1 / 22

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) - 1 atm 760 mmHg 760 torr

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

- GAS LAWS
- Boyles Law P1V1 P2V2
- Charles Law V1 / T1 V2 / T2
- Guy-Lussacs Law P1 / T1 P2 / T2
- Avogadros Law V1 / n1 V2 / n2
- Combined Gas Law P1V1 / T1 P2 V2 / T2
- Ideal Gas Law PV nRT
- P pressure (atm) V volume (L)
- n chemical amount (mol) T Temperature (K)
- R ideal gas constant 0.08206 L-atm / mol-K

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 gases in a rigid Helium filled ball at

25oC exerts a pressure of 4.2 atm. If the ball

is placed in a freezer and the pressure decreases

to 1/8 of its original value, what is the

temperature inside the ball? - First make a list of the measurements made
- P14.2 atm T1 25 oCc 273.15 298.15
- P2 1/8 P1 T2 ?
- From the variables, choose the appropriate

equation, in this case Guy Lussacs Law

P1/T1P2/T2 - (P1) / (298 K) (1/8 P1) / T2
- Solve for T2
- T2 (298 K) (1/8 P1) / (P1) 298 / 8

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

volume of 550L at a certain temperature and

pressure. How many grams of NH3 would have to

be removed from the balloon in order for the

volume to decrease to 250 L under the same

conditions?

Mass of NH3 removed 60.3 g of NH3.

Avogadros Hypothesis

- Avogadro pictured the moving molecule as

occupying a small portion of the larger space

apparently occupied by the gas. Thus the

volume of the gas is related to the spacing

between particles and not to the particle size

itself. - Imagine 3 balloons each filled with a different

gas (He, Ar, Xe). These gases are listed in

increasing particle size, with Xe being the

largest atom. According to Avogadros

Hypothesis, the balloon filled with one mole of

He will occupy that same volume as a balloon

filled with one mole of Xe. - So for a gas, the volume and the moles are

directly related. V a n

Avogadros Hypothesis

- A sample of N2 gas at 3.0 atm and 20.0oC is known

to occupy a volume of 1.43 L. What volume would

a 0.179 mole sample of NH3 gas occupy at the same

pressure and temperature?

First calculate the number of moles of nitrogen

gas PV nRT where P 3.0 atm, V 1.43

L, R 0.082 L-atm/mol-K, and T 20.0 oC 273

293K n PV / RT (3.0 atm x

1.43L) / (0.082 L-atm/mol-K x 293K)

0.179 moles of N2 So since the moles of N2 is

0.179 mol and the moles of ammonia is 0.179 mol

according to Avogadros hypothesis the volume of

NH3 at that pressure and that temperature is 1.43

L, the same!!!

At STP, gas molecules are so far apart that for 1

mole of gas, the overall volume does not

change.STP P 1 atm T 273 K

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 STP. - 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

IDEAL GAS LAW

- . What is the pressure inside a gas balloon if it

filled with 852 g of Xe gas at 25.0oC and

occupies a volume of 7.00 L? - P ? 852 g Xe ( 1 mol / 131 g) 6.50 mol
- V 7.00 L T 25oC 273 298 K
- P nRT
- V
- P (6.50 mol) (0.082 L-atm / mol-K) (298 K)
- 7.00 L
- P 22.7 atm

IDEAL GAS LAW

- What would be the temperature of 100 g of Ar gas

contained in a 500 L sealed container at 0.8976

atm. - How much would a balloon weigh if it contained

40.0 L of O2 gas at 987 mmHg and 45.3 oC?

T2 1914 oC

mass O2 63.7 g

DENSITY OF A GAS

- The density of a gas at STP can be calculated by

- dSTP molar mass/molar volume
- Calculate the density of hydrogen sulfite gas at

STP. - Identify an unknown homonuclear diatomic gas that

was found to have a density of 3.165 g/L at STP.

d (STP) (82 g/mol) / 22.4 L/mol) 3.66 g/L

Cl2

Properties of Gases

- DIFFUSION
- Diffusion is the ability of two or more gases to

mix spontaneously until a uniform mixture is

formed. - Example A person wearing a lot of perfume walks

into an enclosed room, eventually in time, the

entire room will smell like the perfume.

- EFFUSION
- Effusion is the ability of gas particles to pass

through a small opening or membrane from a

container of higher pressure to a container of

lower pressure. - The General Rule is The lighter the gas, the

faster it moves. - Grahams Law of Effusion
- Rate of effusion of gas A v(molar mass B /

molar mass A) - Rate of effusion of gas B
- The rate of effusion of a gas is inversely

proportional to the square root of the molar mass

of that gas.

DALTONS LAW OF PARTIAL PRESSURES

- If there is more than one gas present in a

container, each gas contributes to the total

pressure of the mixture. - Ptotal Pgas A P gas B Pgas C
- If the total pressure of a system was 2.5 atm,

what is the partial pressure of carbon monoxide

if the gas mixture also contained 0.4 atm O2 and

1.48 atm of N2?

PT - PO2 - PN2 PCO 2.5 atm - 0.4 atm - 1.48

atm 0.62 atm

STOICHIOMETRY THE GAS LAWS

- 1. Write a balanced chemical equation
- 2. Convert to moles (if gas, use PVnRT or Molar

Volume) - 3. Use the mole ratio to convert from moles of

A to moles of B. - 4. Convert moles of B to desired measurement,

if a gas use PVnRT.

1. What volume of O2 is needed to combust 348.0 L

of C3H8? C3H8 5 O2 ? 3 CO2 4 H2O Due to

Avogadros Hypothesis, the moles of a gas are

directly related to the volume of a gas therefore

it is possible to use the mole ratio on volumes

of gas. 348.0 L C3H8 (5 mol O2 / 1 mol C3H8)

1740 L O2

STOICHIOMETRY THE GAS LAWS

2. How many grams of CO2 is produced from 348.0 L

of C3H8 if the temperature is 40.0oC and the

pressure is 654 torr? C3H8 5 O2 ? 3 CO2 4

H2O P 654 torr (1 atm / 760 torr) 0.861

atm T 40oC 273 313 K PV / RT n

(0.861 atm) (348.0 L)

/(0.082 L-atm/mol-K) (313 K)

11.67 mol of C3H8 11.67 mol C3H8 (3 mol CO2

/ 1 mol C3H8) 35.02 mol CO2 35.02 mol CO2

(44 g / 1 mol) 1541 g of CO2

STOICHIOMETRY THE GAS LAWS

3. In lab, you decomposed potassium chlorate

into oxygen and potassium chloride. What volume

of O2 at STP can be formed from 3.65 g of

potassium chlorate? 2 KClO3 ? 3 O2 2 KCl 3.65

g (1 mol / 122.6g) 0.02977 mol KClO3 0.02977

mol KClO3 (3 mol O2 / 2 mol KClO3) 0.04466 mol

O2 0.04466 mol O2 ( 22.4 L / 1 mol) 1.00 L

PRACTICE PROBLEMS 20

1. Both hydrogen and helium have been used as

buoyant gas in blimps. If a small leak were to

occur, which gas would effuse more rapidly and by

what factor? 2. At STP, 560 mL of a gas has a

mass of 1.08 g. What is the molecular weight of

the gas? 3. 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? 4. A 50.0 L cylinder of

nitrogen has a pressure of 17.1 atm at 23oC.

What is the mass of nitrogen in the cylinder? 5.

When a 2.0 L bottle of concentrated HCl was

spilled, 3.0 kg of CaCO3 was required to

neutralize the spill. CaCO3 (s) 2HCl (aq)

? CaCl2 (aq) H2O (l) CO2 (g) What

volume of CO2 gas was released by the

neutralization at 735 mmHg and 20 oC?

Hydrogen effuses first by a factor of 1.41

43.2 g/mol

87.3 mL

986 g

745 L

Group Study Problem 20

1. Measured at 65 oC and 500.0 torr, the mass

of 3.21 L of a gas is 3.5 g. What is the molar

mass of this gas 2. A 100.0 mL sample of air is

analyzed and found to contain 0.835 g N2, 0.0640

g CO2 and 0.197 g O2 at 35 oC. What is the

total pressure of the sample and the partial

pressure of each component? 3. What volume

would 5.30 L of H2 gas at STP occupy if the

temperature was increased to 70oF and the

pressure to 830 torr? 4. 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? 5. Hydrogen gas is

produced by the complete reaction of 8.34 g of

aluminum metal with an excess of gaseous hydrogen

sulfate. How many liters of hydrogen will be

produced if the temperature is 50.0 oC and the

pressure is 0.950 atm?

Group Study Problem

Answers 1. 45.9 g/mol 2. PN27.53 atm,

PO21.55 atm, PCO20.380 atm PT 9.46

atm 3. 5.23 L 4. 256 L 5. 12.9 L