1

Molecular Composition of Gases

Chapter 11

2

Gay-Lussac’s law of combining volumes of gases

• At constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers

3

Example

• When 2 L of hydrogen react with 1 L of oxygen 2 L of water vapor are produced.

• Write the balanced chemical equation:

4

You try

• When 1 L of hydrogen gas reacts with 1 L of chlorine gas, 2 L of hydrogen chloride gas are produced.

• Write the balanced chemical equation:

5

Avogadro's Law

• Equal volumes of gases at the same pressure and temperature contain the same number of molecules• Atoms can’t split diatomic

molecules• Gas volume is proportional to the

number of moleculesknV

6

Molar Volume

• 1 mole of any gas contains 6.022 x 1023 molecules.

• According to Avogadro’s law, 1 mole of any gas must have the same volume.

• Standard molar volume: molar volume of 1 mole of any gas at STP• 22.4 L

7

Example

• You are planning an experiment that requires 0.0580 mol of nitrogen monoxide gas. What volume in liters is occupied by this gas at STP?

• 1.30 L NO

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You try

• A chemical reaction produces 2.56 L of oxygen gas at STP. How many moles of oxygen are in this sample?

• 0.114 mol O2

9

Example

• Suppose you need 4.22 g of chlorine gas. What volume at STP would you need to use?

• 1.33 L Cl2

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You try

• What is the mass of 1.33 x 104 mL of oxygen gas at STP?

• 19.0 g O2

11

Discuss

• Explain Gay-Lussac’s law of combining volumes

• State Avogadro’s law and explain its significance.

12

Review

• Boyles Law:

• Charles Law:

• Avogadro’s Law:

PV

1

TV

nV

13

Math

• A quantity that is proportional to each of several quantities is also proportional to their product. Therefore:

nTP

V 1

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More math

• Convert a proportionality

xy

kxy

• to an equality by multiplying by a constant

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Therefore

• We can covert

nTP

V 1

• to

nTP

RV 1

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More neatly

P

nRTV

or

nRTPV

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This means….

• The volume of a gas varies directly with the number of moles and the temperature in Kelvin.

• The volume varies indirectly with pressure.

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What if…

• n and T are constant?• nRT is a constant, k

• Boyle’s Law

• n and P are constant?• nR/P is a constant, k

• Charles’s Law

kPV

kTV

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What if…

• P and T are constant?• RT/P is a constant, k

• Avogadro’s law

knV

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The ideal gas constant

• R• Value depends on units• SI units:

Kmol

J 314.8

R

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Other units

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Solving ideal gas problems

• Make sure the R you use matches the units you have.

• Make sure all your units cancel out correctly.

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Example

• A 2.07 L cylinder contains 2.88 mol of helium gas at 22 °C. What is the pressure in atmospheres of the gas in the cylinder?

• 33.7 atm

24

You try

• A tank of hydrogen gas has a volume of 22.9 L and holds 14.0 mol of the gas at 12 °C. What is the reading on the pressure gauge in atmospheres?

• 14.3 atm

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Example

• A reaction yields 0.00856 mol of oxygen gas. What volume in mL will the gas occupy if it is collected at 43 °C and 0.926 atm pressure?

• 240. mL

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You try

• A researcher collects 9.09 x 10-3 mol of an unknown gas by water displacement at a temperature of 16 °C and 0.873 atm pressure (after the partial pressure of the water vapor has been subtracted). What volume of gas in mL does the researcher have?

• 247 mL

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Finding mass

• Number of moles (n) equals mass (m) divided by molar mass (M).

nRTPV

M

mRTPV

PV

mRTM

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Example

• What mass of ethene gas, C2H4, is contained in a 15.0 L tank that has a pressure of 4.40 atm at a temperature of 305 K?

• 74.0 g

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You try

• NH3 gas is pumped into the reservoir of a refrigeration unit at a pressure of 4.45 atm. The capacity of the reservoir is 19.4 L. The temperature is 24 °C. What is the mass of the gas in kg?

• 6.03 x 10-2 kg

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Example

• A chemist determines the mass of a sample of gas to be 3.17 g. Its volume is 942 mL at a temperature of 14 °C and a pressure of 1.09 atm. What is the molar mass of the gas?

• 72.7 g/mol

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Density

PV

mRTM

V

mD

P

DRTM

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You try

• The density of dry air at sea level (1 atm) is 1.225 g/L at 15 °C. What is the average molar mass of the air?

• 29.0 g/mol

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Stoichiometry

• Involves mass relationships between reactants and products in a chemical reaction

• For gases, the coefficients in the balanced chemical equation show volume ratios as well as mole ratios• All volumes must be measured at the

same temperature and pressure

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Volume-Volume calculations

• From volume of one gas to volume of another gas

• Use volume ratios just like mole ratios in chapter 9

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Example

• Xenon gas reacts with fluorine gas to produce the compound xenon hexafluoride, XeF6. Write the balanced equation for this reaction.• Xe(g) + 3F2(g) XeF6(g)

• If a researcher needs 3.14 L of XeF6 for an experiment, what volumes of xenon and fluorine should be reacted?• 3.14 L of Xe and 9.42 L of F2

36

Example

• Nitric acid can be produced by the reaction of gaseous nitrogen dioxide with water.3NO2(g) + H2O(l) 2HNO3(l) + NO(g)

• If 708 L of NO2 gas react with water, what volume of NO gas will be produced?

• 236 L

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You try

• What volume of hydrogen gas is needed to react completely with 4.55 L of oxygen gas to produce water vapor?

• 9.10 L

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You try

• At STP, what volume of oxygen gas is needed to react completely with 2.79 x 10-2 mol of carbon monoxide gas, CO, to form gaseous carbon dioxide?

• 0.313 L

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You try

• Fluorine gas reacts violently with water to produce hydrogen fluoride and ozone according to the following equation:3F2(g) + 2H2O(l) 6HF(g) + O3(g)

• What volumes of O3 and HF gas would be produced by the complete reaction of 3.60 x 104 mL of fluorine gas?

• 1.20 x 104 mL O3 and 7.20 x 104 mL HF

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You try

• Ammonia is oxidized to make nitrogen monoxide and water4NH3(g) + 5O2(g) 4NO(g) + 6H2O(l)

• At STP, what volume of oxygen will be used in a reaction of 125 mol of NH3? What volume of NO will be produced?

• 3.50 x 103 L O2 and 2.80 x 103 L NO

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Volume-mass and mass-volume

• Converting from volume to mass or from mass to volume

• Must convert to moles in the middle

• Ideal gas law may be useful for finding standard conditions

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Example

• Aluminum granules are a component of some drain cleaners because they react with sodium hydroxide to release both heat and gas bubbles, which help clear the drain clog. The reaction is:2NaOH(aq) + 2Al(s) + 6H2O (l) 2NaAl(OH)4(aq) + 3 H2(g)

• What mass of aluminum would be needed to produce 4.00 L of hydrogen gas at STP?

• 3.21 g

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Example

• Air bags in cars are inflated by the sudden decomposition of sodium azide, NaN3 by the following reaction:2NaN3(s) 3N2(g) + 2Na(s)

• What volume of N2 gas, measured at 1.30 atm and 87 °C, would be produced by the reaction of 70.0 g of NaN3?

• 36.6 L

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You try

• What volume of chlorine gas at 38°C and 1.63 atm is needed to react completely with 10.4 g of sodium to form NaCl?

• 3.54 L Cl2

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Example

• A sample of ethanol burns in O2 to form CO2 and H2O according to the following reaction.C2H5OH + 3O2 2CO2 + 3H2O

• If the combustion uses 55.8 mL of oxygen measured at 2.26 atm and 40.°C, what volume of CO2 is produced when measured at STP?

• 73.3 mL CO2

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You try

• Dinitrogen pentoxide decomposes into nitrogen dioxide and oxygen. If 5.00 L of N2O5 reacts at STP, what volume of NO2 is produced when measured at 64.5 °C and 1.76 atm?

• 7.02 L NO2

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Review

• Diffusion: the gradual mixing of gases due to their random motion

• Effusion: gases in a container randomly pass through a tiny opening in the container

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Rate of effusion

• Depends on relative velocities of gas molecules.

• Velocity varies inversely with mass• Lighter particles move faster

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Kinetic energy

• Depends only on temperature• Equals

• For two gases, A and B, at the same temperature

• Each M stands for molar mass

2

2

1mv

22

2

1

2

1BBAA vMvM

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Algebra time

22

2

1

2

1BBAA vMvM

22BBAA vMvM

A

B

B

A

M

M

v

v2

2

A

B

B

A

M

M

v

v

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Rate of effusion

• Depends on relative velocities of gas molecules.

A

B

M

M

B ofeffusion of rate

A ofeffusion of rate

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Graham’s law of effusion

• The rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.

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Graham’s law

• Graham experimented with densities of gases, not molar masses.

• Density and molar mass are directly proportional

• So we can replace molar mass with density in the equation

A

B

density

density

B ofeffusion of rate

A ofeffusion of rate

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Use of Graham’s law

• Finding the molar mass• Compare rates of effusion of a gas

with known molar mass and a gas with unknown molar mass

• Use Graham’s law equation to solve for the unknown M

• Used to separate isotopes of uranium

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Example

• Compare the rates of effusion of hydrogen and helium at the same temperature and pressure.

• Hydrogen diffuses about 1.41 times faster

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Example

• Nitrogen effuses through a pinhole 1.7 times as fast as another gaseous element at the same conditions. Estimate the other element’s molar mass and determine its probable identity.

• 81 g/mol, krypton

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You try

• Estimate the molar mass of a gas that effuses at 1.6 times the effusion rate of carbon dioxide.

• 17 g/mol