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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.
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/PPV = constant (at constant n and T)
€
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
€
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