Calculating Gibbs Free Energy

When using thermodynamic tables you have to be very careful to remember that the substances referred to are in their standard states.  For liquids this is the pure liquid, for solutions this will be at 1 mol/L concentrations, and for gases at 1 bar (atmospheric pressure).  If you forget this, it is easy to draw wrong conclusions about the meaning of G. 

Let's look at how to do this using an example to which we all know the answer: does ice spontaneously melt at 25 oC?  Obviously yes, ice will spontaneously melt at any temperature above 0 oC if it is at 1 atmosphere pressure.

Step 1: Set up the balanced equation H2O (s) equilsymbol.gif (73 bytes) H2O (l)

Step 2: Calculate the value for H for this reaction using Hess' law.  You can get the necessary values for Hfo from a table of thermodynamic data.

You need the coefficients (which are in mol) in the balanced equation to cancel out the unit of mol in the Hfo values (which are in kJ/mol)

 

 

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Step 3: Calculate the value of S for this reaction:

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Step 4: Substitute into G = H - TS.  Be careful that you get the units correct.  H will probably be in kJ, while S is in J/K.  Its probably best to convert S into kJ as well (divide by 1000).  T must be in K (add 273 to the temperature in oC). 

S = 25.1 J/K = 0.0251 kJ/K
T = 25oC + 273 = 298 K
G = 6.90 kJ - (298 K)(0.0251 kJ/K)
G = 6.90 kJ - 7.48 kJ = -0.58 kJ

Since G is negative, the reaction is spontaneous, which we already knew, since ice melts at 25 oC.

For this second example, work through what happens to ice at -25 oC.  Here we know the reaction is not spontaneous, since ice cannot melt at 1 atmospheric pressure, and a temperature below 0 oC.

We already know the values for H and S from the previous problem.  We need to calculate the temperature in K

Convert the temperature into Kelvin.  What is a temperature of -25 oC in K?
  a) 298 K    b) -298 K    c) 248 K    d) -248 K

Calculate TS =  (in units of kJ)

Calculate G = H - TS =  (in units of kJ)

Is the melting of ice H2O (s) equilsymbol.gif (73 bytes) H2O (l) spontaneous at -25 oC, according to the calculated value of G?
  Yes    No

 

Now, check what happens if the temperature is 0 oC.

What is G for the melting of ice H2O (s) equilsymbol.gif (73 bytes) H2O (l) at 0 oC?

Calculate TS =  (in units of kJ)

Calculate G = H - TS =  (in units of kJ)

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As a final example problem, work out whether the Sabatier methanation reaction

CO2 (g) + 4 H2 (g) CH4 (g) + 2 H2O (g)

will be spontaneous at 400 oC.
  Spontaneous    Not Spontaneous