gases chem ii chapter 10

GasesChem II Chapter 10

Characteristics of Gases

1. Substances that are typically solids or liquids at room temperature are referred to as vapors. (mercury vapor, water vapor, etc.)

Characteristics of Gases

a.Low molar massb.Expand spontaneously to fill its containerc. Form homogenous mixtures with each other regardless of the identities or relative proportions of the component gases.

Pressure

• Pressure is defined as _________ per unit __________.

Pressure

2.Pressure is defined as force per unit _area. • Formula : P = F/A

Pressure

3.Gas particles exert pressure when they collide with themselves or with their container.

Pressure4. B/c the particles in air move in every direction, they exert pressure in all directions.

Figure 10.01

Pressure5. This type of pressure is called atmospheric pressure.

Measuring Pressure6.Italian physicist Evangelista Torricelli (1608 – 1647) was the first to demonstrate that air exerted pressure.

Measuring Pressure7. The device that Toricelli developed was called the barometer.

Figure 10.02

Measuring Pressure8. A barometer is an instrument used to measure atmospheric pressure.

Measuring Pressure9.Gravity pulls down on the column of mercury.

Measuring Pressure10. A manometer is an

instrument used to measure gas pressure in a closed container.

Figure 10.03

Measuring PressureWhen the valve between

the flask and the u tube is open, gas particles diffuse out of the flask and push the mercury in the tube.

Measuring Pressure11. The different heights of

the mercury in the two arms is used to calculate the pressure of gas in the flask.

Units of Pressure12.The SI unit for pressure is

the Pascal - one newton of force per one square meter. ( 1N/m2)

Units of Pressure13. More traditional units include: a. psi - pounds per square inchb.mmHg- millimeters of mercury c. torr = 1 mmHg1atm = 1 atmosphere = 760 mmHg = 760 torrd.barr - 1 x 105 pascal

1 atm = 760 torr= 760 mmHg=101.3 Kpa=1.013 barr

14. Standard atmospheric pressure ( typical pressure at sea level) is 760 torr or 1.01325 x 105 Pa.

Practice conversion

• A.) .357 atmospheres to torr• B.) 6.6 x 10-2 torr to atmospheres• C.) 147.2 KPa to torr• D.) 745 torr to KPa• E.) .975 atmosphere to Pa and then to KPa

• On a certain day the barometer in a laboratory indicates that the atmospheric pressure is764.7 torr. A sample of gas is placed in a vessel attached to an open-end mercury manometer. The level of the mercury in the open end arm of the manometer has a measured height of 136.4 mm and that in the arm that is in contact with the gas a height of 103.8 mm. What is the pressure of the gas in amospheres and in KPa?

The Gas Laws

• Boyles Law:• 4 variables define the condition (state ) of a

gas.• * Temperature (T)• * Pressure ( P)• * amount of gas ( n)• * volume (V)

The Gas Laws

15. The equations that relate these variables are known as the gas laws:

* Boyles * Charles * Gay Lussac * Combined * Ideal

Boyles Law : Pressure - Volume Relationship

16. The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure.


• The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure


17. V = constant x 1/P or PV = constant

• Boyles Law: P1V1 = P2V2


• Robert Boyles made very careful measurements at constant temperature and proved that increasing the pressure by two reduces the volume by ½ : decreasing the pressure by ½ increases the volume by 2.


• PV = constant at constant temperature.

Example:

A sample of helium gas in a balloon is compressed from 4L to 2.5 L at a constant temperature. If the pressure of the gas in the 4L volume is 210 kPa , what will be the pressure at 2.5L?

Charles LawTemperature and Volume Relationship


18.The French physicist Jacques Charles (1746- 1823) studied the relationship between volume and pressure.


19. When the temperature increases the molecules move fast and hit the walls of the container more often and with more force. If pressure remains constant, the volume must increase.


20.Charles Law states:The volume of a given mass of a gas is

directly proportional to its Kelvin temperature at constant pressure.

V1 = V2

T1 T2


The temperature must be expressed in

__________________

Tk = 273 + Tc


21.The temperature must be expressed

in Kelvin.

Tk = 273 + Tc

Charles Law example

A gas sample at 40º C occupies a volume of 2.32 L. If the temperature is raised to 75º C, What will the volume be, assuming pressure is constant?

Gay – Lussac’s Law : Temperature and pressure

22. The pressure of a given mass of gas varies directly with Kelvin temperature.

Gay – Lussac’s Law : Temperature and pressure

• When the pressure remains constant…

P1 = P2

T1 T2

Example Gay-Lussac problem

The pressure of a gas in a tank is 3.2 atm @ 22º C If the temperature raises to 60º C, What will be the gas pressure in the tank?

Combined gas Law :

• 23. The Combined gas law states the relationship among pressure, volume and temperature of a fixed amount of gas.

P1V1 = P2V2

T1 T2

Example Combined Gas Law

• A gas at 110 kPa and 30º C fills a flexible container with an initial volume of 2L. If the temperature is raised to 80º C and the pressure increased to 440kPa, what is the new volume?

24.Avogadro’s Principle :

Equal volumes of gas at the same temperature and pressure contain equal numbers of particles.

Avogadro’s Principle :

25.The molar volume for a gas is the volume that one mole occupies at 0ºC and 1 atm. of pressure.

Avogadro’s Principle :

26. 1 mole of any gas at standard temperature and pressure (STP) will occupy 22.4 L.

Example

a. Calculate the volume that .881 mol of gas at STP will occupy.

Example

b.Calculate the volume that 2kg of methane gas (CH4) will occupy at STP.

Ideal Gas Law

27.The laws of Avogadro, Boyle, Charles and Gay-Lussac can be combined to form the ________ ______ _______:

PV = nRTP = pressure

V = volume n = number of moles

R = the gas constant T= temp in Kelvin

Ideal Gas Law

28.Each of the four variables will affect the others. These variables are all interrelated/ connected

R represents the gas constant

• Units Numerical value L• atm /mol • K 0.08206

J / mol • K 8.314

cal / mol • K 1.987

m 3• Pa/ mol • K 8.314

L• torr /mol • K 62.36

PV = nRT

The above equation is known as the ideal gas equation. This equation would work for an ideal gas which is hypothetical.

29.Ideal gases have no intermolecular attractive forces and the particles take up no space.30.No gas is truly ideal.

Calcium carbonate CaCO3 (s) decomposes upon heating to give CaO(s) and CO2(g), A sample of CaCO3 is decomposed and the carbon dioxide is collected in a 250mL flask. After the decomposition is complete, the gas has a pressure of 1.3 atm at a temperature of 31ºC How many moles of CO2 gas were generated?

Example 10.4 ( page 376)

Practice

Tennis balls are usually filled with air or N2 gas to a pressure above atmospheric pressure to increase their “bounce” If a particular tennis ball has a volume of 144 cm3 and contains 0.33 g of N2 gas, what is the pressure inside the ball at 24ºC?

Example 10.5

The gas pressure in an aerosol can is 1.5 atm. at 25ºC. Assuming that the gas inside obeys the ideal gas equation, what would the pressure be if the can were heated to 450ºC?

• A large natural gas storage tank is arranged so that the pressure is maintained at 2.20 atm. On a cold day in December when the temperature is -15ºC (4ºF) , the volume of gas in the tank is 28,500 ft3. What is the volume of the same quantity of gas on a warm July day when the temperature is 31ºC (88ºF)?

•

Example 10.6

An inflated balloon has a volume of 6.0 L at sea level (1 atm) and is allowed to ascend in altitude until the pressure is 0.45 atm. During ascent the temperature of the gas falls from 22ºC to -21ºC. Calculate the volume of the balloon at its final altitude.

Gas Densities and Molar Mass

31.Density is mass per unit volume.


• Rearrange the ideal gas law (Pv=nRT)

• n = P• V RT


n = P V RTn/V would have the units moles/ LIf you multiply both sides by molarmass ( grams/ mole)


• Moles • grams Liter Mole the units become

grams Liter which are the units for density.


Density = P• M R •T

The density of a gas depends on its pressure, __molar mass and temperature.


* as pressure and molar mass increase the density increases

* as temperature increases the density decreases.

Example 10.7

• What is the density of carbon tetrachloride vapor at 714 torr and 125 ºC?

The mean molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6 g/mol. The surface temperature is 95K, and the pressure is 1.6 atm. Assuming ideal behavior, calculate the density to Titan’s atmosphere.

Example 10.8

• A series of measurements are made in order to determine the molar mass of an unknown gas. Fist, a large flask is evacuated and found weigh 134.567 g. It is then filled with the gas to a pressure of 735 torr at 31º C and reweighed; its mass is now 137.456 g. Finally, the flask is filled with water at 31ºC and found to weigh 1067.9 g. ( The density of the water at this temperature is 0.997 g/mL) Assuming that the ideal gas equation applies, calculate the molar mass of the unknown gas.

•

• Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21ºC and 740.0 torr.

Example 10.9

The safety air bags in cars are inflated by nitrogen gas generated by the rapid decomposition of sodium azide, NaN3;

2NaN3(s) → 3 N2(g) + 2 Na(s)

If an air bag has a volume of 36L and is filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26.0ºC, how many gram of NaN3 must be decomposed?

• Ammonia is synthesized from hydrogen and nitrogen

• N2 + 3H2 → 2NH3 • If 5L of nitrogen reacts completely by this

reaction at constant temperature and pressure of 3 atm and 298K, how many grams of NH3 are produced?

Gas Mixtures and Partial Pressures.

Daltons Law of Partial Pressures32.The total pressure of a mixture of gases is equal to the sum of the pressures of all of the gases in the mixture.Ptotal = P1 + P2 + P3 + …. Pn

Gas Mixtures and Partial Pressures.

• A mixture of oxygen gas (O2), carbon dioxide (CO2) and nitrogen (N2) has a total pressure of .97 atm. What is the partial pressure of O2 if the partial pressure of CO2 is .7 atm and the partial pressure of N2 is .12 atm.

•

Example 10.10

A gaseous mixture made from 6.00 g O2 and 9.00 g CH4 is placed in a 15.0 L vessel at 0ºC What is the partial pressure of each gas and what is the total pressure in the vessel?

Example 10.10

What is the total pressure exerted by a mixture of 2.00 g of H2 and 8.00 g N2 at 273K in a 10.0 L vessel?

Partial Pressure and Mole Fractions

33. We can relate the amount of a given gas in a mixture to its partial pressure.

Partial Pressure and Mole Fraction

P1 = n1RT/V = n1

Pt ntRT/V nt


34. The ratio n1/ nt is called the _mole_fraction of gas 1, which we denote X1.


35. The mole fraction , X, is a dimensionless number that expresses the _ratio_of the number of moles of one component to the total number of moles in the mixture.

For example,

The mole fraction of N2 in air is .78 (78% of the molecules are N2) If the barometric pressure is 760 torr then the partial pressure of N2 is : .78 ( 760 torr) = 590 torr.

Example 10.11

A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5 mol percent CO2, 18.0 mol percent O2, and 80.5 mol percent Ar. (a) calculate the partial pressure of O2 in the mixture if the total pressure of the atmosphere is to be 745 torr. (b) If this atmosphere is to be held in a 120L space at 295 K how many moles of O2 are needed?

Collecting Gases over water

36. The total pressure inside the inverted container is the sum of the pressure of gas collected and the pressure of water vapor in equilibrium with liquid water.


Ptotal = Pgas + PH20


Ptotal = Pgas + PH20

Appendix B has a listing of the pressure exerted by water vapor at various temperatures.

A sample of KClO3 is partially decomposed producing O2 gas that is collected over water. The volume of gas collected is .250L at 26º C and 765 torr total pressure. (a) How many moles of O2 are collected? (b) How many grams of KClO3 were decomposed?

Example 10.12

37. The Kinetic Molecular Theory assumes the following concepts about gases are truea) Gas particles do not attract

or repel each other.

Kinetic Molecular Theory

b.) Gas particles are much smaller than the distances between them ( the particles take up virtually no space)


c.) Gas particles are in constant, random motion


d) No kinetic energy is lost when gas particles collide with each other or with the walls of the container


• e.)All gases have the same average kinetic energy at a given temperature.


38.Pressure is caused by collisions of molecules with the wall of the container. The magnitude of the pressure is determined by both how often and how forcefully the molecules strike the wall.

E= ½ mu2 where u is the average mean squared speed. E is the kinetic energy.


•

• E= ½ mu2 where u is the average mean squared speed. E is the kinetic energy.

•


39.Kinetic molecular theory explains Boyles law because when volume increases there are fewer collisions with container wall so pressure decreases.


40. Gay – Lussac’s law ( P1/T1 = P2/T2) is explained because when temperature is increased at constant volume, the particles have more kinetic energy and strike the container more often and forcefully. Therefore, pressure increases.


A sample of O2 gas initially at STP is compressed to a smaller volume at constant temperature. What effect does this change have on (a) the average kinetic energy of O2 molecules (b) the average speed of O2 molecules(c) the total number of collisions of O2 molecules with the container walls in a unit of time. (d) the number of collisions of O2 molecules with a unit area of container wall per unit time?

Example 10.13

(a) Average kinetic energy is dependent on temperature so compression doesn’t affect kinetic energy.

(b) If average kinetic energy remains the same, speed remains the same.

Example 10.13

( c) number of collisions increases because the molecules are in a smaller volume

(d) # of collisions increases.

Example 10.13

41.The random motion of gas particles causes the gases to mix until they are evenly distributed.

Molecular Effusion and Diffusion

42.Diffusion is the term used to describe the movement of one material through another.


43.Effusion is related to the diffusion. During effusion a gas escapes through an opening


44.Both diffusion and effusion are dependent on mass( size) of the particles.


Rate of effusion α 1 /√molar mass b/ molar massA

The rate of effusion of gasses is proportional to the inverse of the square of their molar masses.

45.Grahams Law of Effusion

Ammonia has a molar mass of 17 g/mol. Hydrogen chloride has a molar mass of 36.5 g/mol. What is the ratio of their diffusion rates?

For example

46.According to the kinetic molecular theory, all gases at the same temperature have the same kinetic energy. Since all gases have different masses, that means the velocity of the particles must be different.• • KE = ½ mv2

47. The lighter particles must have greater speed.

• U = √ 3RT/M• U = root mean square speed

( rms)• R = gas constant• T = temperature in kelvin• M= molar mass

48. b/c M is in the denominator, the greater the mass the smaller the speed. The larger the temp, the larger the speed.• ( page 390 – Figure 10.19)

• Example problem 10.14• Calculate the rms of an N2

molecule at 25ºC.•

49. Diffusion, like effusion is faster for light molecules.

• In 1846, Thomas Graham discovered that the effusion rate of a gas is inversely proportional to the square of its molar mass. The rates of diffusion of the two gases ( r1 and r2) are inversely proportional to the square of their respective molar masses.

• r1/ r2 = √M2/M1

• Example 10.15 • An unknown gas composed of

homonuclear diatomic molecules effuses at a rate that is only .355 times that of O2 at the same temperature. What is the identity of the unknown gas?

• Real Gases: • Deviations from Ideal Behavior

50.In order for a gas to behave according to ideal gas laws predict, the molecules of gas can occupy no space and have no intermolecular attraction

51.At very high pressures and low temperatures gases display non-ideal behavior.

52.At lower pressures ( lower than 10 atmospheres) the deviation is low enough to neglect.• .

53.As temperature increases, the properties of a gas more nearly approach that of an ideal gas. As temperatures increase, the forces of attraction become less significant.

54.As temperature increases, the properties of a gas more nearly approach that of an ideal gas. As temperatures increase, the forces of attraction become less significant.

• Engineers and scientists who work with gases at high pressures or low temperatures cannot use the ideal gas equation.

• Johannes Van der Waals developed an equation to predict the behavior of real gases

• Van der Waals equation:P = (nRT/V – nb ) - ( n2 a/v2)Correction for volume of correction for molecularMolecules attraction

54. volume is decreased by nb. “b” is a measure of the actual volume occupied by a mole of gas molecules.

55.Pressure is decreased by the factor n2a/v2 which accounts for the attractive force between gas molecules.

• Look at table 10.3• Notice that the larger

molecules not only have larger volumes, but also greater intermolecular forces.

• Notice that the larger molecules not only have larger volumes, but also greater intermolecular forces.

gases chem ii chapter 10

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