TOPIC 15

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TOPIC 15

ENERGETICS/THERMODYNAMICS

15.2 ENTROPY AND SPONTANEITY

By: Merinda Sautel Alameda Int’l Jr/Sr High School Lakewood, CO [email protected]

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ESSENTIAL IDEA

A reaction is spontaneous if the overall transformation leads to an increase in total

entropy (system plus surroundings). The direction of spontaneous change always

increases the total entropy of the universe at the expense of energy available to do useful

work. This is known as the second law of thermodynamics.

NATURE OF SCIENCE (2.2)

Theories can be superseded – the idea of entropy has evolved through the years as a result of developments

in statistics and probability.

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INTERNATIONAL- MINDEDNESS

Sustainable energy is a UN initiative with a goal of doubling of global sustainable

energy resources by 2030.

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THEORY OF KNOWLEDGE

Entropy is a technical term which has a precise meaning. How

important are such technical terms

in different areas of knowledge?

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UNDERSTANDING/KEY IDEA 15.2.A

Entropy (S) refers to the distribution of available

energy among the particles.

The more ways the energy

can be distributed the higher

the entropy.

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• The standard entropy S

^⁰

of a system is the degree of disorder.

• All things tend to a state of disorder.

• The more disordered the system, the more positive the entropy value.

• Spontaneous changes occur without the

need to do work.

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• An expression of the 2

^nd

Law of Thermodynamics is that as time

moves forward, matter and energy

become more disordered and the

entropy of the universe increases.

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UNDERSTANDING/KEY IDEA 15.2.C

Entropy of gas > liquid >

solid under the same

conditions.

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Entropy Factors

• The solid state is the most ordered state.

• Entropy (disorder) increases as a solid changes to a liquid and a

liquid changes to a gas.

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• Doubling the number of particles doubles the entropy.

• When predicting entropy changes,

changes in number of particles in

the gaseous state is the overruling

factor.

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APPLICATION/SKILLS

Be able to predict whether a change will result in an

increase or decrease in

entropy by considering the

states of the reactants and

products.

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• When you increase disorder, S is positive.

• When you decrease disorder, S is

negative.

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Examples

• Br

_2(l)

Br

_2(g)

Delta S is positive: one mole of a liquid changed into one mole of a gas. More disorder.

• 2Cu

_(s)

+ O

_2(g)

2CuO

_(s)

Delta S is negative: one mole of a gas changed into no moles of gas.

More examples on page 251 in the IB textbook.

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APPLICATION/SKILLS

Be able to calculate entropy changes (ΔS) from given

standard entropy values (S

^◦

).

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• Unlike enthalpy, the absolute

entropy (S

^◦

) of substances can be calculated.

• A perfectly ordered solid crystal

has an entropy of zero. All other

substances have disorder so they

have positive entropy values.

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Important Note

• The units for entropy are J K

^-1

mol

^-1

• The units for enthalpy are kJ mol

^-1

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Calculating ΔS ^⁰

ΔS

^⁰

= ∑nS

⁰(products)

- ∑nS

⁰(reactants)

• You can calculate the standard entropy

change of a reaction (ΔS

^⁰

) for any reaction using the above equation.

• You will be given values in a table, plug

them into the above equation and multiply

these values by the number of moles in the

equation. Then solve.

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Sample Problem

• Calculate the entropy change for the following reaction given the standard entropy values.

• C

₂

H

_4(g)

+ H

_2(g)

C

₂

H

_6(g)

• S

^⁰

of C

2

H

4(g)

= 220 J K

^-1

mol

^-1

• S

^⁰

of H

2(g)

= 131 J K

^-1

mol

^-1

• S

^⁰

of C

2

H

6 (g)

= 230 J K

^-1

mol

^-1

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• Before you do the math, you should predict the sign of the entropy change. In this case, 2 moles of gas are going to 1 mole of gas so the expected entropy value should be

negative.

• C

₂

H

_4(g)

+ H

_2(g)

C

₂

H

_6(g)

• 220 131 230

• • ΔS

^⁰

= ∑nS

⁰(products)

- ∑nS

⁰(reactants)

• = 230 – (220 + 131)

• = -121 J K

^-1

mol

^-1

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UNDERSTANDING/KEY IDEA 15.2.B

Gibbs Free Energy (G) relates the energy that can be

obtained from a chemical reaction to the change in enthalpy (ΔH), change in

entropy (ΔS), and absolute

temperature (T).

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• Remember that “spontaneity” means a

reaction can occur without the need to

do work. (Sometimes activation energy

must be applied.)

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• Gibb’s Free Energy ΔG

is the measure of the energy which is free to do useful work

rather than just leave the system as heat.

• Enthalpy is a measure of the quantity of heat change during a chemical reaction.

• Gibb’s Free Energy gives a measure of the

quality of the energy available.

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• If a process is spontaneous, ΔG

must be negative.

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Three ways to calculate ΔG ^⁰

Hess’s Law

ΔG

^⁰

= ∑ ΔG

⁰(products)

- ∑ ΔG

⁰(reactants)

ΔG

^⁰

= ΔH

^⁰

- TΔS

^⁰

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APPLICATION/SKILLS

Be able to apply

ΔG

^◦

= ΔH

^◦

– TΔS

^◦

in predicting spontaneity and calculate

various conditions of

enthalpy and temperature

that will affect this.

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GUIDANCE

Thermodynamic data is given in section 12 of the data

booklet.

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GUIDANCE

Be able to examine various

conditions that affect ΔG.

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• You can predict the effect of a change in temperature on the spontaneity of a reaction, using standard entropy and enthalpy changes and the equation

ΔG

^⁰

= ΔH

^⁰

- TΔS

^⁰

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ΔG ^⁰ = ΔH ^⁰ - TΔS ^⁰

ΔH^⁰ ΔS^⁰

Exothermic (neg) High disorder (pos) Always spontaneous Exothermic (neg) Low disorder (neg) Spont at low temps Endothermic (pos) High Disorder (pos) Spont at high temps Endothermic (pos) Low Disorder (neg) Never spontaneous

Effect of temperature on spontaneity

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GUIDANCE

ΔG is a convenient way to take into account both the direct

entropy change resulting from the transformation of the chemicals,

and the indirect entropy change

of the surroundings as a result of

the gain/loss of heat energy.

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• An exothermic reaction results in a increase in entropy in the

surroundings because the heat released into the surroundings causes more disorder.

• An endothermic reaction results in a decrease in entropy in the

surroundings because it is pulling heat from the surroundings

causing disorder to decrease.

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APPLICATION/SKILLS

Be able to relate ΔG to the

position of equilibrium.

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• Equilibrium occurs when a reaction mixture is at the minimum value of Gibbs free energy.

• Equilibrium exists when the rate of

the forward reaction is the same as

the rate of the reverse reaction.

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• If ΔG

^⁰

is negative, the reaction is

spontaneous and proceeds in the forward direction (product favored).

• If ΔG

^⁰

is positive, the reaction is

nonspontaneous and proceeds in the backward direction (reactant favored).

• If ΔG

^⁰

is zero, the reaction is at equilibrium.

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ΔG

^⁰

= ∑ ΔG

^⁰_(products)

- ∑ ΔG

^⁰(reactants)

• If the system is at equilibrium, ΔG

^⁰

is zero so rearranging the

equation gives

∑ ΔG

⁰(products)

= ∑ ΔG

⁰(reactants)

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• To summarize:

• A value of ΔG

^⁰

that is both large and negative indicates a reaction that is spontaneous and has an equilibrium

mixture with a high amount of products.

• A value of ΔG

^⁰

that is both large and positive indicates a reaction that is

nonspontaneous and has an equilibrium

mixture with a high amount of reactants.

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• ΔG

^⁰

> +30 kJ/mol (large and positive)

• Non spontaneous – no reaction

• The equilibrium ratio of products/reactants is way less than one.

• No products produced.

• 0 kJ/mol < ΔG

^⁰

< +30 kJ/mol (positive)

• Non spontaneous – slight reaction

• The equilibrium ratio of products/reactants is less than one.

• The reaction is highly reactant favored with

very little product produced.

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• ΔG

^⁰

= 0 kJ/mol

The equilibrium ratio of products/reactants is equal to one.

• The reaction is at equilibrium.

• 0 kJ/mol > ΔG

^⁰

> -30 kJ/mol (negative)

• Spontaneous – slight reaction

• The equilibrium ratio of products/reactants is greater than one.

• The reaction is product favored.

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• ΔG

^⁰

< -30 kJ/mol (negative)

• Spontaneous

• The equilibrium ratio of products/reactants is much greater than one.

• The reaction goes to completion.

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Citations

International Baccalaureate Organization. Chemistry Guide, First assessment 2016. Updated 2015.

Brown, Catrin, and Mike Ford. Higher Level Chemistry. 2nd ed. N.p.: Pearson Baccalaureate, 2014. Print.

ISBN 978 1 447 95975 5 eBook 978 1 447 95976 2

Most of the information found in this power point comes directly from this textbook.

The power point has been made to directly complement the Higher Level Chemistry textbook by Brown and Ford and is used for direct instructional purposes only.