it. A gas molecule that moves faster gets more chances to hit the hole. At the same temperature, lighter molecules move faster than heavier molecules.

An Effusion Calculation

Which gas effuses faster: hydrogen or chlorine? How much faster?

• About 6 times (5.92) faster.