Calculate the standard entropy change for the reaction:C8 H 18 (l) + 25 ⁄2 O 2 (g) ® 8 CO 2 (g) + 9 H 2 O (g)given the following information:Substance S° [J mol-1 K -1 )]C8 H 18 329.3O 2 205.2CO 2 213.8H 2 O 70.0
Question
Calculate the standard entropy change for the reaction:C8 H 18 (l) + 25 ⁄2 O 2 (g) ® 8 CO 2 (g) + 9 H 2 O (g)given the following information:Substance S° [J mol-1 K -1 )]C8 H 18 329.3O 2 205.2CO 2 213.8H 2 O 70.0
Solution
The standard entropy change for a reaction can be calculated using the formula:
ΔS° = Σ S°(products) - Σ S°(reactants)
where S° is the standard molar entropy.
For the given reaction:
C8H18(l) + 25/2 O2(g) → 8 CO2(g) + 9 H2O(g)
The standard molar entropies are given as:
S°(C8H18) = 329.3 J mol-1 K-1 S°(O2) = 205.2 J mol-1 K-1 S°(CO2) = 213.8 J mol-1 K-1 S°(H2O) = 70.0 J mol-1 K-1
We can substitute these values into the formula:
ΔS° = [8S°(CO2) + 9S°(H2O)] - [S°(C8H18) + 25/2*S°(O2)]
ΔS° = [8213.8 J mol-1 K-1 + 970.0 J mol-1 K-1] - [329.3 J mol-1 K-1 + 25/2*205.2 J mol-1 K-1]
ΔS° = [1710.4 J mol-1 K-1 + 630.0 J mol-1 K-1] - [329.3 J mol-1 K-1 + 2565.0 J mol-1 K-1]
ΔS° = 2340.4 J mol-1 K-1 - 2894.3 J mol-1 K-1
ΔS° = -553.9 J mol-1 K-1
So, the standard entropy change for the reaction is -553.9 J mol-1 K-1.
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