Kinetic Molecular Theory

- Matter is composed of tiny particles (atoms,

molecules or ions) with definite and

characteristic sizes that never change. - The particles are in constant random motion, that

is they possess kinetic energy. Ek 1/2 mv2 - The particles interact with each other through

attractive and repulsive forces (electrostatic

interactions), that is the possess potential

energy. U mgh - The velocity of the particles increases as the

temperature is increased therefore the average

kinetic energy of all the particles in a system

depends on the temperature. - The particles in a system transfer energy form

one to another during collisions yet no net

energy is lost from the system. The energy of

the system is conserved but the energy of the

individual particles is continually changing.

PRESSURE

- A physical property of matter that describes the

force particles have on a surface. Pressure is

the force per unit area, P F/A - Pressure can be measured in
- atmosphere (atm)
- millimeters of mercury (mmHg)
- (torr) after Torricelli, the inventor of the

mercury barometer (1643) - pounds per square inch (psi)
- 1 atm 760 mmHg 760 torr 14.69 psi

TEMPERATURE

- A physical property of matter that determines the

direction of heat flow. - Measured on three scales.
- Fahrenheit oF Celsius

oC - Kelvin K
- oF (1.8 oC) 32 oC (oF - 32)/1.8
- K oC 273.15

- EMPIRICAL GAS LAWS
- Boyles Law P1V1 P2V2
- Charles Law V1 / T1 V2 / T2
- Combined Gas Law P1V1 / T1 P2 V2 / T2

Empirical Gas Laws

- 1. At 25oC, a sample of N2 gas under a pressure

of 689 mmHg occupies 124 mL in a piston-cylinder

arrangement before compression. If the gas is

compressed to 75 of its original volume, what

must be the new pressure (in atm) at 25oC? - First make a list of the measurements made
- P1689 mmHg V1 124 mL
- P2 ? V2 75 V1
- From the variables, choose the appropriate

equation, in this case Boyles Law P1V1P2V2 - (689 mmHg) (124 mL) P2 (0.75 x 124 mL)
- Solve for P2
- P2 (689mmHg) (124 mL) / (93 mL) 919 mmHg
- Now convert to atm
- 919 mmHg (1 atm / 760 mmHg) 1.21 atm

Empirical Gas Laws

- 2. The gas in a Helium filled ball at 25oC

exerts a volume of 4.2 L. If the ball is placed

in a freezer and the volume decreases to 1/8 of

its original value, what is the temperature

inside the ball? - First make a list of the measurements made
- V14.2 atm T1 25 oCc 273.15 298.15
- V2 1/8 P1 T2 ?
- From the variables, choose the appropriate

equation, in this case Charles Law V1/T1V2/T2 - (V1) / (298 K) (1/8 V1) / T2
- Solve for T2
- T2 (298 K) (1/8 V1) / (V1) 298 / 8

37.3 K or -235 oC - 3. A balloon containing 6.50 grams of NH3 has a

volume of 10.30 L at a temperature of 20.0oC and

a pressure of 689.2 torr. What would be the

pressure of NH3 if the volume decreased to 2.50 L

without a change in temperature?

Pressure of NH3 2.84 x 103 torr.

COMBINED GAS LAW

- A gas occupies a volume of 720 mL at 37oC and 640

mmHg pressure. Calculate the volume the gas would

occupy at 273 K and 1 atm. - P1V1 / T1 P2V2 / T2
- rearranged to solve for V2 is
- V2 P1 V1 T2 / P2 T1
- V2 (640 mmHg)(720 mL) (273 K) / (760 mmHg)

(310 K) - V2 534 mL

COMBINED GAS LAW

- A gas occupies a volume of 720 mL at 37oC and 640

mmHg pressure. - Calculate the pressure if the temperature is

increased to 1000oC the volume expands to 900

mL. - Calculate the temperature if the pressure is

decreased to 10 torr the volume is reduced to

500 mL.

P2 2.1 x 103 mmHg

T2 3.4 K or -270 oC

PRACTICE PROBLEM 20a

1. You prepared carbon dioxide by adding

aqueous HCl to marble chips, calcium carbonate.

According to your calculations, you should obtain

79.4 mL of carbon dioxide at 0 oC and 760 mmHg.

How many milliliters of gas would you obtain at

27oC at the same pressure? 2. Divers working

from a North Sea drilling platform experiences

pressures of 50 atm at a depth of 5.0 x 102 m.

If a balloon is inflated to a volume of 5.0 L

(the volume of a lung) at that depth at a water

temperature of 4.0oC, what would the volume of

the balloon be on the surface (1.0 atm) at a

temperature of 11 oC? 3. What volume would

5.30 L of H2 gas at 0 oC and 760 mmHg occupy if

the temperature was increased to 70oF and the

pressure to 830 torr? 4. The pressure gauge

reads 125 psi on a 0.140-m3 compressed air tank

when the gas is at 33.0 oC. To what volume will

the contents of the tank expand if they are

released to an atmospheric pressure of 751 torr

and a temperature of 13oC? 5. A gas has a

volume of 397.0 mL at 14.70 atm. What will be

its pressure (in torr) if the volume is changed

to 4.100 L?

87.3 mL

256 L

5.23 L

1.126 m3

1082 torr

PRACTICE PROBLEM 20a

- 6. Which of the following statements is false?
- a) If the Celsius temperature is doubled, the

pressure of a fixed volume of gas would double. - b) All collisions between gas molecules are

perfectly elastic (no energy is lost) according

to KMT. - c) The volume of gas is inversely proportional

to the temperature of gas present (P constant) - d) Gases are capable of being greatly

compressed. - 7. Which of the following statements are true?
- a) In a large container of O2 gas the pressure

exerted by the oxygen will be greater at the

bottom of the container. - b) Of the three states of matter, gases are the

most compact and the most mobile. - c) The formula of ozone is 3 O2.
- d) Molecules of O2 gas and H2 gas at the same

temperature will have the same average kinetic

energies and the same average velocities.

C

D

GROUP STUDY PROBLEMS

1. A sample of O2 gas initially at 0oC and 1.0

atm is transferred from a 2-L container to a 1-L

container at constant temperature. a) What

effect does this change have on the average

kinetic energy of the gas molecules? b) What

effect does the total number of collisions of O2

molecules with the container walls in a unit

time? 2. At constant pressure, a student needed

to decrease a volume of 155 mL of Ne gas by

32.0. To what temperature, (in oC), must the

gas be cooled if the initial temperature was

21oC? 3. A sample of CO2 gas has a volume of

125.0 L at a pressure of 789 torr and a

temperature of 30oC. What will be the

temperature if the pressure was increased to 900

torr the volume decreased to 95.0 L? 4. F2 gas,

which is dangerously reactive, is shipped in

steel containers of 30.0 L capacity, at a

pressure of 10.0 atm at 26.0 oC. What should be

the volume of the tank if the pressure is

increased to 820.0 torr the temperature is 43.0

oC?