Calculate the standard entropy change for the following reaction at 25 °C.
2 Al (s) + 3 ZnO (s) --> Al2O3 (s) + Zn (s) answer is in J/K mol
To calculate the standard entropy change for a reaction, we need to know the standard molar entropies of the reactants and products involved. The standard molar entropies (S°) are usually given in units of J/(K⋅mol).
Here is the step-by-step process to calculate the standard entropy change:
Step 1: Write down the balanced chemical equation for the reaction:
2 Al (s) + 3 ZnO (s) → Al2O3 (s) + Zn (s)
Step 2: Look up the standard molar entropies (S°) for each component involved in the reaction. You can find these values in reference books or online databases.
The standard molar entropies (S°) of the reactants and products are:
Al (s): 28.3 J/(K⋅mol)
ZnO (s): 51.1 J/(K⋅mol)
Al2O3 (s): 50.9 J/(K⋅mol)
Zn (s): 41.6 J/(K⋅mol)
Step 3: Apply the formula to calculate the standard entropy change (ΔS°) for the reaction:
ΔS° = Σn[S°(products)] - Σn[S°(reactants)]
In this equation, Σn indicates the stoichiometric coefficient of each component.
Using the given values:
ΔS° = [2 × S°(Al2O3)] + [1 × S°(Zn)] - [2 × S°(Al)] - [3 × S°(ZnO)]
Substituting the values:
ΔS° = [2 × 50.9 J/(K⋅mol)] + [1 × 41.6 J/(K⋅mol)] - [2 × 28.3 J/(K⋅mol)] - [3 × 51.1 J/(K⋅mol)]
Calculating:
ΔS° = 101.8 J/(K⋅mol) + 41.6 J/(K⋅mol) - 56.6 J/(K⋅mol) - 153.3 J/(K⋅mol)
Simplifying:
ΔS° = -63.3 J/(K⋅mol)
Therefore, the standard entropy change for the given reaction at 25 °C is -63.3 J/(K⋅mol).
dSf rxn = (n*dSf products) - (n*dSf reactants)
Look up the S values in tables in your text/notes, substitute, and solve for dS rxn