Download - Copyright©2000 by Houghton Mifflin Company. All rights reserved. 1 Gases

Copyright©2000 by Houghton Mifflin Company. All rights reserved.

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Gases


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A Gas Uniformly fills any container. Can be compressed. Mixes completely with any other gas Exerts pressure on its surroundings. Can diffuse into other gases. Can be described in terms of its volume,

temperature, pressure, and the amount present.


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Pressure

is equal to force/unit area

SI units = Newton/meter2 = 1 Pascal (Pa)

1 standard atmosphere = 101,325 Pa

1 standard atmosphere = 1 atm =

760 mm Hg = 760 torr


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A Torricellian Barometer

At sea level, latitude 45o north (or south), the average atmospheric pressure supports a column of mercury 760 mm high in a simple mercury barometer at 0oC This average pressure is called one atmosphere.


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The Effects of Decreasing the Volume of a Sample of Gas at Constant Temperature


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Boyle’s Law*

Pressure Volume = Constant (T = constant)

P1V1 = P2V2 (T = constant)

V 1/P (T = constant)

(*Holds precisely only at very low pressures.)


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Plotting Boyle’s Data from Table 5.1


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A Plot of PV versus P for Several Gases at Pressures Below 1 ATM


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A gas that strictly obeys Boyle’s Law is called an ideal gas.


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Example: Boyle’s Law

At 25 oC, a sample of oxygen occupies 100. mL under a pressure of 380. torr. What volume would it occupy under a pressure of 1.00 atm at the same temperature?


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Answer

50.0 mL


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Example

At 100. oC a sample of neon occupies 200. mL under a pressure of 4.00 atmospheres. What must the pressure be for it to occupy 800. mL at 100. oC?


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Answer

1.00 atm.


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The Effects of Increasing the Temperature of a Sample of Gas at Constant Pressure


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Charles’s Law

The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.

V = bT (P = constant)

b = a proportionality constant


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Charles’s Law

VT

VT

P1

1

2

2 ( constant)


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Amazing

Experiments have shown that when a 273 mL sample of gas at 0 oC is heated to 1 oC, its volume increases by 1 mL to 274 mL. Conversely each degree the gas is cooled its volume decreases 1 mL. What will the volume of the gas be at –273 oC?


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Plots of V Versus T (ºC) for Several Gases


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The Kelvin Temperature Scale

The temperature at –273 oC, the lowest temperature possible is known as absolute zero. It is the basis of the Kelvin (absolute) temperature.

K = oC + 273


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Plots of V Versus T


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Example Charles’ Law

A sample of hydrogen, H2, occupies 100. mL at 25 oC and 740. torr. What volume would it occupy at 50.0 oC and 740. torr?


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Answer

108 mL


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Example

A sample of oxygen, O2, occupies 200. mL at 100. oC and 1.00 atm. At what temperature (oC) will the oxygen occupy 400. mL if the pressure remains constant?


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Answer

746 K

473 oC


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The Effects of Increasing the Temperature of a Sample of Gas at Constant Volume:

Who’s Law?


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Gay-Lussac’s Law

P1 P2

T1 T2

=


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Combined Gas Law

Boyle’s and Charles’ Laws can be combined together into the following mathematical expression:

P1V1 = P2V2

T1 T2


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A very convenient form:

V2= V1 P1 T2 P2 T1

The relationship has six variables. If any five are known, the sixth can be calculated.


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Example

A sample of nitrogen, N2, occupies 200. mL at 57 oC under a pressure of 840. torr. What volume would it occupy at 0 oC and 1.00 atm pressure?


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Answer

183 mL


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Example

A sample of methane, CH4, the main component of natural gas occupies 400. mL at 96 oC under a pressure of 0.500 atm. What volume would it occupy at 0 oC under a pressure of 1200 torr?


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Answer

93.7 mL


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Avogadro’s Law

For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures).

V = an

a = proportionality constantV = volume of the gasn = number of moles of gas


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Standard Temperature and Pressure

“STP”P = 1 atmosphere

T = CThe molar volume of an ideal gas is 22.42 liters at STP


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A Mole of Any Gas Occupies a Volume of Approximately 22.4 L at STP


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Example

What volume does 36.3 g of oxygen, O2, occupy at STP?


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Answer

25.4 L


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Molecular Weight

• Application of the gas laws provides a method of calculating the molecular weight of a gas.

• This plus elemental analysis provides mechanism for determining molecular formula


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Example

If 2.00 g of a gas occupies 560.mL at STP, what is its molecular weight?


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Answer

80.0 g/mol


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Example

A compound containing only carbon and hydrogen is 80.0% C and 20.0% H by mass. At STP 280. mL of the gas weighs 0.375 g. What is the molecular formula for the compound?


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Answer

C2H6


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Ideal Gas Law

An equation of state for a gas. “state” is the condition of the gas at a given

time. Can be determined by combining Boyle’s

Law, Charles’ Law, and Avogadro’s Law


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Ideal Gas LawPV = nRT

R = proportionality constant = 0.0821 L atm mol

P = pressure in atm V = volume in liters n = moles T = temperature in Kelvins Holds closely at P < 1 atm


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Example

What volume does 48.0 g of methane, CH4, occupy at 140. oC under a pressure of 1280 torr?


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Answer

60.4 L


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Example

A 250. mL flask contains a mixture of nitrogen, oxygen, and helium at a temperature of 27 oC and a pressure of 0.850 atm. How many moles of gas are present?


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Answer

8.63 x 10-3 moles


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Example

What pressure in kilopascals is exerted by 0.480 g of carbon dioxide in a 1.00 L flask at 100 oC?


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Answer

33.8 kPa


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Density

Density has the units of mass per unit volume. We can arrange the ideal gas equation to obtain density

D =PM

RT

Where M is the gram molar mass;D is in g/L


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Example

What is the density of formaldehyde, CH2O, vapors at 95 oC and a pressure of 650. torr?


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Answer

0.849 g/L


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Gram Molecular Mass

The Ideal Gas Equation can be rearranged to solve directly for gram molecular mass.

mRT

PVM =


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Example

A 0.1842 g sample of phosphorus vapor in a 169 mL bulb exerts a pressure of 45.6 kPa at 350. oC. Calculate both the molecular mass and molecular formula of phosphorus vapor. (R = 8.31 kPa L/ mol K)


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Answer

124 g/mol

P4


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Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .


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Partial Pressure of Each Gas in a Mixture


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Example

If 100 mL of hydrogen and 100. mL of oxygen, both measured at 25 oC and 1.00 atm pressure, were forced into one of the containers at 25 oC, what would be the total pressure of the two gases?


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Answer

2 atm


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Collecting Gas Over Water• A gas can be collected by displacement of water• This results in a mixture of gases:

– The gas you are collecting

– Water vapor


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Collecting Gas Over Water

• Vapor pressure is temperature dependent.

• Ptotal = Pgas + Pwater

• How do we correct for the water vapor?

ExampleA sample of solid potassium chlorate (KClO3) was heated in a test tube and decomposed by the following reaction:

2KClO3(s) 2KCl(s) + 3O2(g)

The oxygen produced was collected by displacement of water at 22.0 C at a total pressure of 754 torr. The volume of the gas collected was 0.650 L, and the vapor pressure of the water at 22.0 is 21 torr. Calculate the partial pressure of O2 in the gas collected and the mass of KClO3 in the sample that was decomposed.


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Solution

• First, find the partial pressure of O2 from Dalton’s Law of partial pressures

• Next, use the ideal gas law to find the number of moles of O2

• Calculate the moles of KClO3 needed to produce this quantity of O2


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Answers

• PO2 = 733 torr

• nO2 = 2.59 x 10-2

• 2.12 g KClO3


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Kinetic Molecular Theory

1. Gases consist of tiny discrete molecules that are relatively far apart.

2. Gases consist of molecules in continuous random motion.

3. Molecular collisions are elastic

4. The average kinetic energy of gaseous molecules is proportional to the absolute temperature. KE = ½ mv2


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Examples

• Explain Gay Lussac’s Law on the basis of the Kinetic Molecular Theory

• Explain Boyle’s Law on the basis of the Kinetic Molecular Theory

• Explain Charles’ Law on the basis of the Kinetic Molecular Theory


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Effusion: describes the passage of gas into an evacuated chamber.

Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.


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The Effusion of a Gas into an Evacuated Chamber


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Rate of effusion for gas 1Rate of effusion for gas 2

2

1

MM

Distance traveled by gas 1Distance traveled by gas 2

2

1

MM

Effusion:Effusion:

Diffusion:Diffusion:


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Example

The average speed of oxygen molecules at 25 oC is 4.8 x 104 cm/s. What would be the average speed of sulfur dioxide molecules at the same temperature?


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Answer

3.39 x 104 cm/s


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Example

The time required for a volume of an unknown gas to effuse through a pin hole was 71.5 sec. The time required for the same volume of oxygen was 63.0 sec. Calculate the molecular weight of the unknown gas.


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Answer

41.2 g/mol


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HCI(g) and NH3(g) Meet in a Tube


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Real Gases

• At ordinary temperatures and pressures, most gases obey the gas laws reasonably well.

• Under what conditions does a gas deviate significantly form ideality? Why?


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Real Gases

Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).


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Real Gases

P +( n2 a

V2 ) (V – n b) = nRT

van der Waals Equation

corrected pressurecorrected pressure

PPidealideal

corrected volumecorrected volume

VVidealideal


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Van der Waals’ Constants

Gas a (L2atm/mol2 b (L/mol)

He 0.03412 0.02370

O2 1.360 0.03803

Cl2 6.493 0.05622

NH3 4.170 0.03707

H2O 5.464 0.03049


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Example

Calculate the pressure in atmospheres exerted by 48.0 g of ammonia, NH3, in a 1.00 L container at 100. oC using the ideal gas equation.


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Answer

86.5 atm


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Now…

Solve the previous problem using the van der Walls equation.

NH3 4.170 0.0371

Gas a (L2atm/mol2 b (L/mol)

P +( n2 a

V2 ) (V – n b) = nRT


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Answer

63.3 atm


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The Meaning of Temperature

Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

(KE)32avg RT


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Path of One Particle in a Gas


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A Plot of the Relative Number of O2 Molecules That Have a Given Velocity at STP


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A Plot of the Relative Number of N2 Molecules That Have a Given Velocity at Three Temperatures

Download - Copyright©2000 by Houghton Mifflin Company. All rights reserved. 1 Gases

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