Energetics: SL



6.1 Exothermic and endothermic reactions

If a reaction produces heat (increases the temperature of the surroundings) it is exothermic. If the temperature of the reaction mixture decreases (ie heat is absorbed) then the reaction is endothermic.

Enthalpy of reaction: The change in internal (chemical) energy (H) in a reaction = ΔH.

The most stable state is where all energy has been released. When going to a more stable state, energy will be released, and when going to a less stable state, energy will be gained (from the surroundings). On an enthalpy level diagram, higher positions will be less stable (with more internal energy) therefore, if the product is lower, heat is released (more stable, ΔH is -ve) but if it is higher, heat is gained (less stable, ΔH is +ve).


6.2 Calculation of enthalpy changes

Change in energy = mass x specific heat capacity x change in temperature --> E = m x c x ΔT

Enthalpy changes (ΔH) are related to the number of mols in the reaction...if all the coefficients are doubled, then the value of ΔH will be doubled.

When a reaction is carried out in aqueous solution, the water will gain or lose heat from (or to) the reactants. Therefore, the change in energy, and so the ΔH value, can be calculated from E = m x c x ΔT where m is the mass of water present (kilograms), and c = 4.18 kJ Kg-1 K-1. The ΔH value can then be calculated back to find the molar enthalpy change for the reaction.

Experimental

A known mass of solution should be placed in a container, as insulated as possible, to prevent as much heat as possible from escaping. The temperature is measured continuously, the value used in the equation is the maximum change in temperature from the initial reading.

The result will be a change in temperature. This can be converted into a change in heat (or energy) by using the above equation E = m x c x ΔT.

Δ-H may then be calculated for the amount of reactants present, and then this can be used to calculate for a given number of mols.


6.3 Hess' Law

Hess' Law states that the total enthalpy change between given reactants and products is that same regardless of any intermediate steps (or the reaction pathway).

Any equations can be mathematically manipulated using the four rules of number to construct other equations.


6.4 Bond enthalpy and bond dissociation enthalpy

Bond dissociation enthalpy is the enthalpy change when one mole of specific bonds are broken.

X-Y(g) -> X(g) + Y(g) : ΔH(dissociation).

Bond enthalpy is the average value of a particular type of bond which has been measured over a range of molecules.

Example:

CH4 has four C-H bonds, and so will have four different bond dissociation enthalpies corresponding to the following bonds breaking:

CH4 --> CH3 + H

CH3 --> CH2 + H

CH2 --> CH + H

CH   --> C + H

the C-H bond enthalpy is the average value of the four bond dissociation enthalpies.

Bond energies (enthalpies) can be used to calculate unknown enthalpy changes in reactions where only a few bonds are being formed/broken.

Bonds broken (left hand side) - bonds formed (right hand side) = enthalpy change for the reaction.
(all bond values positive)


6.5 Entropy

This is considered to be the degree of disorder of a system. Gas particles have random motion and three degrees of freedom (translation, rotation and vibration) and consequently have high entropy values. Liquids have much lower entropies and solids lower still.

The entropy is really a measure of the number of ways that energy can be distributed over a set of particles and so the more energy a system has (ie the hotter it is) the more entropy it has.

Disorder can also arise by mixing different components. For instance a mixture of two different gases will have greater entropy than the sum of the entropies of the two gases alone.

Entropy is symbolised by the letter S

Entropy changes during reactions

If the number of moles of gas increases in a chemical reaction (as shown by the stoichiometry of the reaction) then the entropy also increases.

Example:

dinitrogen tetroxide nitrogen dioxide

N2O4(g) 2NO2(g)

In this example there are two moles of gas on the right hand side and only one mole of gas on the left hand side - the entropy increases going from left to right (reactants to products). The entropy change of a reaction is given the symbol ΔS

6.6 Spontaneity

The spontaneity of a reaction (ie whether or not it is able to occur) depends both on the energy change and the entropy change of the reaction. As the entropy increases with temperature (energy available) then this must also be factored into the equation.

If the result of the equation ΔH-TΔS is negative then a reaction can happen (it is spontaneous). This value is called Gibb's free energy and is given the symbol ΔG

Hence, if the relationship ΔG = ΔH - TΔS has a negative value then the reaction can happen and it is said to be spontaneous

To predict the spontaneity of a reaction given values for enthalpy and entropy change the values must by put into the Gibb's free energy equation for different temperatures.

Example:

In the Haber process for the manufacture of ammonia

Equation Enthalpy change Entropy change
N2 + 3H2 2NH3 ΔH = -93Kj / mol ΔS = -198 j / mol K

The fact that both terms are negative means that the Gibbs free energy equation is balanced and temperature dependent:

ΔG = ΔH - TΔS

ΔG = -93000 - (T x -198) note that the enthalpy is given in kilojoules
 
if ΔG = 0 then the system is at the limit of reaction spontaneity
 
When ΔG = 0 then (T x -198) = -93000
 
and T = 93000/198 Kelvin
 
therefore the reaction becomes spontaneous when T = 469 K (196 ºC)
 

below this temperature the reaction is spontaneous.


Summary of Gibbs free energy

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