Kinetic Molecular Theory of Gases

1. Volume occupied by gas is negligible compared to the volume of container.

2. Gas molecules exert neither attractive nor repulsive forces on one another (i.e. there are no intermolecular forces).

3. Gas molecules are in constant random motion.

4. Collisions among molecules are perfectly elastic: no kinetic energy is lost in collisions.

1

Most probable speed vs T

The most probable speed increases as the temperature increases.

2

Boyle’s Law

5

P α 1/V

If volume is decreased, then the frequency of

collisions in the container increases and

pressure increases. (at constant T and n)

Charles’s Law

6

V α T

Higher temperature increases KE of gas

molecules which would increase pressure. To

keep P constant, volume must increase.

Avogadro’s Law

7

V α n

Adding more gas molecules would increase

collisions, therefore pressure. To keep P

constant, volume must increase.

Dalton’s Law of Partial Pressure

8

Each gas acts independently of one another.

The more substances colliding with each other,

the higher the pressure.

Ideal Gas Law and Stoichiometry

What is the volume of CO2 produced at

37°C and 1.00 atm when 5.60 g of glucose

is consumed in the following reaction:

9

P, V, T

of gas A

Amount (mol)

of gas A

Amount (mol)

of gas B

P, V, T

of gas B

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

Balanced

Equation

4.76 L

Exercise

Sulfuric acid reacts with sodium

chloride to form aqueous sodium

sulfate and hydrogen chloride gas.

How many milliliters of gas form at

STP when 0.117 kg of sodium chloride

reacts with excess sulfuric acid?

10

4.48 x 104 mL

Exercise

The alkali metals react with the

halogens to form ionic metal halides.

What mass of potassium chloride

forms when 5.25 L of chlorine gas at

0.950 atm and 293 K reacts with 17.0

g of potassium?

11

30.9 g KCl

Real Gases

The ideal gas law fails at high pressures and

low temperatures.

At moderate P: intermolecular forces

between gas particles alter elastic collisions.

At high P: molecule volume becomes a

significant portion of total volume.

12

At Moderately High Pressure

13

Low Pressure Moderate Pressure

Pactual < Pideal

At High Pressure

14

Low Pressure High Pressure

Vactual > Videal

Van de Waals Equation

Used to predict the behavior of

non-ideal gases at low T and high P.

Corrects the ideal gas law for 2

things:

◦ a accounts for intermolecular

forces of attraction

◦ b accounts for volume of gas

molecules 15

Deviations from Ideal Behavior

1 mole of ideal gas:

16

n = PV RT

= 1.0

Repulsive Forces

Attractive Forces

Practice Problem

1. How many grams of potassium

chlorate decompose to potassium

chloride and 638 mL of O2 at 128 ºC

and 752 torr?

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

17

[5.39]

Practice Problem

2. Roasting galena [lead(II) sulfide] is

an early step in the industrial

isolation of lead. How many liters of

sulfur dioxide, measured at STP, are

produced by the reaction of 3.75 kg

of galena with 228 L of oxygen gas

at 220 ºC and 2.0 atm? Lead(II)

oxide also forms.

18

[5.51]

Practice Problem

3. Hemoglobin is the protein that

transports O2 through the blood

from the lungs to the rest of the

body. In doing so, each molecule of

hemoglobin combines with four

molecules of O2. If 1.00 g of

hemoglobin combines with 1.53 mL

of O2 at 37 ºC and 743 torr, what is

the molar mass of hemoglobin?

19

[5.68]

Practice Problem 4. A baker uses sodium hydrogen carbonate

(baking soda) as the leavening agent in a

banana-nut quickbread. The baking soda

decomposes according to two possible

reactions:

a. 2NaHCO3(s) Na2CO3(s) + H2O(l) + CO2(g)

b. NaHCO3(s) + H+(aq) H2O(l) + CO2(g) +

Na+(aq)

Calculate the volume (in mL) of CO2 that

forms at 200 ºC and 0.975 atm per gram of

NaHCO3 by each of the reaction processes. 20

[5.69]

Announcement

Quiz #5 on Feb 4, Wednesday

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