CHAPTER 5

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CHAPTER 5. THE GASEOUS STATE. I. Characteristics of a Gas. A) Gases assume the shape and volume of a container. B) Gases are the most compressible of all the states of matter. C) Gases will mix evenly and completely when confined to the same container.

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CHAPTER 5

THE GASEOUS STATE

I. Characteristics of a Gas

A) Gases assume the shape and volume of a container.

B) Gases are the most compressible of all the states of matter.

C) Gases will mix evenly and completely when confined to the same container.

D) Gases have lower densities than liquids or solids.

II. Historical Perspective

A) It was the first state studied in detail.

B) It is the easiest state to understand - for the purposes of general chemistry, there is a simple mathematical equation for the general description of a gas which works well in the real world, over a certain range of temperatures and pressures.

C) The study of gases and its results formed the primary experimental evidence for our belief that matter is made up of particles. MATTER IS NOT CONTINUOUS.

III. Measurable Properties of a Gas

A) Mass - moles - symbol is n

B) Pressure - symbol is P

C) Volume - symbol is V

D) Temperature - must be in K - symbol is T

IV. Measuring the Mass of a Gas is Difficult.

Demonstration of Balloons

A) Balloons appear to lose mass when certain gases are added to them. WHY?

All expandable containers have this problem.

B) Constant volume containers, like glass flasks, have a different problem.

What is that problem? How is it solved?

How are these problems overcome?

V. Pressure and Its Measurement

A) Pressure is defined as the force exerted per unit area of surface.

B) Think of a gas confined in a box - the top, bottom, and sides of the box are areas - the gas exerts force on all sides of the box which are AREAS

C) In the U.S., the units of pressure seen on tires, tire gauges, reported by mechanics are _________.

D) Pounds must be a unit of _________, and square inches is a unit of _________.

FORCE = MASS X ACCELERATION

WEIGHT = mg = mass x the acceleration due to gravity

E) In the SI system, the unit of pressure is the pascal, Pa.

1 Newton is the resultant force which imparts to a 1 kilogram mass an acceleration of 1 m/sec2 .

A penny on a table exerts a force of about 100 Pa of pressure – 1 Pa is a very small unit of pressure. Chemists have not wholeheartedly adopted this unit.

F) With respect to gases:

How can inches (a unit of length) be equated with force/area?

In the lab you will measure the pressure in mm of Hg, with a barometer invented by Torricelli (another unit of pressure, the torr, is named after him), mm is another unit of length.

a) What is a barometer?

How do you get the Hg up the tube?

What holds it up there?

Does the diameter of the glass tube affect the height of Hg in the tube?

Units of pressure and their relationships are: 1 atm = 760 mm Hg = 760 torr = 101.3 kPa = 14.7 psi = 29.92 inches of Hg

VI.MEASURE THE VOLUME OF A GAS

A) A gas occupies all the volume enclosing it. B) How do we know when the flask is full of gas at the external pressure?

C) The unit used by chemists is the L.

VII. MEASURING TEMPERATURE OF A GAS

USE A THERMOMETER TO MEASURE DEGREES C, then add 273(.15) to change to the KELVIN scale.

VIII. THE RELATIONSHIP BETWEEN PRESSURE AND VOLUME OF A GAS AT CONSTANT TEMPERATURE

A) Boyle's Law Apparatus show relationship.

B) What kind of a graph do we get when we plot the V vs. P data?

What name do we give to this curve?

V1 X P1 = Area1

V2 X P2 = Area2

Area1 = Area2

V1 X P1 = V2 X P2

THE LARGER THE P1 the smaller the V1

Let's say that P X V = 30

If P is 5 then V is _______

If P is 10 then V is ______

If P is 15 then V is ______

As P decreases V increases; or as P increases, V decreases.

C) What kind of a graph do we get if we plot 1/V vs P?

What kind of curve is this?

What is the equation for this curve?

EXAMPLE PROBLEMS

1) A sample of gas occupies a volume of 20.0 L at 1.50 atm. What will the volume be if the pressure changes to 0.250 atm and the temperature and the amount of gas remain the same?

Is the final volume larger or smaller than the original 20.0 L?

Is it 0.250/1.50 (1/6) times as large or 1.50/0.250 (6) times larger?

2) A sample of gas occupies a volume of 25.0 L at 1.00 atm. What will the pressure be if the volume changes to 5.00 L ? The temperature and the amount of gas remain the same.

V is going down, P must go up

3) What volume will 22.4 L of H2 gas measured at 1.00 atm occupy at a pressure of 1900. mm of Hg with the temp. and amt. of gas remaining constant?

Notice that what we are actually doing here is multiplying the initial volume by a fraction relating the pressures to obtain a new volume OR taking an original pressure and multiplying it by a fraction relating the two volumes and obtaining the new pressure.

Vi X fp= Vf

Pi X fv = Vf

IX. TEMPERATURE EFFECTS AND

CHARLES’ LAW

A) When we plot volume in L vs. T in degrees C for a constant amount of gas at constant P we obtain what kind of graph?

B) We see that when we extrapolate this line to where it intersects the x axis, we will obtain a temperature of -273oC.

C) What are the implications of this?

What happens in reality? What is the difference between a real gas and an ideal gas?

D) If we plot T in oC vs V we get a straight line, it follows the general formula____________.

oC = mV + (-273)

oC +273 = mV

Kelvins = mV

KELVINS ARE PROPORTIONAL TO VOLUME

Vi = kTi

Vf = kTf

SAMPLE PROBLEMS

1) A sample of gas occupies a volume of 20.0 mL at 25oC and 1.00 atm. What is its volume at 50oC at the same pressure?

Will it be twice as big? Is the temperature twice as big?

A sample of gas occupies a volume of 30.0 mL at 25oC and 0.600 atm. What is its volume at STP (standard temperature and pressure - 0oC - 273K and 1.00 atm)?

XI. REACTIONS INVOLVING GASES A) Gay-Lussac's and Avogadro's Laws

1) 1808 - Joseph-Louis Gay-Lussac published the results of some experiments on reactions of gases which resulted in the Gay-Lussac Law of Combining Volumes. When gases react, the volumes of the product and reactant gases at a given temp and pressure are in the ratios of small whole numbers.

2 liters of CO gas react with 1 liter of O2 gas to yield 2 liters of CO2 gas.

2 CO(g) + 1 O2(g)2 CO2(g)

2) HOW CAN THIS BE POSSIBLE?

B) Avogadro's Law - EQUAL VOLUMES OF DIFFERENT GASES CONTAIN EQUAL NUMBERS OF MOLECULES WHEN MEASURED AT THE SAME TERMPERATURE AND PRESSURE.

1) The volume of a gas is directly proportional to the number of molecules (moles) of gas at the same T and P.

2) One mole of any gas occupies the same volume for a given T and P and contains the same number of particles - atoms - molecules.

3) This volume is called the molar volume and is 22.414 L for an ideal gas at 0oC and 1 atm.

4) V is directly proportional to n at constant P and T.

5) Some real gas volumes at STP are: O2-22.397 L; N2-22.402 L;H-22.433L

XII. THE IDEAL GAS EQUATION

A) At the beginning of our study of gases, I said that there was a simple mathematical relationship which describes a gas: the equation of state for an ideal gas.

B) That equation is: PV = nRT

This equation is for an ideal gas: one which follows Boyle's, Charles’ and Avogadro's Laws perfectly. No real gas does this.

When P is low and T is high, real gases behave this way. It keeps scuba divers and people needing oxygen gas alive and other processes using gases at normal T and P working correctly

C) We have looked at the relationship between V & P, V & T, and V & n separately. Now we can put them all together using the gas constant, R.

D) We can use the following relationship to find R for an ideal gas: 1.000 mol of an ideal gas at 273.15 K and 1.000 atm occupies 22.414 L. What is the value of R?

If you use 3 significant figures, as we will usually do

We can see that the value of R changes depending on the units of pressure and volume which are used. mol and K stay the same.

E) We can solve a variety of problems with the Ideal Gas Equation. 1) Calculate the volume of 2.63 mol of O2 gas at 25oC and 0.986 atm pressure. Assume O2 behaves as an ideal gas under these conditions.

From this we see how chemists could obtain the molar masses of substances which were gases or could easily be changed to the gaseous form before the invention of the mass spectrometer.

In the laboratory you will find the molar mass of a volatile liquid using the Ideal Gas Equation.

4) Calculate the approximate molar mass of a gas which has a density of 1.782 g/L at 27oC and 670 mm Hg.

XIII. MIXTURES OF GASES

A) Many studies involve mixtures of gases which do not react, for example air.

B) What is the relationship between the total pressure of the gas mixture and the pressure of each component of the mixture?

1) The total pressure of a mixture of ideal gases is the sum of the pressures that each gas would exert if it were present alone.

You will use this important concept in the laboratory when you collect a gas over water -

Pbar = Pinside = Pgas + Pwater vapor

Pgas = Pbar - Pwatervapor

XIV. DIFFUSION OF GASES

A) In 1832, Graham studied the rates of diffusion of gases: the speeds at which gases move through each other. SPEED is a difficult concept for many of my students. What does speed mean to you???

You should think of miles per hour - a distance in the numerator and a time in the denominator.

What is the distance?

What is the time?

What is the fraction?

Distance time

B) Effusion - a process in which a gas flows through a small hole and is theoretically simpler than diffusion since we don't have to be concerned with molecules hitting each other and zigzagging across the room.

C) Graham's Law of Effusion - Under the same conditions of pressure and temperature, the rates of effusion of gases are inversely proportional to the square roots of their molar masses.

D) What does this mean?

E) How many times faster does H2 effuse than O2 at the same temperature and pressure?

The rate of effusion of H2 is 4 times faster than the rate of effusion of O2.

If it takes 205 seconds for 1.50 L of an unknown gas to effuse through a porous cup, and 95 seconds for the same volume of N2 at the same T and P, what is the approximate molar mass of the gas?

XV. MOLECULAR BEHAVIOR OF GASES

A) We have now considered in detail the ideal gas law which was formulated from experimental evidence.

B) Starting in the 1850's, Boltzmann in Germany and Maxwell in England found that properties of gases could be satisfactorily explained in terms of the motion of the individual gas molecules.

C) This gave rise to what we call the Kinetic Molecular Theory of Gases.

D) This theory applies to an Ideal Gas perfectly.

E) The Kinetic Molecular Theory has 5 postulates about the nature of an ideal gas.

1) Gases are composed of molecules whose size is negligible compared with the average distance between them. (Ideal gas molecules are point masses.)

2) Gas molecules are in constant motion, in random directions, and at various speeds. (Properties of a gas that depend on motion like pressure are the same in all directions.)

3) Ideal gas molecules exert neither an attractive force nor repulsive force on each other.

4) When molecules collide with one another, the collisions are elastic. What does this mean?

5) The average kinetic energy of the molecules is proportional to the temperature on the Kelvin scale. What does this mean?

All gases at the same temperature on the K scale have the same average kinetic energy.

K.E. = 1/2 mv2 or 1/2 mu2 where v is velocity and is a vector quantity, and u is speed which is a scaler quantity.

Two gases at the same T have the same average K.E.

If one gas is heavier than the other, what must be different if the average K.E. must be the same?

This is the basis for Graham's Law.

avg. KEA = avg. KEB

1/2 mAu2A = 1/2 mBu2B

mAu2A = mBu2B

F) Distribution of Molecular Speeds

1) According to KMT, in a given sample of gas, the speeds of the molecules vary over a wide range of values - a few are moving very slow, a few are moving very fast, most have intermediate speeds.

2) Graphically we represent it as: