Chapter 4: The Gas Laws

• In this chapter, we’ll study the gas laws which will allow us to predict the properties of any gas

• We’ll cover sections 1 through 11 over the next three days

The Nature of Gases

• Eleven elements are gases under normal conditions

• Despite the fact that the elements are VERY different, their physical properties in the gas phase are very similar

• Gases are compressible examples of bulk matter– Gases fill the entirety of whatever

closed volume they occupy– Gas molecules are in constant motion

PressurePressure = Force per unit area

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P =F

A

The SI Unit of Pressure is the pascal, Pa

1 Pa = 1 kg·m-1·s-2

The pressure of a gas exerted on the walls of a container is a result of the collisions of gas molecules with the surface of the walls.

Pressure

Measuring Pressure

• The atmosphere of the planet is filled with gas molecules. These molecules exert a force on the surface of the earth

• We use a barometer to measure the pressure of atmospheric gases.

Vacuum Gauges• A manometer is a

device used to measure the pressure inside a vessel

• We measure the pressure on the atmospheric side and the pressure on the device side– The difference is the

pressure in the device

The Gas Laws

• Studies on the effect of temperature, pressure and volume have been carried out by many scientists, but 4 stand out:

1. Robert Boyle: (1662) Studied the relationship between Volume and Pressure

2. Jacques Charles and Joseph-Louis Gay-Lussac: (1810) Studied the relationship between Volume and temperature while hot air ballooning over Paris

3. Avedeo Avogadro: Helped prove atoms exist by confirming the relationship between Volume and the number of molecules of a gas

Boyle’s Law

• Took a closed tube with an air bubble on the closed end and poured Hg into the open end– As he added more

Hg, the air bubble shrank

Boyle’s Law

• Pressure is inversely related to volume.

• V 1/P• PV = constant (at constant n)

Boyle’s Law

Pressure is inversely related to volume.V 1/PPV = constant (at constant n and T)

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P1V1 = P2V2

Charles’s Law

• Charles and Gay-Lussac were balloonists and while trying to improve their balloons, they found that:

At constant pressure, the volume of a gas increases with temperature

Charles’s Law

•We could also state Charles’s Law in terms of Pressure.

•The Pressure of a sample is directly proportional to the absolute temperature

Charles’s Law

Volume absolute temperature @ constant n, constant P

V=(constant) T

Pressure absolute temperature @ constant n, constant V

P=(constant) T

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V1T1=V2T2

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P1T1=P2T2

or

@ constant n, constant P @ constant n, constant V

Absolute Temperature

• Note: The absolute temperature is the temperature on the Kelvin scale

• For the remainder of the semester, whenever you use a temperature, you may need to convert it to the Kelvin scale

• Many of the constants and relationships that use them will only be valid when temperature is on the absolute, or Kelvin, scale

0C = 273.15 K 1 degree C = 1 Kelvin 25C = 298.15 K

Charles’s Law

• If we double the absolute temperature, the volume of the gas doubles OR the pressure of the gas doubles

Avogadro’s Principle

• Avogadro found that under the same conditions of temperature and pressure, a given number of gas molecules occupy the same volume regardless of their chemical identity

At 273.15K and 1 atm, all gases occupy approximately 22.4L

Vm=Molar volume of gas = V/n

V=nVm

The Gas Laws: Summary

1. Boyle’s Law: P1V1=P2V2 @ constant n, constant T

2. Charles’s Law: V1/T1=V2/T2 @ constant n, constant P

P1/T1=P2/T2 @ constant n, constant V

1. Avogadro’s Law: As more molecules are added to a sample of gas at constant temperature and pressure, the volume must increase

OR As more molecules are added to a sample of gas at constant temperature and volume, the pressure must increase

Putting it all together: The Ideal Gas Law

We can combine the relationships stated in the three laws to create a single equation that will allow us to predict the pressure, volume or temperature of a certain number of moles of gas

V= n • (constant) • PV= n • (constant) • TP= n • (constant) • T

PV= n • (constant) • T

The Ideal Gas Law PV=nRT where R=8.314 J/Kmol

• The ideal gas law is an equation of state, an equation that describes the pressure, volume and temperature of a certain amount of a substance

• We can use the equation by itself or we can use it to determine the properties of an ideal gas at 2 sets of conditions by using the combined gas law

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P1V1n1T1

=P2V2n2T2