CHEMICAL

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12 Gases and Kinetic Molecular Theory

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Pressure

• Pressure is force per unit area.– lb/in2

– N/m2

• Gas pressure as most people think of it.

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Pressure

• Atmospheric pressure is measured using a barometer.

• Definitions of standard pressure– 76 cm Hg– 760 mm Hg– 760 torr– 1 atmosphere– 101.3 kPa

Hg density = 13.6 g/mL

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Summary of Gas Laws:The Ideal Gas Law

• Boyle’s Law - V 1/P (at constant T & n)• Charles’ Law – V T (at constant P & n)• Avogadro’s Law – V n (at constant T & P)• Combine these three laws into one statement

V nT/P• Convert the proportionality into an equality.

V = nRT/P

• This provides the Ideal Gas Law.PV = nRT

• R is a proportionality constant called the universal gas constant.

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Summary of Gas Laws:The Ideal Gas Law• We must determine the value of R.

– Recognize that for one mole of a gas at 1.00 atm, and 273 K (STP), the volume is 22.4 L.

– Use these values in the ideal gas law.

R = PVnT

1.00 atm L1.00 mol K

L atmmol K

22 4273

0 0821

.

.

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Summary of Gas Laws:The Ideal Gas Law

Example 12-7: Calculate the number of moles in, and the mass of, an 8.96 L sample of methane, CH4, measured at standard conditions.

You do it!You do it!

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Determination of Molecular Weights and Molecular Formulas of Gaseous Substances

Example 12-10: A 1.74 g sample of a compound that contains only carbon and hydrogen contains 1.44 g of carbon and 0.300 g of hydrogen. At STP 101 mL of the gas has a mass of 0.262 gram. What is its molecular formula?


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Dalton’s Law of Partial Pressures• Dalton’s law states that the pressure

exerted by a mixture of gases is the sum of the partial pressures of the individual gases.

Ptotal = PA + PB + PC + .....

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Dalton’s Law of Partial Pressures

Example 12-11: If 1.00 x 102 mL of hydrogen, measured at 25.0 oC and 3.00 atm pressure, and 1.00 x 102 mL of oxygen, measured at 25.0 oC and 2.00 atm pressure, were forced into one of the containers at 25.0 oC, what would be the pressure of the mixture of gases?

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Dalton’s Law of Partial Pressures• Vapor Pressure is the pressure exerted by

a substance’s vapor over the substance’s liquid at equilibrium.

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Dalton’s Law of Partial Pressures

Example 12-13: A sample of oxygen was collected by displacement of water. The oxygen occupied 742 mL at 27.0 oC. The barometric pressure was 753 torr. What volume would the dry oxygen occupy at STP?


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Mass-Volume Relationships in Reactions Involving Gases

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2 mol KClO3 yields 2 mol KCl and 3 mol O2

2(122.6g) yields 2 (74.6g) and 3 (32.0g)Those 3 moles of O2 can also be thought of as:

3(22.4L) or 67.2 L at STP

g)(2(s)&MnO

(s)3 O 3 + KCl 2KClO 2 2

•In this section we are looking at reaction stoichiometry, like in Chapter 3, just including gases in the calculations.

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Example 12-14: What volume of oxygen measured at STP, can be produced by the thermal decomposition of 120.0 g of KClO3?


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The Kinetic-Molecular Theory

• The basic assumptions of kinetic-molecular theory are:

• Postulate 1– Gases consist of discrete molecules that are

relatively far apart.– Gases have few intermolecular attractions.– The volume of individual molecules is very

small compared to the gas’s volume.• Proof - Gases are easily compressible.

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• Postulate 2– Gas molecules are in constant, random,

straight line motion with varying velocities.• Proof - Brownian motion displays

molecular motion.

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• Postulate 3– Gas molecules have elastic collisions with

themselves and the container.– Total energy is conserved during a collision.

• Proof - A confined gas in an insulated and sealed container exhibits no pressure drop over time.

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• Postulate 4– The kinetic energy of the molecules is

proportional to the absolute temperature.– The average kinetic energies of molecules

of different gases are equal at a given temperature.

• Proof - Brownian motion increases as temperature increases.

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• The kinetic energy of the molecules is proportional to the absolute temperature. • Displayed in a Maxwellian distribution.

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The Kinetic-Molecular Theory• The gas laws that we have looked at earlier in this chapter are confirmations

that kinetic-molecular theory is the basis of gaseous behavior.• Boyle’s Law

– P 1/V – As the V increases the molecular collisions with container walls decrease

and the P decreases.• Dalton’s Law

– Ptotal = PA + PB + PC + .....– Because gases have few intermolecular attractions, their pressures are

independent of other gases in the container.• Charles’ Law

– V T – An increase in temperature raises the molecular velocities, thus the V

increases to keep the P constant.

CHEMICAL

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