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CHAPTER 12 Gases and the

Kinetic-Molecular Theory

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Gases vs. Liquids & Solids

GasesGases Weak interactions

between molecules

Molecules move rapidly

Fast diffusion rates

Low densities

Easy to compress

Liquids & SolidsLiquids & Solids Strong interactions

between molecules

Molecules move slowly

Slow diffusion rates

High densities

Hard to compress

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Pressure

Force per unit area Units of pressure:

pounds per square inch (psi)mm Hg = torratmospheres (atm)pascals (Pa)

Normal atmospheric pressure – the pressure of air at the sea level at 0°C (=32 F)

1 atm = 760 mm Hg = 760 torr = 101,325 Pa ≈ 101.3 kPa

(Evangelista Torricelli – 1608-1647)

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Kinetic-Molecular Theory

Explains the behavior of gases in terms of molecular motion

The kinetic energy of gas molecules depends on their velocities:

The gas exerts pressure due to the molecular motion: many molecules have to strike the surface to produce this macroscopic effect

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2mvE

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Boyle’s Law p ×V = const = k

p – pressureV – volume(at constant temperature and amount of gas)

pp1 1 ××VV11 = = pp22 ××VV22

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The amount of gas (the number of gas molecules) remains constant

The temperature is constant and therefore the kinetic energy of gas molecules remains about the same

If the volume is decreased, then higher number of gas molecules strike a unit area, therefore the pressure increases

If the volume is increased, the reverse effect takes place – the pressure decreases

Boyle’s Law – Molecular Picture

pp1 1 ××VV11 = = pp22 ××VV22

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A 1.00 L sample of gas at 760 mm Hg is compressed to 0.800 L at constant temperature. Calculate the final pressure of the gas.

Boyle’s Law – Example

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V T or V = kT(at constant pressure and amount of gas)

This equation defines a straight line

Extrapolating this line to V =0 results in the absolute zero of temperature on the Kelvin temperature scale

Charles’ Law

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The amount of gas (the number of gas molecules) remains constant

As the temperature increases, the thermal energy is converted into the kinetic energy and gas molecules move faster

The gas molecules strike the surface more vigorously and, if the pressure is to be kept constant, the gas has to expand

If the temperature is decreased, the volume also decreases

Charles’ Law – Molecular Picture

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A sample of gas at 1.20 atm and 27°C is heated at constant pressure to 57°C. Its final volume is 4.75 L. What was its original volume?

Charles’ Law – Example

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Both Boyle’s Law and Charles’ Law can be derived from the Combined Gas Law

The reverse is not true !

Combined Gas Law For a constant amount of gas

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A 4.00 L sample of gas at 30°C and 1.00 atm is changed to 0°C and 800 mm Hg. What is its new volume?

Combined Gas Law – Example

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Ideal Gas Equation

p – pressure

V – volume

n – # of moles of the gas

T – temperature

R – universal gas constantR = 8.3144 J/(mol·K) = 0.08206 (L·atm)/(mol·K)

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Ideal Gas Equation

Let’s calculate the volume of 1 mole of some gas at 0°C and 1 atm:

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Standard Molar Volume The standard molar volumestandard molar volume of an ideal

gas is equal to 22.414 liters per mole at standard temperature and pressure

Standard temperature and pressure (STP)

T = 273.15 K = 0°C = 32 Fp = 760 torr = 1 atm = 101,325 Pa

1 mole of an ideal gas occupies 22.414 L volume ONLY at standard temperature and pressure

To find the volume of 1 mole at different conditions we have to use other gas laws

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Avogadro’s Law At the same temperature and pressure,

equal volumes of all gases contain the same number of molecules

At constant T and p, the volume V occupied by a sample of gas is directly proportional to the number of moles n

V n or V = kn

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What volume will be occupied by 32.0 g of oxygen at STP? How will this volume change if the pressure is increased to 3 atm and the temperature is raised to 100°C?

Standard Molar Volume – Example

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At 750 torr and 27°C, 0.60 g of a certain gas occupies 0.50 L. Calculate its molecular weight.

Ideal Gas Equation – Example

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A gas is composed of 30.4% N and 69.6% O. Its density is 11.1 g/L at -20°C and 2.50 atm. What is the molecular formula of the gas?

Ideal Gas Equation – Example

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What volume of hydrogen will be produced in the reaction of 3 g of zinc with the excess of diluted hydrochloric acid, if the reaction is carried out at room temperature (25°C) and standard atmospheric pressure (1 atm)?

Ideal Gas Equation – Example

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Dalton’s Law Mixture of gases: A, B, C, …

Partial pressure – pressure that a gas would exert if it alone occupied all the volume occupied by the mixture of gases

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Dalton’s Law – Example Calculate the pressure of the mixture

of 0.25 mol of H2 and 0.75 mol of N2 if at 25°C it occupies the volume of 12 L.

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Mole Fraction Mixture of gases: A, B, C, …

Mole fraction of gas A:

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Mole Fraction Mixture of gases: A, B, C, …

Mole fraction of gas A:

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Dalton’s Law – Example Into a 5.00 L container at 18°C are placed 2.00

g H2, 44.0 g CO2, and 16.0 g O2. Calculate the total pressure in the container, the partial pressure and the mole fraction of each gas.

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Assignments & Reminders

Read Sections 12-1 through 12-13

Homework #8 is now accessible on OWL

HAPPY THANKSGIVING !