17-6 the gas laws and absolute temperaturezuhairusnizam.uitm.edu.my/lecture notes/pse4_lecture_ch17...

17-6 The Gas Laws and Absolute Temperature

The relationship between the volume, Temperature

pressure, temperature, and mass of a gas is called an equation of state.

We will deal here with gases that are not too densedense.

Boyle’s law: the volume of a given amount of gas is g ginversely proportional to the pressure as long as the p gtemperature is constant.

Copyright © 2009 Pearson Education, Inc.


The volume is linearly

TemperatureThe volume is linearly proportional to the temperature as long as thetemperature, as long as the temperature is somewhat above the condensationabove the condensation point and the pressure is constant Extrapolating theconstant. Extrapolating, the volume becomes zero at −273 15°C; this−273.15 C; this temperature is called absolute zero


absolute zero.


The concept of absolute zero allows us to

TemperatureThe concept of absolute zero allows us to define a third temperature scale—the absolute, or Kelvin, scale. This scale starts with 0 K ator Kelvin, scale. This scale starts with 0 K at absolute zero, but otherwise is the same as the Celsius scale. Therefore, the freezing point of Ce s us sca e e e o e, t e ee g po t owater is 273.15 K, and the boiling point is 373.15 K.

Finally, when the volume is constant, the i di tl ti l t thpressure is directly proportional to the

temperature.



Conceptual Example 17-9: Why you should not throw a closed glass jar into a campfire.

What can happen if you did throw an empty glass jar, with the lid on tight, into a fire, and why?


17-7 The Ideal Gas LawWe can combine the three relations just derived into a single relation:

What about the amount of gas present? IfWhat about the amount of gas present? If the temperature and pressure are constant, the volume is proportional to the amount ofthe volume is proportional to the amount of gas:


17-7 The Ideal Gas LawA mole (mol) is defined as the number of grams of a substance that is numericallygrams of a substance that is numerically equal to the molecular mass of the substance:

1 l H h f 21 mol H2 has a mass of 2 g.

1 mol Ne has a mass of 20 g.1 mol Ne has a mass of 20 g.

1 mol CO2 has a mass of 44 g.

The number of moles in a certain mass of material:material:


17-7 The Ideal Gas LawWe can now write the ideal gas law:

where n is the number of moles andwhere n is the number of moles and R is the universal gas constant.


17-8 Problem Solving with the Ideal Gas Law

Standard temperature and pressure (STP):Gas Law

p p ( )T = 273 K (0°C)

P = 1 00 atm = 1 013 N/m2 = 101 3 kPaP = 1.00 atm = 1.013 N/m2 = 101.3 kPa.

Example 17-10: Volume of one mole at pSTP.

D t i th l f 1 00 l fDetermine the volume of 1.00 mol of any gas, assuming it behaves like an ideal

t STPgas, at STP.



Example 17 11: Helium balloonExample 17-11: Helium balloon.

A helium party balloon, assumed to be a perfect sphere, has a radius of 18.0 cm. At room temperature (20°C), its internal pressure is 1.05 atm. Find the number of moles of helium in the balloon and the mass of helium needed to inflate the balloon to these values.



Example 17-12: Mass of air in a room.

Estimate the mass of air in a room whose dimensions are 5 m x 3 m x 2.5 m high, at STP.


17-8 Problem Solving with the Ideal G LGas Law

• Volume of 1 mol of an ideal gas is 22.4 L

If th t f d t h• If the amount of gas does not change:

• Always measure T in kelvins

• P must be the absolute pressure



Example 17-13: Check tires cold.Example 17 13: Check tires cold.

An automobile tire is filled to a gauge pressure of 200 kPa at 10°C. After a drive of 100 km, the temperature within the tire rises to 40°C. What is the pressure within the tire now?tire rises to 40 C. What is the pressure within the tire now?


17-9 Ideal Gas Law in Terms of Molecules: Avogadro’s NumberMolecules: Avogadro’s Number

Since the gas constant is universal, g ,the number of molecules in one mole is the same for all gases. That number gis called Avogadro’s number:


17-9 Ideal Gas Law in Terms of Molecules: Avogadro’s Number

Th f it

Molecules: Avogadro’s Number

Therefore we can write:

or

where k is called Boltzmann’s constant.


17-9 Ideal Gas Law in Terms of Molecules: Avogadro’s Number

Example 17-14: Hydrogen atom massExample 17-14: Hydrogen atom mass.

Use Avogadro’s number to determine the mass of a hydrogen atom.


Example 17-15: How many molecules in one breath?

Estimate how many molecules you breathe in with a 1.0-L breath of air.


18-1 The Ideal Gas Law and the Molecular Interpretation of Temperature

Assumptions of kinetic theory:

• large number of molecules, moving in randomlarge number of molecules, moving in randomdirections with a variety of speeds

f• molecules are far apart, on average

• molecules obey laws of classical mechanicsmolecules obey laws of classical mechanics and interact only when colliding

lli i f tl l ti• collisions are perfectly elastic


18-1 The Ideal Gas Law and the M l l I i f T

The force exerted on the wall byMolecular Interpretation of Temperature

The force exerted on the wall by the collision of one molecule is

Then the force due to allThen the force due to allmolecules colliding with that wall iswall is



The averages of the squares of the speeds in all Molecular Interpretation of Temperature

three directions are equal:

So the pressure is:p



Rewriting

Molecular Interpretation of Temperature

Rewriting,

so

The average translational kinetic energy of the molecules in an ideal gas is directly proportional to the temperature of the gas.



Example 18-1: Molecular kinetic energy.

What is the average translational kinetic energy of molecules in an ideal gas at 37°C?an ideal gas at 37°C?


18-1 The Ideal Gas Law and the Molecular Interpretation of TemperatureMolecular Interpretation of Temperature

We can now calculate the average speed of molecules in a gas as a function ofmolecules in a gas as a function of temperature:



Example 18-2: Speeds of air molecules.

What is the rms speed of air molecules (O2 and N2) at room temperature (20°C)?



Conceptual Example 18 3: Less gas in the tankConceptual Example 18-3: Less gas in the tank.

A tank of helium is used to fill balloons. As each balloon is filled, the number of helium atoms remaining in the , gtank decreases. How does this affect the rms speed of molecules remaining in the tank?



E l 18 4 A d d dExample 18-4: Average speed and rms speed.

Eight particles have the following speeds, given in m/s: 1.0, 6 0 4 0 2 0 6 0 3 0 2 0 5 0 Calculate (a) the average speed6.0, 4.0, 2.0, 6.0, 3.0, 2.0, 5.0. Calculate (a) the average speed and (b) the rms speed.


17-6 the gas laws and absolute temperaturezuhairusnizam.uitm.edu.my/lecture notes/pse4_lecture_ch17...

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