The standard reaction free energy [tex]$\Delta G^0=29 . kJ$[/tex] for this reaction:
[tex]$Fe_2 O_3(g)+2 H_2(g) \rightarrow 2 Fe(s)+3 H_2 O(l)$[/tex]
Use this information to complete the table below. Round each of your answers to the nearest kJ.
| reaction | [tex]$\Delta G^0$[/tex] |
|---|---|
| [tex]$2 Fe _2 O _3(g)+4 H _2(g) \rightarrow 4 Fe ( s )+6 H _2 O ( l )$[/tex] | -12 kJ |
| [tex]$\frac{2}{3} Fe ( s )+ H _2 O ( l ) \rightarrow \frac{1}{3} Fe _2 O _3(g)+\frac{2}{3} H _2(g)$[/tex] | 12 kJ |
| [tex]$2 Fe ( s )+3 H _2 O ( l ) \rightarrow Fe _2 O _3(g)+2 H _2(g)$[/tex] | 29 kJ |
Answer (1)
The Gibbs free energy change for the reaction 2 F e 2 O 3 ( g ) + 4 H 2 ( g ) → 4 F e ( s ) + 6 H 2 O ( l ) is twice the original, so it's 2 × 29 = 58 kJ.
The Gibbs free energy change for the reaction 3 2 F e ( s ) + H 2 O ( l ) → 3 1 F e 2 O 3 ( g ) + 3 2 H 2 ( g ) is one-third of the reverse of the original, so it's 3 1 × ( − 29 ) ≈ − 10 kJ.
The Gibbs free energy change for the reaction 2 F e ( s ) + 3 H 2 O ( l ) → F e 2 O 3 ( g ) + 2 H 2 ( g ) is the reverse of the original, so it's − 29 kJ.
The final answers are 58 , − 10 , and − 29 kJ.
Explanation
Problem Analysis We are given the standard Gibbs free energy change for the reaction: F e 2 O 3 ( g ) + 2 H 2 ( g ) → 2 F e ( s ) + 3 H 2 O ( l ) , Δ G 0 = 29 kJ We need to find the standard Gibbs free energy change for the following reactions:
2 F e 2 O 3 ( g ) + 4 H 2 ( g ) → 4 F e ( s ) + 6 H 2 O ( l )
3 2 F e ( s ) + H 2 O ( l ) → 3 1 F e 2 O 3 ( g ) + 3 2 H 2 ( g )
2 F e ( s ) + 3 H 2 O ( l ) → F e 2 O 3 ( g ) + 2 H 2 ( g )
Reaction 1 For the first reaction, we observe that it is twice the original reaction. When a reaction is multiplied by a factor, the Gibbs free energy change is also multiplied by the same factor. Therefore, Δ G 1 = 2 × 29 kJ = 58 kJ So, the standard Gibbs free energy change for the first reaction is 58 kJ.
Reaction 2 For the second reaction, we observe that it is one-third of the reverse of the original reaction. Reversing a reaction changes the sign of the Gibbs free energy change, and multiplying by a factor multiplies the Gibbs free energy change by the same factor. Therefore, Δ G 2 = 3 1 × ( − 29 kJ ) = − 3 29 kJ ≈ − 9.67 kJ Rounding to the nearest kJ, we get -10 kJ.
Reaction 3 For the third reaction, we observe that it is the reverse of the original reaction. Reversing a reaction changes the sign of the Gibbs free energy change. Therefore, Δ G 3 = − 29 kJ So, the standard Gibbs free energy change for the third reaction is -29 kJ.
Final Answer In summary, the standard Gibbs free energy changes for the three reactions are:
Δ G 1 = 58 kJ
Δ G 2 = − 10 kJ
Δ G 3 = − 29 kJ
Examples
Gibbs free energy is a crucial concept in thermodynamics that helps predict the spontaneity of chemical reactions. For instance, consider designing a new type of battery. By calculating the Gibbs free energy change for the battery's chemical reactions, engineers can determine whether the battery will function spontaneously under certain conditions. A negative Gibbs free energy change indicates a spontaneous reaction, meaning the battery can produce electricity. Conversely, a positive Gibbs free energy change suggests the reaction requires external energy input to proceed. This principle guides the selection of appropriate materials and reaction conditions to optimize battery performance and efficiency.
