Topic 05 - States of Matter - Tutors Copy

St’ Andrew’s Junior CollegeJC1 H2 Chemistry 2011

St. Andrew’s Junior College

H2 Chemistry 2011

Lecture Notes 5

States of Matter

Assessment Objectives:

Candidates should be able to:a) state the basic assumptions of the kinetic theory as applied to an ideal gasb) explain qualitatively in terms of intermolecular forces and molecular size:

(i) the conditions necessary for a gas to approach ideal behaviour(ii) the limitations of ideality at very high pressures and very low temperatures

c) state and use the general gas equation pV = nRT in calculations, including the determination of Mr

Lecture Outline1. Kinetic Theory of Matter

2. Real and Ideal Gases2.1 Features of a Real Gas2.2 Features of an Ideal Gas

3. The Gas Laws3.1 Avogadro’s Law3.2 Boyle's Law3.3 Charles' Law3.4 The Ideal Gas Equation / The General Gas Law

4. Mixture of Gases4.1 Partial Pressure4.2 Dalton's Law of Partial Pressure4.3 Mole Fraction, Partial Pressure and Total Pressure

5. Deviation from Ideal Gas Behaviours5.1 Negative Deviation5.2 Positive Deviation

Recommended Materials:1) Cann, Peter and Hughes, Peter, Chapter 4, Chemistry for advanced level, 2002

Web Animations:1. Kinetic Theory of Matter Animation

http://www.harcourtschool.com/activity/states_of_matter/2. Boyle’s Law

http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html3. Ideal Gas Law

http://www.phy.ntnu.edu.tw/java/idealGas/idealGas.html1. Introduction: Kinetic Theory of Matter

1

http://www.phy.ntnu.edu.tw/java/idealGas/idealGas.html

http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html

http://www.harcourtschool.com/activity/states_of_matter/


The Kinetic Theory describes the particles in solids, liquids and gases and

the movement of these particles. Some of the characteristics that distinguish

these three states of matters are:

Property Solids Liquids Gases

Volume Fixed FixedTakes the volume

of the container

Shape FixedFills or partially fills

the containerFills the container

fullyForces between

particlesStrong Less strong Weak

Arrangement of particles

Orderly mannerNot in orderly

mannerRandom

arrangement

Packing of particles

CloseClose but not as close as solids

Far apart

Density

High; packed closely, the

volume is very small

HighLow; far apart, high volume

Compressibility Nil Almost Nil High

Boiling / Melting point

High Moderate to high Low

Movement of particles

Vibrate and rotate about fixed

position

Vibrate, rotate and move anywhere but at a lower speed as compared to gases

Vibrate, rotate and move anywhere

within the container

Energy LittleMore than solids but

less than gasesHigh

Pressure NegligibleDepends on the

depth of the liquid

Yes due to particles bouncing off the walls of the

container

Changes of States

2

melting vaporisation

freezing condensation

deposition

sublimation

Solid Liquid Gas


Vapour pressure of a liquid is the pressure exerted by those molecules

that escape from the liquid to form a separate vapour phase above the

liquid.

Saturated vapour pressure is the maximum vapour pressure that is

exerted by a vapour when it is in dynamic equilibrium with its liquid (in a

closed container).

Boiling: A liquid boils when its saturated vapour pressure equals the

external pressure. When external pressure decreases, the boiling point

also decreases.

E.g. H2O boils at 100ºC at 1 atm (101kPa) but boils at 93ºC at 80 kPa.

2. Real and Ideal Gases

Candidates should be able to:

a) state the basic assumptions of the kinetic theory as applied to an ideal gas.

2.1 Features of a Real Gas

The particles have a certain volume, i.e., the volume of particles is not

completely negligible in comparison to the total volume of the gas.

There are forces of attraction between particles, though they are usually

very weak.

When the particles collide, the collision is not elastic, i.e., there is loss of

kinetic energy and the molecules stick together after collision.

2.2 Features of an Ideal Gas (Assumptions of the Kinetic Theory applied to

Ideal Gases)

The particles have negligible volume as compared to the volume

occupied by the gas.

There are negligible forces of attraction between particles.

When the particles collide, the collision is perfectly elastic, i.e., the

particles bounce apart after they collide with no loss of kinetic energy

and molecules do not stick together after collision.

The gas particles are in constant random motion.

The average kinetic energy of the particles is proportional to the absolute

temperature.

3


3. Gas Laws


c) state and use the general gas equation pV = nRT in calculations, including the

determination of Mr

3.1 Avogadro’s Law

At a constant temperature and constant pressure, the volume of a gas, V, is

directly proportional to the number of moles of the gas, n.

V n

3.2 Boyle’s Law

At a constant temperature, the volume of a given mass of gas, V, is inversely

proportional to the pressure, p.

4


p

pV = Constant

p1V1 = p2V2

Do you know?A diver's body can be affected by Boyle's law. As the diver goes deeper into the sea,

water pressure increases and this causes the volume of the compressible body areas

(which contain air spaces such as, air canals, lungs, sinuses nasal passages and

hollow organs) to decrease. As a result, the diver would suffer the consequences as

explained by Boyle's law in them. This way, it is very important that divers foresee the

problems which their bodies might have to face.

3.3 Charles’ Law

At a constant pressure, the volume of a given mass of gas, V, is directly

proportional to its absolute temperature, T.

5

V T


3.4 The Ideal Gas Equation / The General Gas Law

From Avogadro’s Law, V n

From Boyle’s Law, p

From Charles’ Law, V T

Combining Avogadro’s Law, Boyle’s Law and Charles’ Law,

V

For 1 mole of gas, constant R is designated as molar gas constant, R.

R is also known as universal gas constant.

These expressions can be combined to form one single equation for the

behaviour of gases: The Ideal Gas Equation. It gives the relationship between

the volume of a given mass of gas and the prevailing conditions (temperature,

pressure and the number of moles).

Ideal Gas equation / General Gas Equation

Where R: Universal Gas Constant (Molar gas constant)

Value of R depends on units of P, V, n and T

P Pressure Pa or Nm-2 atm

V Volume m3 dm3

6


n No. of moles mol mol

T Temperature K K

R Universal Gas

Constant

8.31 J K-1 mol-1

(S.I. units)

0.0821 atm dm3 mol-1 K-1

Determination of molar gas constant, R

Useful conversions:

1 mol of gas occupies 22.4 dm3 at s.t.p, i.e., 0oC and 101325 Pa or Nm-2

V = 22.4 dm3 = 0.0224 m3

pV = nRT

R =

=

= 8.31 Nm K-1 mol-1

= 8.31 J K-1 mol-1

The ideal gas equation can also be used to find the relative molecular mass

(Mr) or the density () of the gas. Given that and ,

7

1 atm = 760 mmHg = 101325 Pa

1 dm3 = 1000 cm3 = 10-3 m3

1 cm3 = 10-6 m3


Exercise 1

1. Calculate the pressure exerted by 0.05 mol of gas at 25oC and having a volume of

500 cm3.

Solution:

2. A sample of a gas exerts a pressure of 82.5 kPa in a 300 cm3 container at 25oC. What

pressure would the same gas sample exert in a 500 cm3 container at 50oC?

Solution:

3. 0.574 g of a gas occupies 548 cm3 at 22oC and 740 mmHg pressure. Calculate the

relative molecular mass, Mr, of the gas.

Solution:

8


4. Which of the following diagrams correctly describes the behaviour of a fixed mass of an ideal gas? Give reasons for your choice. [T is measured in K] J86 & N91

A B C D E

P

V

constant T constant V constant T constant T constant P

P

P

T V T

PV PV V

Ans: E

5. Which graph is correct for a given mass of an ideal gas at constant pressure? Give reasons for your choice. J2000 A B C D

V

T/ºC T/ºC T/ºC T/ºC

V V V

Ans: C

9


For each of the questions below, one or more of the three numbered statements 1 to 3

may be correct. The responses A to D should be selected on the basis of

A B C D

1, 2 and 3 are

correct

1 and 2 only are

correct

2 and 3 only are

correct

1 only is correct

6. Which of the following equations apply to an ideal gas?

(p = pressure, V = volume, m = mass, M = molar mass, = density,

c = concentration, R = gas constant, T = temperature) J91

1 p = 2 pV = MRT 3 pV =

Ans: D

7. Which statements correctly represent the behaviour of an ideal gas? (p denotes

pressure, Vm molar gas volume, M molar mass, c concentration, d density and T

temperature) J96

1 pVm T 2 pM dT 3 p cT

Ans: A

8. The Gas Laws can be summarised in the ideal gas equation, pV = nRT, where each

symbol has its usual meaning. Which of the following statements are correct? N92

1 One mole of any ideal gas occupies the same volume under the same conditions

10


of temperature and pressure.

2 The density of an ideal gas at constant pressure is inversely proportional to

temperature.

3 The volume of a given mass of an ideal gas is doubled if its temperature is

raised from 250C to 50OC at constant pressure.

Ans: B

4. Mixture of Gases

4.1 Partial Pressure

The pressure of gas is due to the particles bouncing off the walls of the container

after hitting onto them. For a mixture of gases which do not react with each other,

each gas exerts its own pressure (independent of the other gases) - known as its

partial pressure. The partial pressure of each gas is the pressure it would exert

if it alone occupied the same volume.

4.2 Dalton's Law of Partial Pressure

At constant temperature, for gases which do not react chemically, the total

pressure of a mixture of gases in a given volume is equal to the sum of the

partial pressures of the constituent gases.

4.3 Mole Fraction, Partial Pressure and Total Pressure

Assuming a mixture of gas A and gas B contained in a volume, V, at

temperature, T kelvin,

Partial pressure of gas A: pA =

Partial pressure of gas B: pB =

Total pressure, pT = pA + pB

= +

11

pT = pA + pB + pC + ….


=

pA / pT = /

= x

= nA / (nA + nB)

Hence partial pressure of a particular gas is the product of the mole fraction of

the gas and the total pressure of the mixture.

Where nA / (nA + nB) = χA

Exercise 2

9. A 2.0 dm3 flask contained 0.2 mol of nitrogen and 0.4 mol of oxygen at 400K.

Calculate:

(a) the partial pressure of nitrogen

(b) the partial pressure of oxygen

(c) the total pressure in the flask.

Solution: PV = nRT

a) pN2 = (0.2 x 8.31 x 400) / 2 x 10-3 = 332400 Pa

b) pO2 = (0.4 x 8.31 x 400) / 2 x 10-3 = 664800 Pa

c) pT = pN2 + pO2 = 332400 + 664800 = 997200 Pa = 9.97 X 105 Pa

10. A gas mixture consists of 0.4 mol of N2, 0.6 mol of O2 and 0.2 mol of Ar at a total

pressure of 300 kPa. Calculate the partial pressure of each gas in the mixture.

Solution: pN2 = χN2pT = 0.4 / (0.4 + 0.6 + 0.2) x 300 = 100 kPa

12

pA = χApT


pO2 = 0.6 / 1.2 x 300 = 150 kPa

pAr = 0.2 / 1.2 x 300 = 50 kPa

11. A 2 dm3 flask containing a gas N at a pressure of 7 atm was connected to another

flask containing a gas M with a volume of 3 dm3 at a pressure of 4 atm. What is the

final pressure, assuming that the 2 gases do not react and temperature was constant

throughout?

Solution: For gas N, For gas M,

pbeforeVbefore = pafterVafter pbeforeVbefore = pafterVafter

7 x 2 = pN (5) 4 x 3 = PM (5)

pN = 2.8 atm pM = 2.4 atm

pT = pN + pM = 2.8 + 2.4 = 5.2 atm

5. Deviation from Ideal Gas Behaviours


b) explain qualitatively in terms of intermolecular forces and molecular size:

(i) the conditions necessary for a gas to approach ideal behaviour

(ii) the limitations of ideality at very high pressures and very low temperatures.

An ideal gas (one which obeys the ideal gas equation) is hypothetical in nature.

All real gases do not obey the ideal gas equation. Deviations from the ideal gas

behaviour can be observed by plotting versus p. An ideal gas will have a

constant value of 1 since pV = nRT = constant.

13


NOTE:

z = is known as the compressibility factor of a gas.

z = 1 if the gas is ideal.

If z < 1 (negative deviation), the gas is more compressible than an ideal gas.

If z > 1 (positive deviation), the gas is less compressible than an ideal gas.

Deviation from ideality is due to:

attractive forces between gas molecules &

significant volume occupied by the gas molecules.

Factors affecting the extent and type of deviation are namely

nature of gas

pressure

temperature

A real gas behaves like an ideal gas under low pressure and high

temperature (at least ten times greater than the boiling point of gas)

conditions:

At low pressure, the particles are so far apart that

(i) the attractive forces between them are negligible.

(ii) the volume of particles is negligible as compared to the volume

occupied by the gas.

At high temperature, the particles possess high kinetic energy and

move about quickly. The particles can thus overcome the forces of

attraction between them and do not stick together after collision. The

collision is hence elastic.

A real gas shows deviation from ideal gas behaviour especially at high pressure

and low temperature (not far from the boiling point).

14


Fig 1: Graph of pV/RT vs p (atm) for 1 mol of nitrogen gas at 3 different

temperatures

Fig 2: Graph of pV/RT vs p (atm) for 1mol of several gases at 300K. The data for CO2 is perched at 313K as CO2 liquefies under high pressure at 300K.

5.1 Negative Deviation

Real gases tend to exhibit negative deviation when the temperature is low (not

far from boiling point of gas). At low temperature, the gas molecules are moving

slowly and thus are not able to overcome attractive forces between them. As

such, the intermolecular forces of attraction become significant and that the basic

assumptions of the Kinetic Theory are violated.

In the presence of intermolecular forces of attraction, the force with which a gas

molecule strikes the wall of container is reduced. Thus, the measured pressure

(due to the impact of the molecules with the wall of container) of the gas will be

lower. As such, the product of pV will be lower than expected as calculated

based on the ideal gas equation.

15


From fig 1, as the temperature gets higher, the extent of deviation gets lesser

and the gas tends to ideality. The stronger the intermolecular attraction, the

greater will be the extent of negative deviation. From fig 2, the extent of negative

deviation for CO2 is greater than that for N2 as the induced dipole-induced dipole

interaction for CO2 is stronger than that for N2 (to be covered in lecture of

chemical bonding)

5.2 Positive Deviation

Real gases show positive deviation at high pressure. This is because at high

pressure, the gas molecules are closer, causing the collective volume of the

particles to be significant with respect to the volume that they occupy (i.e the

volume of the container). The gas thus becomes less compressible and the

volume of the gas will be larger than expected. As a result, the product pV is

larger than expected as calculated based on the ideal gas equation.

For gases with the same type of intermolecular attraction, the larger the size of

the gas, the greater the positive deviation. From fig 2, N2 shows greater positive

deviation from ideal behaviour than H2 because of its larger molecular size.

16

Pressure of real gas < Pressure of ideal gas

of real gas < of ideal gas

of real gas < 1 (Negative Deviation)

Volume of real gas > Volume of ideal gas

of real gas > of ideal gas

of real gas > 1 (Positive Deviation)


Exercise 3

12. The value of pV is plotted against p for two gases, an ideal gas and a non-ideal

gas, where p is the pressure and V is the volume of the gas. N94, J98

Which of the following gases shows the greatest deviation from ideality?

A Ammonia C Methane

B Ethene D Nitrogen Ans: A

13. Which gas is likely to deviate most from ideal gas behaviour? N96

A HCl C CH4

B He D N2

Ans: A

17

pV

0p

Ideal gas

Non - ideal gas

Topic 05 - States of Matter - Tutors Copy

Documents

Transcript of Topic 05 - States of Matter - Tutors Copy