Gibbs free energy

• The feasibility of a reaction is determined by two factors
  • The?enthalpy?and?entropy change
• The two factors come together in a fundamental thermodynamic concept called the?Gibbs free energy (G)
• The Gibbs equation is:

ΔG??= ΔHreaction??–?TΔSsystem?

• • The units of ΔG??are in kJ mol–1
  • The units of ΔHreaction?are in kJ mol–1
  • The units of?T?are in K
  • The units of ΔSsystem??are in J K-1?mol–1(and must therefore be converted to kJ K–1?mol–1by dividing by 1000)

   

• For a reaction to be feasible, ΔG??must be?equal or less than zero

Calculating ΔGΘ

• This can be done by?using the Gibbs equation, using enthalpy change, ΔH?, and entropy change, ΔS?, values

Answer:

Step 1:?Convert the entropy value in kilojoules

ΔS??= +344 J K-1?mol-1??÷ 1000 = +0.344 kJ K-1?mol-1

Step 2:?Substitute the terms into the Gibbs Equation

ΔG?= ΔHreaction?– TΔSsystem?

= +135 – (298 x 0.344)

=?+32.49 kJ mol-1

The temperature is 298 K since standard values are quoted in the question

• Rearranging the Gibbs equation allows you to determine the temperature at which a non-spontaneous reaction become feasible

ΔG??= ΔHreaction??- TΔSsystem?

• Remember, for a reaction to be feasible ΔGΘ?must be zero or negative

0 = ΔH??- TΔS?

ΔH??= TΔS?

T?= ΔH??÷ ΔS?

Answer:

• • If ΔG??= 0 then T?= ΔH??÷?ΔS?
  • Covert ΔS??to kJ K-1?mol-1?by dividing by 1000
  • T?= 1336 ÷ (581/1000)
  • T?= 2299 K

Temperature and Gibbs free energy?

• When ΔG??is?negative, the reaction is?spontaneous / feasible?and likely to occur
• When ΔG??is?positive, the reaction is?not spontaneous / feasible?and unlikely to occur
• We can also look at the the values for enthalpy change, ΔH, and entropy change, ΔS
  • Depending on the value for ΔH?and ΔS?we can determine whether the reaction is spontaneous at a given temperature (T)

   

Summary for temperature and Gibbs free energy