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The following notes were written for the previous IB syllabus (2009). The new IB syllabus for first examinations 2016 can be accessed by clicking the link below.

# Energetics (hl)

### 15.1 - Standard enthalpy changes of reaction

#### Definitions

Standard state -- Pressure 101 kPa, temperature 298 K (or 1 atm, 25 degrees celsius). The standard state of an element or compound is the form in which it exists under standard conditions (not to be confused with STP)

Standard enthalpy change of formation -- The enthalpy change when 1 mol of a substance is made from its elements in their standard states

 Example: The enthalpy of formation of methane. C(graphite) + 2H2(g) -> CH4(g)

#### Hess' Law

The energy difference between two states is independent of the route between them.

This allows calculation of energy changes from other data by the manipulation of chemical equations. Equations may be treated using the four rules of number (doing the same operation on the energy value).

Example: Calculate the enthalpy of formation of methane.

Data:

• ΔH combustion (carbon) = -394kj
• ΔH combustion (hydrogen) =-242kj
• ΔHcombustion (methane) =-891kj

ΔHf methane is represented by the equation:

C(s) + 2H2(g) CH4 (g)

This equation can be constructed using the equations for combustion of the reactants (carbon and hydrogen) and the product (methane)

 C(s) + O2(g) CO2(g) -394kj enthalpy 1 H2(g) + 1/2O2(g) H2O(l) -242kj enthalpy 2 multiply this equation by 2 to get 2H2(g) + O2(g) 2H2O(l) -484kj enthalpy 3 Add the first and third equation together to get: C(s) + 2O2(g) + 2H2(g) CO2(g) + 2H2O(l) -878kj enthalpy (1 + 3) = 4 Now take away the equation for the combustion of methane CH4 (g) + 2O2(g) CO2(g) + 2H2O(l) -891kj enthalpy 5 And after rearrangement ( take the CH4 to the right hand side) the result is the equation for the formation of methane C(s) + 2H2(g) CH4 (g) +13kj enthalpy ( 4 - 5)

### 15.2 - Born Haber Cycles

Born Haber cycles are the application of Hess' law to ionic systems. An ionic solid consists of a giant structure of ions held together in a giant lattice.

Application of Hess law tells us that the enthalpy of formation of an ionic crystal is equal to the sum of the energies of formation of the ions plus the enthalpy of the lattice. It is a several step process that is best represented by a diagram showing the individual steps as endothermic upwards and exothermic downwards.

animation

### 15.3 - Entropy

Chemistry is concerned with the statistical likelyhood of a process occurring. This is related to the number of possible states which the particles can adopt. This can be regarded as the degree of disorder or Entropy of the system. Factors which increase disorder in a system are:

• Increased number of particles (when more gas particles are produced, this is far more important than the other factors)

• Mixing of particles

• Change of state to greater distance between particles (solid->liquid or liquid->gas)

• Increased particle movement (temperature)

Δ-S is positive when entropy increases (more disorder) and negative when entropy decreases (less disorder).

Calculations can be carried out using absolute entropy values in the same way as enthalpy values in Hess' law. The change in entropy form one state to another will always be the same regardless of the route taken.

The standard entropy change can be calculated by subtracting the absolute entropy of the reactants from that of the products.

ΔS (products) - ΔS (reactants) = standard entropy change for a reaction

### 15.4 - Spontaneity of a reaction - Gibbs Free Energy

Reactions which release heat (and so increase stability) tend to occur. Reactions which increase entropy (ΔS is positive) tend to occur, but neither can be used to accurately predict spontaneity alone.

Gibbs free energy (G) is defined as a measure of the total entropy of the universe. Hence the change in Gibbs free energy (ΔG) is the change in the total entropy of the universe. The total entropy of the universe must increase for any process to occur.

When heat is released in a reaction (exothermic change) this energy heats up the universe and effectively increases its entropy (there are a greater number of possible energy states that the particles in the universe can adopt).

The total entropy of the universe must increase and consequently exothermic reactions are favourable.

If the entropy of a reaction mixture increases then this is also favourable as the total entropy of the universe also increases.

#### Gibbs free energy change = ΔH - TΔS

If Gibbs free energy change is negative (convention) then the total entropy of the universe increases and the reaction is spontaneous. Why is the sign negative?

When ΔG is negative, the reaction is spontaneous, when it's positive, the reaction is not.

#### Gibbs free energy calculations

Enthalpy changes can be calculated indirectly by summing the enthalpy values of related equations using Hess' law. Entropy changes can be calculated in the same way. It follows then that Gibbs free energy changes can be calculated from a knowledge of Gibbs free energy values in related equations.

Spontaneity of reaction

Determined by the relationship

ΔG = ΔH - Temperature(in kelvin) x ΔS

See standard level entropy for a fuller treatment

 Enthalpy change Entropy change Gibbs free energy Spontaneity positive positive depends on T, may be + or - yes, if the temperature is high enough negative positive always negative always spontaneous negative negative depends on T, may be + or - yes, if the temperature is low enough positive negative always positive never spontaneous

Notes:

Electrostatic attraction

This is the most important force in chemistry. It depends on two factors:

1. The size of the charged particles (eg ionic radius)
2. The magnitude of the charge Z1 and Z2

The electrostatic attractive force may be considered proportional to the product of the charge magnitudes divided by the distance between them. Smaller charged particles can approach closer and therefore exert a greater force of attraction.

Examples

NaCl - the charges on the ions are single plus and single minus respectively

MgCl2 - in this case the magnesium has a double positive charge and consequently exerts a much larger force than the sodium ion in sodium chloride. The MgCl2 lattice is much stronger than NaCl- higher mp and greater lattice enthalpy

LiCl - In this case the Li+ ion has the same charge as the Na+ ion but it is much smaller and can get closer to the chloride ion exerting a greater force. The lattice is stronger than NaCl and has a higher mp

Gibbs free energy equation

Why is the sign negative?

This is because of the convention adopted for enthalpy. If the enthalpy is negative it's an exothermic process and the entropy of the universe increases as explained above. The second term in the equation is a negative term (-TΔS) and if the entropy increases it makes Gibbs free energy more negative.

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