TOPIC 15.2 ENERGETICS/THERMODYNAMICS ENTROPY AND SPONTANEITY

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 NATURE OF SCIENCE (2.2) Theories can be superseded – the idea of entropy has evolved through the years as a result of developments in statistics and probability.

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.

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.

An expression of the 2nd Law of Thermodynamics is that as time moves forward, matter and energy become more disordered and the entropy of the universe increases.

UNDERSTANDING/KEY IDEA 15.2.C Entropy of gas > liquid > solid under the same conditions.

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.

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.

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.

When you increase disorder, S is positive. When you decrease disorder, S is negative.

Examples Br2(l) Br2(g) 2Cu(s) + O2(g) 2CuO(s) Delta S is positive: one mole of a liquid changed into one mole of a gas. More disorder. 2Cu(s) + O2(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.

APPLICATION/SKILLS Be able to calculate entropy changes (ΔS) from given standard entropy values (S◦).

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.

Important Note The units for entropy are J K-1 mol-1 The units for enthalpy are kJ mol-1

Calculating ΔS⁰ ΔS⁰ = ∑nS ⁰(products) - ∑nS ⁰(reactants) You can calculate the standard entropy change of a reaction (ΔS⁰) 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.

Sample Problem Calculate the entropy change for the following reaction given the standard entropy values. C2H4(g) + H2(g) C2H6(g) S⁰ of C2H4(g) = 220 J K-1 mol-1 S⁰ of H2(g) = 131 J K-1 mol-1 S⁰ of C2H6 (g) = 230 J K-1 mol-1

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. C2H4(g) + H2(g) C2H6(g) 220 131 230 ΔS⁰ = ∑nS ⁰(products) - ∑nS ⁰(reactants) = 230 – (220 + 131) = -121 J K-1 mol-1

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).

Remember that “spontaneity” means a reaction can occur without the need to do work. (Sometimes activation energy must be applied.)

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.

If a process is spontaneous, ΔG must be negative.

Three ways to calculate ΔG ⁰ Hess’s Law ΔG⁰ = ∑ ΔG ⁰(products) - ∑ ΔG ⁰(reactants) ΔG ⁰ = ΔH ⁰ - TΔS ⁰

APPLICATION/SKILLS Be able to apply ΔG◦ = ΔH ◦ – TΔS◦ in predicting spontaneity and calculate various conditions of enthalpy and temperature that will affect this.

GUIDANCE Thermodynamic data is given in section 12 of the data booklet.

GUIDANCE Be able to examine various conditions that affect ΔG.

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

ΔG ⁰ = ΔH ⁰ - TΔS ⁰ Effect of temperature on spontaneity ΔH ⁰ ΔS ⁰ Exothermic (neg) High disorder (pos) Always spontaneous Low disorder (neg) Spont at low temps Endothermic (pos) High Disorder (pos) Spont at high temps Low Disorder (neg) Never spontaneous

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.

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.

APPLICATION/SKILLS Be able to relate ΔG to the position of equilibrium.

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.

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.

ΔG⁰ = ∑ 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)

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.

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.

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

ΔG ⁰< -30 kJ/mol (negative) Spontaneous The equilibrium ratio of products/reactants is much greater than one. The reaction goes to completion.

Citations Brown, Catrin, and Mike Ford. Higher Level Chemistry. 2nd ed. N.p.: Pearson Baccalaureate, 2014. Print. 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 Catrin and Brown and is used for direct instructional purposes only.