Let’s look at your discussions

Learning Objectives

• 3.4 The student is able to relate quantities

(measured mass of substances, volumes of

solutions, or volumes and pressures of

gases) to identify stoichiometric

relationships for reaction.

Elements that exist as gases at 250C and 1 atmosphere

5.1

5.1

• Gases assume the volume and shape of their containers.

• Gases are the most compressible state of matter.

• Gases will mix evenly and completely when confined to

the same container.

• Gases have much lower densities than liquids and solids.

5.1

Physical Characteristics of Gases

Kinetic Molecular Theory of Gases

1. A gas is composed of molecules that are separated from

each other by distances far greater than their own

dimensions. The molecules can be considered to be points;

that is, they possess mass but have negligible volume.

2. Gas molecules are in constant motion in random directions.

Collisions among molecules are perfectly elastic.

3. Gas molecules exert neither attractive nor repulsive forces

on one another.

4. The average kinetic energy of the molecules is proportional

to the temperature of the gas in kelvins. Any two gases at

the same temperature will have the same average kinetic

energy

5.7

Units of Pressure

1 pascal (Pa) = 1 N/m2

1 atm = 760 mm Hg = 760 torr

= 101,325 Pa

= 14.7 psi

= 29.92 in. Hg

5.2Barometer

Pressure = ForceArea

(force = mass x acceleration)

Sea level 1 atm

4 miles 0.5 atm

10 miles 0.2 atm

5.2

Boyle’s LawP α 1/VThis means Pressure and

Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). For example, P goes up as V goes down.

P1V1 = P2 V2

Robert Boyle

(1627-1691).

Son of Earl of

Cork, Ireland.

Charles’s LawIf n and P are constant,

then V α T

V and T are directly proportional.

V1 V2

=

T1 T2

• If one temperature goes up, the volume goes up!

Jacques Charles (1746-

1823). Isolated boron

and studied gases.

Balloonist.

Plots of V vs. T(ºC)

Charles’s Law

Experiment results

Demonstrates a

unique absolute

zero at -273.15 oC

Gay-Lussac’s LawIf n and V are

constant, then P α T

P and T are directly proportional.

P1 P2

=

T1 T2

If one temperature goes up, the pressure goes up!

Joseph Louis Gay-

Lussac (1778-1850)

Combined Gas Law• The good news is that you don’t

have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!

P1 V1 P2 V2

=

T1 T2

No, it’s not related to R2D2

And now, we pause for this

commercial message from STP

OK, so it’s really not THIS kind

of STP…

STP in chemistry stands for

Standard Temperature and

Pressure

Standard Pressure =

1 atm

(or an equivalent)

Standard Temperature

= 0 deg C (273 K)

STP allows us to

compare amounts of

gases between different

pressures and

temperatures

Avagadro’s law

Amadeo Avagadro noticed this first in 1811.

Basically the more moles of a gas, then the higher the

volume.

V1/n2 =V2/n2

What does this statement assume? Avogadro’s Law - equal

volumes of gas contain equal particles of gas

V = k n

Ideal Gas Equation

5.4

Charles’ law: V a T (at constant n and P)

Avogadro’s law: V a n (at constant P and T)

Boyle’s law: V a (at constant n and T)1P

V anT

P

V = constant x = RnT

P

nT

PR is the gas constant

PV = nRT

The conditions 0 0C and 1 atm are called standard

temperature and pressure (STP).

PV = nRT

R = PV

nT=

(1 atm)(22.414L)

(1 mol)(273.15 K)

R = 0.082057 L • atm / (mol • K)

5.4

Experiments show that at STP, 1 mole of an ideal

gas occupies 22.414 L.

Gas Stoichiometry

What is the volume of CO2 produced at 370 C and 1.00

atm when 5.60 g of glucose are used up in the reaction:

C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l)

g C6H12O6 mol C6H12O6 mol CO2 V CO2

5.60 g C6H12O6

1 mol C6H12O6

180 g C6H12O6

x6 mol CO2

1 mol C6H12O6

x = 0.187 mol CO2

V = nRT

P

0.187 mol x 0.0821 x 310.15 KL•atm

mol•K

1.00 atm= = 4.76 L

5.5

Dalton’s Law of Partial Pressures

V and T

are constant

P1 P2 Ptotal = P1 + P2

5.6

Consider a case in which two gases, A and B, are in a

container of volume V.

PA = nART

V

PB = nBRT

V

nA is the number of moles of A

nB is the number of moles of B

PT = PA + PB XA = nA

nA + nB

XB = nB

nA + nB

PA = XA PT PB = XB PT

Pi = Xi PT

5.6

mole fraction (Xi) = ni

nT

A sample of natural gas contains 8.24 moles of CH4,

0.421 moles of C2H6, and 0.116 moles of C3H8. If the

total pressure of the gases is 1.37 atm, what is the

partial pressure of propane (C3H8)?

Pi = Xi PT

Xpropane = 0.116

8.24 + 0.421 + 0.116

PT = 1.37 atm

= 0.0132

Ppropane = 0.0132 x 1.37 atm = 0.0181 atm

5.6

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

Bottle full of oxygen

gas and water vapor

PT = PO + PH O2 2 5.6

5.6

Chemistry in Action:

Scuba Diving and the Gas Laws

P V

Depth (ft) Pressure

(atm)

0 1

33 2

66 3

5.6

Ideal vs. Real Gases

• All of the gases are real!!! They just

behave “ideally” at certain temperatures

and pressures.

• Think of the KMT assumptions, what

conditions would gases “fail” to act ideally.

• Low temperatures (gases condense) & High

pressures (force the gases together so they

have to interact)

Deviations from Ideal Behavior

1 mole of ideal gas

PV = nRT

n = PVRT

= 1.0

5.8

Repulsive Forces

Attractive Forces

Plot of PV/nRT vs. P for N2 Gas

This graph shows

that at higher

temperatures gases

behave closer to

ideal even at high

pressures.

Recall that gases

behave “ideally” at

low pressures and

high temperatures.

van der Waals Equation

• van der Waals equation is entire gas law

relationship with corrections for real volume and

molecular attractions. pg.225 textbook with

Table 5.3 for some common gases

(Pobs + correction) x ( V - nb) = nRT

This formula is also given on AP exam sheet.

Values of the van der Waals

Constants for Common Gases

a is a measure of

intermolecular attractions (it

is the correction to the

pressure to account for

attractions for each other)

b is a measure of size of

the molecule (it is the

volume correction)

The distribution of speeds

for nitrogen gas molecules

at three different temperatures

The distribution of speeds

of three different gases

at the same temperature

5.7

urms = 3RTM

Velocity of a Gas

Gas diffusion is the gradual mixing of molecules of one gas

with molecules of another by virtue of their kinetic properties.

5.7

NH3

17 g/mol

HCl

36 g/mol

NH4Cl

Gas Diffusionrelation of mass to rate of diffusion

• HCl and NH3 diffuse

from opposite ends of

tube.

• Gases meet to form

NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl

forms closer to HCl

end of tube.

GAS DIFFUSION AND EFFUSION

• diffusion is the

gradual mixing of

molecules of

different gases.

• effusion is the movement of molecules through a small hole into an empty container.

GAS DIFFUSION AND EFFUSION

Graham’s law governs effusion and diffusion of gas molecules. KE=1/2 mv2

Thomas Graham, 1805-1869.

Professor in Glasgow and London.

Rate of effusion is

inversely proportional

to its molar mass.

M of A

M of B

Rate for B

Rate for A