Calculate the standard reaction entropy at 298 K of
(1) 2 CH3CHO(g) + O2(g)→2 CH3COOH(l)
(2) 2 AgCl(s) + Br2(l)→2 AgBr(s) + Cl2(g)
(3) Hg(l) + Cl2(g)→HgCl2(s)
The Correct Answer and Explanation is :
To calculate the standard reaction entropy (ΔS°) at 298 K for each of the given reactions, we use the formula:
ΔS° = ΣS°(products) − ΣS°(reactants)
where S° represents the standard molar entropy of each substance involved. Standard entropy values are typically expressed in J/mol·K.
Reaction (1):
2 CH₃CHO(g) + O₂(g) → 2 CH₃COOH(l)
Using standard entropy values at 298 K:
- S°(CH₃CHO(g)) = 250.3 J/mol·K
- S°(O₂(g)) = 205.0 J/mol·K
- S°(CH₃COOH(l)) = 159.8 J/mol·K
Calculating ΔS°:
ΔS° = [2 × S°(CH₃COOH(l))] − [2 × S°(CH₃CHO(g)) + S°(O₂(g))]
ΔS° = [2 × 159.8] − [2 × 250.3 + 205.0]
ΔS° = 319.6 − [500.6 + 205.0]
ΔS° = 319.6 − 705.6
ΔS° = −386.0 J/mol·K
Reaction (2):
2 AgCl(s) + Br₂(l) → 2 AgBr(s) + Cl₂(g)
Standard entropy values:
- S°(AgCl(s)) = 96.2 J/mol·K
- S°(Br₂(l)) = 152.2 J/mol·K
- S°(AgBr(s)) = 107.1 J/mol·K
- S°(Cl₂(g)) = 223.0 J/mol·K
Calculating ΔS°:
ΔS° = [2 × S°(AgBr(s)) + S°(Cl₂(g))] − [2 × S°(AgCl(s)) + S°(Br₂(l))]
ΔS° = [2 × 107.1 + 223.0] − [2 × 96.2 + 152.2]
ΔS° = [214.2 + 223.0] − [192.4 + 152.2]
ΔS° = 437.2 − 344.6
ΔS° = 92.6 J/mol·K
Reaction (3):
Hg(l) + Cl₂(g) → HgCl₂(s)
Standard entropy values:
- S°(Hg(l)) = 76.0 J/mol·K
- S°(Cl₂(g)) = 223.0 J/mol·K
- S°(HgCl₂(s)) = 144.3 J/mol·K
Calculating ΔS°:
ΔS° = S°(HgCl₂(s)) − [S°(Hg(l)) + S°(Cl₂(g))]
ΔS° = 144.3 − [76.0 + 223.0]
ΔS° = 144.3 − 299.0
ΔS° = −154.7 J/mol·K
Explanation:
The standard reaction entropy (ΔS°) measures the change in entropy, or disorder, between reactants and products under standard conditions (298 K and 1 atm). A negative ΔS° indicates a decrease in disorder, often associated with the formation of more ordered products from less ordered reactants. Conversely, a positive ΔS° suggests an increase in disorder.
In reactions (1) and (3), the negative ΔS° values imply that the products are more ordered than the reactants, leading to a decrease in entropy. In reaction (2), the positive ΔS° indicates that the products are less ordered, resulting in an increase in entropy.
Note on Image:
Providing an image of the entropy values or reaction mechanisms would require visual content, which is not possible in this text-based format. However, you can refer to standard chemistry textbooks or reputable online databases for visual representations and more detailed explanations.