Chapter 5 Gas Laws and Kinetic Theory_2

ChaPtEChaPtER 5 :R 5 :

GAS LAWS & GAS LAWS &

KINETIC KINETIC

THEORYTHEORY

SCOPE OF STUDYSCOPE OF STUDY

Gas Laws

& Kinetic

Theory

Gas Laws

& Kinetic

TheoryIdeal Gas

law

Real Gas

Gay-Lussac’s

Law

Boyle’s Law

Charles’ Law

Absolute Temperatur

e

gasesgasesElements that exist as gases at 250C and 1 atmosphere

gasesgases

gasesgases

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.

Physical Characteristics of Gases

gasesgases

By international agreement, the reference element is chosen to be the

most abundant type of carbon, called carbon-12, and its atomic mass is

defined to be exactly twelve atomic mass units, or 12 u.

Atomic mass unit, Atomic mass unit, uu

The molecular mass of a molecule is the sum of the atomic masses of

its atoms.

For instance, hydrogen and oxygen have atomic masses of

1.007 94 u and 15.9994 u, respectively.

The molecular mass of a water molecule (H2O) is:

2(1.007 94 u) + 15.9994 u = 18.0153 u.

Molecular massMolecular mass

AVOGADRO’S AVOGADRO’S NUMBERNUMBER

The number of atoms per mole is known as Avogadro's number NA,

after the Italian scientist Amedeo Avogadro (1776–1856):

Number of molesNumber of molesThe number of moles n contained in any sample is the number of

particles N in the sample divided by the number of particles per

mole NA (Avogadro's number):

The number of moles contained in a sample can also be found from

its mass.

BOYLE’S LAWBOYLE’S LAW

DEFINITIONDEFINITION

The volume of a gas is inversely proportional

to the absolute pressure applied to it when

temperature is constant

BOYLE’S LAWBOYLE’S LAWGRAPH :


P α 1/VP α 1/V

P x V = constantP x V = constant

P1 x V1 = P2 x V2P1 x V1 = P2 x V2

Constant temperature

Constant amount of gas

Constant temperature

Constant amount of gas

FORMULA

Example :

A sample of chlorine gas occupies a volume of 946 mL at a

pressure of 726 mmHg. What is the pressure of the gas (in mmHg)

if the volume is reduced at constant temperature to 154 mL?


P1 x V1 = P2 x V2

P1 = 726 mmHg P2 = ?

V1 = 946 mLV2 = 154 mL

P2 = P1 x V1

V2

726 mmHg x 946 mL

154 mL= = 4460 mmHg

charles’S LAWcharles’S LAW


The volume of a gas is directly proportional

to the absolute temperature when the pressure

is constant

charles’S LAWcharles’S LAWGRAPH :

charles’S LAWcharles’S LAW

V α TV α T

FORMULA

V = constant x TV = constant x T

V1/T1 = V2/T2V1/T1 = V2/T2

Temperature must bein Kelvin

Temperature must bein Kelvin

T (K) = t (0C) + 273.15 T (K) = t (0C) + 273.15

charles’S LAWcharles’S LAWA sample of carbon monoxide gas occupies 3.20 L at 125

0C. At what temperature will the gas occupy a volume of

1.54 L if the pressure remains constant?

V1/T1 = V2/T2

V1 = 3.20 L V2 = 1.54 L

T1 = 398.15 K T2 = ?

T2 = V2 x T1

V1

1.54 L x 398.15 K

3.20 L= = 192 K

Gay-lussac’S LAWGay-lussac’S LAW


The absolute pressure of a gas is directly

proportional to the absolute temperature

when the volume is constant

Gay-lussac’S LAWGay-lussac’S LAWGRAPH :

Temperature is a measure of average

kinetic energy. As temperature

increases, particles move faster. As

the temperature of a gas increases the

particles will hit the walls with more

force.

Temperature is a measure of average

kinetic energy. As temperature

increases, particles move faster. As

the temperature of a gas increases the

particles will hit the walls with more

force.

FORMULA

P α TP α T


P = constant x TP = constant x T

P1/T1 = P2/T2P1/T1 = P2/T2

Constant volume

Constant amount of gas, n

Constant volume

Constant amount of gas, n

Gay-lussac’S LAWGay-lussac’S LAWA gas has a pressure at 2.0 atm at 18°C. What is the newpressure when the temperature is 62°C? (V and n constant).

1. Set up a data table; Conditions 1 Conditions 2

P1 = 2.0 atm P2 =

T1 = 18°C + 273 T2 = 62°C + 273

= 291 K = 335 K

?


2. Solve Gay-Lussac’s Law for P2:

P1 = P2

T1 T2

P2 = P1 x T2

T1

P2 = 2.0 atm x 335 K = 2.3 atm 291 K

Temperature ratioincreases pressure

Ideal gas LAWIdeal gas LAW

Exhibits certain theoretical properties. Specifically, an

ideal gas :

Obeys all of the gas laws under all conditions.

Does not condense into a liquid when cooled.

Shows perfectly straight lines when its V and T & P and

T relationships are plotted on a graph.

Ideal gas LAWIdeal gas LAWDEFINITIONDEFINITION

The absolute pressure of an ideal gas is directly

proportional to the Kelvin temperature and the number of

moles of the gas and is inversely proportional to the volume

of the gas.

V

nRTP OR

Ideal Gas Equation

P V = n R T

Universal Gas ConstantVolume

No. of moles

Temperature

Pressure

R = 0.0821 atm L / mol K

R = 8.314 kPa L / mol K

Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 366

PV = nRT

P = pressureV = volumeT = temperature (Kelvin)n = number of molesR = gas constant

Standard Temperature and Pressure (STP)

T = 0 oC or 273 K

P = 1 atm = 101.3 kPa = 760 mm Hg

Solve for constant (R)

PV nT

= R

Substitute values:

(1 atm) (22.4 L) (1 mole)(273 K)

R = 0.0821 atm L / mol K or R = 8.31 kPa L / mol K

R = 0.0821 atm L mol K

Recall: 1 atm = 101.3 kPa

(101.3 kPa)

( 1 atm)= 8.31 kPa L mol K

1 mol = 22.4 L @ STP


How many moles of H2 is in a 3.1 L sample of H2

measured at 300 kPa and 20°C?

Task 1 :

PV = nRT

P = 300 kPa, V = 3.1 L, T = 293 K

(300 kPa)(3.1 L) = n (8.31 kPa•L/K•mol)(293 K)

(8.31 kPa•L/K•mol)(293 K)

(300 kPa)(3.1 L)= n = 0.38 mol

Solution :


How many grams of O2 are in a 315 mL container that has a

pressure of 12 atm at 25°C?

Task 2 :

Solution :PV = nRT

P= 1215.9 kPa, V= 0.315 L, T= 298 K

(8.31 kPa•L/K•mol)(298 K)

(1215.9 kPa)(0.315 L)= n = 0.1547 mol

0.1547 mol x 32 g/mol = 4.95 g

Ideal gas LAWIdeal gas LAWWhat is the volume that 500 g of iodine will occupy under the

conditions: Temp = 300oC and Pressure = 740 mm Hg?

Step 1) Write down given information.

mass = 500 g iodine

n = 1.9685 mol I2

T = 573 K (300oC)

P = 0.9737 atm (740 mm Hg)

R = 0.0821 atm . L / mol . K

V = ? L

Task 3 :

Solution :


Step 2) Equation: PV = nRT

Step 3) Solve for variable

V =nRT

P

Step 4) Substitute in numbers and solve

V (1.9685 mol)(0.0821 atm . L / mol . K)(573 K)

0.9737 atm=

V = 95.1 L I2

Ideal gas LAWIdeal gas LAW If the amount of gas does not change:

NkTTN

RNnRTPV

A

AN

Nn

Number of molecules

KJ1038.1

mol106.022

KmolJ31.8 23123

AN

Rk

Boltzmann’s constant.

Ideal gas LAWIdeal gas LAWTask 4: Hydrogen atom mass.

Use Avogadro’s number to determine the mass of a hydrogen atom.

Solution :

Dive the mass of 1 mol by the number of atoms in a mole; the mass is 1.67 x

10-27 kg.

Task 5: How many molecules in one breath?

Estimate how many molecules you breathe in with a 1.0-L breath of air.

Solution :

1 L is about 0.045 mol, and contains about 3 x 1022 molecules.

Absolute Absolute temperaturetemperature

Temperature measured using the Kelvin scale where zero

is absolute zero.

Kelvin scale is a thermodynamic (absolute) temperature scale

where absolute zero, the theoretical absence of all thermal energy,

is zero (0 K).

Kelvin unit and its scale, by international agreement, are defined

by two points: absolute zero, and the triple point.


Absolute zero is the temperature at which nothing could be colder and no

heat energy remains in a substance - exactly 0 K and −273.15 °C.

The triple point of water is, by definition, exactly 273.16 K and 0.01 °C.

This definition does three things:

It fixes the magnitude of the kelvin unit as being exactly 1 part in

273.16 of the difference between absolute zero and the triple point of

water;

It establishes that one kelvin has exactly the same magnitude as a one-

degree increment on the Celsius scale;

It establishes the difference between the two scales’ null points as being

exactly 273.15 kelvins (0 K ≡ −273.15 °C and 273.16 K ≡ 0.01 °C).


Triple Point of water :

The point where water in the solid, liquid and gas states can

coexist in equilibrium. The pressure of triple point is 4.58

torr and the temperature is 0.01 degree Celsius.

Triple Point of water :

The point where water in the solid, liquid and gas states can

coexist in equilibrium. The pressure of triple point is 4.58

torr and the temperature is 0.01 degree Celsius.


Phase diagram of water.Phase diagram of water.


The absolute temperature, T at any points for an ideal gas is defined :The absolute temperature, T at any points for an ideal gas is defined :

where : P = Pressure in the thermometer when it is at point

where T is determined

PTP = Pressure of gas in the thermometer at the

triple point temperature of water

REAL gas REAL gas DEFINITIONDEFINITION

Most like an ideal gas when the real

gas is at low pressure and high

temperature.

REAL gas REAL gas At high pressures gas particles are close therefore the volume of

the gas particles is considered.

At low temperatures gas particles have low kinetic energy

therefore particles have some attractive force

In real gases, particles attract each other reducing the pressure

Real gases behave more like ideal gases as pressure approaches

zero.

Example : Dry ice, liquid oxygen and nitrogen

Kinetic theory of gas Kinetic theory of gas

Kinetic Molecular Theory (KMT) for an ideal gas states

that all gas particles:

are in random, constant, straight-line motion.

are separated by great distances relative to their size; the

volume of the gas particles is considered negligible.

have no attractive forces between them.

have collisions that may result in the transfer of energy

between gas particles, but the total energy of the system

remains constant.

Kinetic Molecular Theory (KMT) for an ideal gas states

that all gas particles:

are in random, constant, straight-line motion.

are separated by great distances relative to their size; the

volume of the gas particles is considered negligible.

have no attractive forces between them.

have collisions that may result in the transfer of energy

between gas particles, but the total energy of the system

remains constant.

The average translational kinetic energy of the molecules in an

ideal gas is directly proportional to the temperature of the gas.

The average translational kinetic energy of the molecules in an

ideal gas is directly proportional to the temperature of the gas.

Kinetic theory of gas Kinetic theory of gas

The average speed of molecules in a gas as a function of

temperature:

The average speed of molecules in a gas as a function of

temperature:

The end The end “NEVER STAND

BEGGING FOR THAT WHICH YOU HAVE POWER TO EARN”

-MIGUEL DE CERVANTES-

Chapter 5 Gas Laws and Kinetic Theory_2

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