Calculate the standard entropy change for the following reaction:
[tex]$N _2 O _4(g) \rightarrow 2 NO _{2(g)}$[/tex]
Given that:
Substance (Formula) | Molar entropies | [tex]$S ^{\circ}$[/tex] in J/K
---|---|---
[tex]$N _2 O _4$[/tex] | 304.2 |
[tex]$NO _2$[/tex] | 240.0 |
Answer (2)
The standard entropy change is calculated using the formula: Δ S ∘ = ∑ S ∘ ( products ) − ∑ S ∘ ( reactants ) .
For the reaction N 2 O 4 ( g ) → 2 N O 2 ( g ) , the formula becomes Δ S ∘ = 2 × S ∘ ( N O 2 ) − S ∘ ( N 2 O 4 ) .
Substituting the given values, Δ S ∘ = 2 × ( 240.0 J/K ) − 304.2 J/K .
The standard entropy change for the reaction is 175.8 J/K .
Explanation
Problem Analysis We are given the reaction N 2 O 4 ( g ) i g h t ha r p oo n u p 2 N O 2 ( g ) , and the standard molar entropies S ∘ ( N 2 O 4 ) = 304.2 J/K and S ∘ ( N O 2 ) = 240.0 J/K . We need to calculate the standard entropy change for this reaction.
Formula for Entropy Change The standard entropy change of a reaction is given by the difference between the sum of the standard entropies of the products and the sum of the standard entropies of the reactants, each multiplied by their stoichiometric coefficients. In this case, we have: Δ S ∘ = ∑ S ∘ ( products ) − ∑ S ∘ ( reactants )
Applying the Formula to the Reaction For the given reaction, the formula becomes: Δ S ∘ = 2 × S ∘ ( N O 2 ) − S ∘ ( N 2 O 4 ) This is because we have 2 moles of N O 2 as the product and 1 mole of N 2 O 4 as the reactant.
Calculation Now, we substitute the given values into the formula: Δ S ∘ = 2 × ( 240.0 J/K ) − 304.2 J/K Δ S ∘ = 480.0 J/K − 304.2 J/K Δ S ∘ = 175.8 J/K
Final Answer Therefore, the standard entropy change for the reaction is 175.8 J/K .
Examples
Entropy changes are crucial in understanding the spontaneity of chemical reactions. For instance, consider designing an efficient industrial process for producing ammonia ( N H 3 ) from nitrogen and hydrogen. By calculating the entropy change, along with enthalpy changes, engineers can optimize reaction conditions (temperature, pressure) to maximize ammonia yield and minimize energy consumption, leading to a more sustainable and cost-effective manufacturing process. This ensures that the reaction proceeds favorably under specific conditions, making the production economically viable.
The standard entropy change for the reaction N 2 O 4 ( g ) → 2 N O 2 ( g ) is calculated to be 175.8 J/K . This indicates an increase in the disorder of the system as a result of the reaction. The calculation follows the formula Δ S ∘ = ∑ S ∘ ( products ) − ∑ S ∘ ( reactants ) .
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