PRESSURE



1. SC6. Students will understand the effects motion of atoms and molecules in chemical and physical processes.

1. a. Compare and contrast atomic/molecular motion in solids, liquids, gases, and plasmas.

PRESSURE

(Chapter 12)

Pressure is the force per unit area. Gases exert pressure when they hit the walls of their container. Even though a gas molecule has little mass, million of millions of millions of gas molecule’s pressure can add up.

There is pressure exerted by the atmosphere. At sea level this pressure is equal to one atmosphere. Move up in altitude and the pressure decreases. There is less atmosphere pushing down.

To measure air pressure, you might use a barometer or a manometer. A barometer measures atmospheric pressure. A manometer measures the pressure of a gas enclosed in a series of tubes and flasks.

Pressure is measured in a variety of units. See the table below.

Unit Abbreviation Compare to 1 atm

Kilopascal kPa 101.3 kPa

Millimeters of mercury mmHg 760.0 mmHg

Torr torr 760.0 torr

Atmosphere atm 1.0 atm

Pounds per square inch psi 14.7 psi

VIDEODISC: Racing Hot Air Balloons

1. Why is it easier for pilots to control the vertical direction of a balloon’s flight than the horizontal direction?

2. Why did Julie say that a thermal is not a good word for balloonists?

GASES

(Chapter 13)

Physical Properties of Gases:

• Gases have mass.

• Gas particles do not attract or repel each other – the spaces between each particle are too great.

• It is easy to compress gases.

• The fact that gas molecules are in constant motion allows gases to fill their containers completely

• Different gases can move through each other quite rapidly. This movement is called DIFFUSION. EFFUSION is when diffusion occurs through a small opening.

• Gases exert pressure.

• The pressure of a gas depends on its temperature and volume.

Remember that gases consist of very small particles, the particles have large distances between them, they are in constant, rapid, random motion and have elastic collisions.

Actual gases (in real life) do not obey all the suppositions stated in the kinetic-molecular theory. But most gases behavior approximates ideal gases.

In order to accurately measure a gas sample, you must know the quantity of particles (moles), pressure, temperature, and volume of a gas.

THE GAS LAWS

Contained gas behavior can be explained by four relationships using the kinetic theory:

1. Boyle’s Law: relationship between volume and pressure; inversely proportional.

2. Charles’ Law: relationship between temperature and volume; directly proportional.

3. Gay-Lussac’s Law: relationship between pressure and temperature; directly proportional.

3. Avogadro’ Principle: relationship between number of particles (moles) and pressure or volume; directly proportional.

VIDEODISC: Breathing and Boyle’s Law

1. Why does the balloon expand?

2. What does this demo have to do with breathing?

3. Have you ever heard the phrase “nature abhors a vacuum?” What do you think it means?

Boyle’s Law

For a given mass of gas, at a constant temperature, the volume varies inversely with the pressure:

P1V1 = P2V2

PRACTICE:

The pressure in a 9.0 L balloon is 2.1 atm. If the volume is reduced to 5.0 L, what will the resulting pressure be? (Temperature does not change.)

V1 = 9.0 L V2 = 5.0 L

P1 = 2.1 atm P2 = ? atm

P1V1 = P2V2 P2 = P1V1 =

V2

Charles’ Law

The volume of a fixed mass of a gas is directly proportional to its KELVIN temperature if the pressure is constant. If pressure is kept constant, then volume must change to keep temperature the same.

V1 = V2

T1 T2

You must use the Kelvin temperature scale!

PRACTICE:

The temperature of a sample of gas is 300.0 K. The gas’ volume is 25.0 L. What will be the new volume of the gas if the temperature is dropped to 125.0 K?

V1 = 25.0 L V2 = ? L V2 = T2V1 =

T1 = 300.0 K T2 = 125.0 K T1

VIDEODISC: Imploding Can

1. Why did the can implode?

2. How does the demonstration you just saw relate to a barometer?

3. How is a vacuum seal created on a jar of homemade preserves?

Gay-Lussac’s Law

An increase in temperature increases the frequency of collisions between gas particles. In a given volume, raising the KELVIN temperature also raises the pressure.

P1 = P2

T1 T2

You must use Kelvin temperature scale!

PRACTICE:

The temperature of a sample of gas is 300.0 K. The gas’ pressure is 1.4 atm. What will be the new pressure of the gas be if the temperature is dropped to 125.0 K?

P1 = 1.4 atm P2 = ? atm P2 = T2P1 =

T1 = 300.0 K T2 = 125.0 K T1

Avogadro’s Principle

Particles of different gases vary greatly in sizes. But since the gas particles are so far apart, size is not a factor when determining volume if you are talking about a fixed number of particles. Avogadro’s Principle states that equal volumes of gases at the same temperature and same pressure contain equal number of particles. In gas law problems moles is designated by an “n”. One mole of a gas has a volume of 22.4 L (dm3) at standard temperature and pressure (STP).

Dalton’s Law of Partial Pressures

(Chapter 12)

The sum of the partial pressures of all components of a gas mixture is equal to the total pressure of the gas mixture.

Ptotal = P1 + P2 + P3 + P4 +.....

PRACTICE (Easy Type):

What is the atmospheric pressure if the partial pressures of nitrogen, oxygen, and argon are 604.5 mm Hg, 162.8 mm Hg, and 0.500 mm Hg, respectively?

Ptotal = P1 + P2 + P3

Ptotal =

PRACTICE (Hard Type):

A quantity of oxygen gas is collected over water at 8(C in a 0.353 L vessel. The pressure is 84.5 kPa. What volume would the DRY oxygen gas occupy at standard atmospheric pressure (101.3 kPa) and 8(C. (The dry gas pressure of water at 8(C is 1.1 kPa)

T1 = 8ºC T2 = 8ºC

V1 = 0.353L V2 = ?

P1 = 84.5 kPa – 1.1 kPa = 83.4 kPa P2 = 101.3 kPa

You must correct the pressure so that you can have the DRY gas without the water pressure added in.

VIDEODISC: Scuba Diving

1. Think of your lungs as a flexible 6-liter container full of a gas at STP. How would lung volume change at a depth of 30 meters?

2. Why not increase oxygen to 100% and go really deep?

3. What are the bends? How do divers avoid them?

COMBINING THE GAS LAWS

From the Boyle’s, Charles’, and Gay-Lussac’s laws, we can derive the Combined Gas Law: P1V1 = P2V2

T1 T2

WHY: Laboratory experiments are almost always made at pressures and temperatures other than the standard. Because this affects volume, it is necessary to correct the laboratory volumes of gases for both temperatures and pressures.

PRACTICE:

The volume of a gas measured at 75.6 kPa pressure and 60.0°C is to be corrected to correspond to the volume it would occupy at STP. The measured volume of the gas is 10.0 cm3.

P1 = 75.6 kPa P2 = 101.3 kPa P1V1 = P2V2

V1 = 0.010 L V2 = ? T1 T2

T1 = 333K T2 = 273 K

V2 = P1V1T2 = ___________________________

T1P2

PRACTICE:

Correct the volume for a gas at 7.51 m3 at 5.0°C and 59.9 kPa to STP.

THE IDEAL GAS LAW

Ideal Gas Equation: PV = nRT

“R” is the universal gas constant.

There are four due to the four different units for pressure.

R = 0.0821 L• atm or 62.4 L•mm Hg or 62.4 L • torr or 8.31 L • kPa

mol • K mol • K mol • K mol • K

You decide which “R” to use based on what pressure you are given or are trying to find.

STANDARDS

T = 0°C = 273 K

P = 1.00 atm = 101.3 kPa = 760.0 mm Hg = 760.0 torr

V = 22.4 L (at STP)

Remember:

1. Always change the temperature to KELVINS and convert volume to LITERS

2. Check the units of pressure to make sure they are consistent with the “R” constant given or convert the pressure to the gas constant (“R”) you want to use.

PRACTICE:

How many moles of a gas at 100.0°C does it take to fill a 1.00 L flask to a pressure of 1.50 atm?

V = 1.00 L T = 100.0°C = 373.0 K

P = 1.50 atm R = 0.0821 atm•L

n = ? mol•K

PV = nRT

n = PV = __________________________________________________ =

RT

PRACTICE:

What is the volume occupied by 9.45g of C2H2 at STP? Hint - convert grams to moles.....

GRAHAM’S LAW OF EFFUSION/DIFFUSION

(Chapter 12)

The rate of diffusion/effusion is inversely proportional to the square root of its molar mass under identical conditions of temperature and pressure. If two bodies of different masses have the same kinetic energy, the lighter body moves faster.

Diffusion: random mixing of gas molecules due to kinetic properties – think of perfume

Rate (velocity) a Formula mass b

=

Rate (velocity) b Formula mass a

Compare ammonia and hydrochloric acid:

velocity NH3 = 36.46g/mol HCl = 1.46 NH3 is 1.463 times faster than HCl

velocity HCl 17.04g/mol NH3

REAL vs IDEAL GASES

The ideal gas equation, PV = nRT, is simple to use and accurately predicts gas behavior in many everyday situations. However, it is an approximation and does not describe the behavior of real gases exactly.

Under very high pressure, real gases have trouble compressing completely. The ideal gas law fails. Ideal gases have no volume, but real gases do. At very low temperatures, attractive forces between real gas molecules become significant and real gases liquefy.

The ideal gas law can be used under ordinary conditions only.

GAS STOICHIOMETRY

We are now going to add to our MOLE CITY diagram, adding volume of a mole of gas.

VOLUME

1 mol 22.4 L @ STP

1 mole 1 mole

PARTICLES MOLE MASS

(atoms or 6.02 x 1023 mass from the

molecules) periodic table

(molar mass)

You can now solve volume-mole, mole-volume, volume-mass, and other problems.

PRACTICE

A. Determine the volume in 2.0 moles of H2.

?? volume = 2.0 mol H2 22.4 L H2 = 44.8 L H2

1 mol H2

B. Determine the volume in 10.3 moles of CO2.

?? volume = __________________________________

C. Determine the moles in 251 L of O2.

?? moles = __________________________________

D. What volume of hydrogen gas is needed for the complete reaction between nitrogen gas and hydrogen gas to produce ammonia? You are given 5.0L of nitrogen gas. This problem involves not a “mass to mass” problem but a “volume to volume” problem. The balanced equation is N2 + 3H2 ( 2NH3

Step One:

Step Two:

Steps Three/Four/Five:

E. What volume of oxygen gas is needed for the complete reaction between oxygen gas and potassium chloride to produce potassium chlorate? You are given 45.0g KCl. This problem involves not a “volume to volume” problem but a “mass to volume” problem. The balanced equation is 2KCl + 3O2 ( 2KClO3

Step One:

Step Two:

Steps Three/Four/Five:

DETERMINING MOLAR MASS

We can use the ideal gas equation to calculate the molecular (molar) mass of a gas from laboratory measurements.

The number of moles of a substance is equal to: moles, n = mass, m

Molar mass, M

The ideal gas equation can be written as PV = mRT or M = mRT

M P V

PRACTICE:

What is the molar mass of a gas if 100.0 dm3 has a mass of 7.202g at 110°C and 107.0 kPa?

m = P =

R = V =

T =

M = mRT = _____________________________________________

P V

DETERMINING DENSITY

This modified version of the ideal gas equation can also be used to solve for the density of a gas:

D = m = PM D = PM

V RT RT

PRACTICE:

Find the density of NH3 in g/L at 752 mm Hg and 55°C.

M = T =

R = P =

D = PM = _________________________________________________

RT

PRACTICE:

1. Calculate the molar mass, M, of a gas if 150.0 dm3 has a mass of 75.0 g at 100°C and 95 kPa.

2. Determine the density of chloroform gas, CHCl3 if a sample massing is collected in a flask with at 37°C and a pressure of 728 mm Hg.

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