Final answer:
The standard entropy change (ΔSº) for the reaction C(g) + 2H₂(g) → CH₄(g) is calculated as -80.7 J/(mol·K), using the provided standard entropy values and the entropy change formula.
Step-by-step explanation:
Calculating Standard Entropy Change (ΔSº)
To calculate the standard entropy change (ΔSº) for the reaction C(g) + 2H₂(g) → CH₄(g), we will use the standard entropy values (Sº) provided for each substance:
- S°(C(g)) = 5.7 J/(mol·K)
- S°(H₂(g)) = 130.6 J/(mol·K)
- S°(CH₄(g)) = 186.2 J/(mol·K)
The formula to calculate ΔSº is:
ΔSº = ΣS°(products) - ΣS°(reactants)
In this reaction:
ΔSº = S°(CH₄(g)) - [S°(C(g)) + 2 × S°(H₂(g))]
ΔSº = 186.2 J/(mol·K) - [5.7 J/(mol·K) + 2 × 130.6 J/(mol·K)]
ΔSº = 186.2 J/(mol·K) - [5.7 J/(mol·K) + 261.2 J/(mol·K)]
ΔSº = 186.2 J/(mol·K) - 266.9 J/(mol·K)
ΔSº = -80.7 J/(mol·K)
Therefore, the standard entropy change for the given reaction is -80.7 J/(mol·K).