Enthalpy and Entropy

 
 

Entropy

Entropy is a measure of how disordered or chaotic a system is. In chemistry, an increase in entropy describes a more disordered arrangement of particles. It can be used outside of chemistry too. Knocking a pack of cards off a table, leaves falling off trees and the expanding universe are all examples of increasing entropy.

The more disordered the arrangement of particles, the higher the entropy. This means that entropy increases as the state of a substance changes from a solid to a liquid then to a gas.

 
 

Entropy also increases when the number of particles increases. For example, if you have a reaction where two reactants react to form three or more products, entropy has increased. This is because there are more particles so there are more possible arrangements.

Calculating entropy

You can calculate the entropy change of a reaction by subtracting the total entropy of the reactants from the total entropy of the products, as shown in the equation below.

 
 

The units of entropy are always J K-1 mol-1.

For a reaction to be feasible, the change in entropy should be positive. A positive entropy change indicates that the reaction is becoming more disordered, which is more thermodynamically stable than a reaction where entropy decreases. A feasible reaction is one that can happen on its own, without the input of energy.

Reactions with a positive entropy change aren’t always feasible. This is because whether a reaction happens spontaneously depends on two things – entropy and enthalpy. If the enthalpy change is very endothermic (i.e. it has a positive value), this may make reactions unfeasible despite the fact that entropy is increasing. For reactions to be feasible, they usually have a positive value for enthalpy (disorder increasing) and a negative value for enthalpy (exothermic).

Gibbs free energy

Gibbs free energy describes whether a reaction is feasible – i.e. whether it can happen on its own without having to put in energy. For a reaction to be feasible, the change in Gibb’s energy needs to be negative. The equation for calculating the change in Gibb’s free energy is:

 
 

When you are calculating Gibb’s free energy, be aware that the units of enthalpy and entropy changes are different so you’ll need to convert between them! The units for enthalpy change is kJ mol-1 while the unit for entropy change is J K-1 mol-1. To convert from J to kJ, divide by 1000.

Worked example – calculating Gibb’s free energy

Hydrogen reacts with carbon disulfide as shown below.

 
 

For this reaction, ΔH = –234 kJ mol–1 and ΔS = –164 J K–1 mol–1. Explain, with a calculation, whether this reaction is feasible at 25oC.

  • Change in Gibbs = enthalpy change – (temperature x entropy change)
  • Convert temperature to Kelvin = 25 + 273 = 298
  • Convert entropy to kJ = -164/1000 = -0.164
  • Change in Gibbs = -234 – (298 x -0.164)
  • Change in Gibbs = -185 kJ mol-1
  • The reaction is feasible at 25oC since the change in Gibb’s free energy is negative.

Calculating the temperature where a reaction is feasible

We have already seen how reactions are feasible when the change in Gibb’s has a negative value. This means that when ΔG = 0, the reaction is just feasible. We can therefore remove ΔG from the Gibb’s equation and rearrange to find the temperature at which the change in Gibb’s free energy is equal to zero.

 
 

Worked example – calculating feasible temperatures

Tungsten is extracted from wolframite by reduction with hydrogen:

 
 

ΔH = +115 kJ mol-1 ΔS = + 131 J K-1 mol-1

Calculate the minimum temperature, in K, at which this reaction becomes feasible.

  • T = ΔH / ΔS
  • Convert ΔS from J to kJ = 131/1000 = 0.131
  • T = 115 / 0.131
  • T = 878 K

Feasibility

Just because a reaction has a negative value for ΔG doesn’t necessarily mean that it will actually happen. Some feasible reactions have such a high activation energy that their rate of reaction is incredibly slow and the reaction is basically not happening.

Remember that in general:

  • Reactions where ΔH is negative and ΔS is positive will tend to be feasible (depending on the temperature).

  • Reactions where ΔH is positive and ΔS is negative will tend to not be feasible (depending on the temperature).