What is the value for [tex]$\Delta G$[/tex] at 100 K if [tex]$\Delta H=27 kJ / mol$[/tex] and [tex]$\Delta S$ =0.09 kJ /( mol \cdot K )$[/tex] ?
A. [tex]$\Delta G=2700 kJ / mol$[/tex]
B. [tex]$\Delta G=-36 kJ / mol$[/tex]
C. [tex]$\Delta G=18 kJ / mol$[/tex]
D. [tex]$\Delta G=0 kJ / mol$[/tex]

Use the Gibbs free energy equation: Δ G = Δ H − T Δ S .
Substitute the given values: Δ H = 27 kJ/mol , Δ S = 0.09 kJ/(mol ⋅ K) , and T = 100 K .
Calculate Δ G : Δ G = 27 − ( 100 × 0.09 ) = 27 − 9 = 18 kJ/mol .
The value for Δ G at 100 K is 18 kJ/mol ​ .

Explanation

Problem Analysis We are given the enthalpy change ( Δ H ), entropy change ( Δ S ), and temperature (T), and we want to find the Gibbs free energy change ( Δ G ).

Gibbs Free Energy Equation We will use the Gibbs free energy equation: Δ G = Δ H − T Δ S

Given Values We are given: Δ H = 27 kJ/mol
Δ S = 0.09 kJ/(mol ⋅ K) T = 100 \text{ K}

Substitution Substitute the given values into the Gibbs free energy equation: Δ G = 27 kJ/mol − ( 100 K ) × ( 0.09 kJ/(mol ⋅ K) )

Calculation Calculate the value of Δ G : Δ G = 27 − ( 100 × 0.09 ) = 27 − 9 = 18 kJ/mol

Final Answer Therefore, the value for Δ G at 100 K is 18 kJ/mol.


Examples
The Gibbs free energy change is a crucial concept in thermodynamics, indicating the spontaneity of a reaction. For instance, consider a chemical reaction in a lab setting at a specific temperature. By calculating Δ G , scientists can determine whether the reaction will proceed spontaneously ( Δ G < 0 ), is at equilibrium ( Δ G = 0 ), or requires external energy to proceed ( 0"> Δ G > 0 ). This helps in designing efficient chemical processes and predicting reaction outcomes.

Answered by GinnyAnswer | 2025-07-03

The value for Δ G at 100 K is 18 kJ/mol based on the Gibbs free energy equation. By substituting the provided Δ H and Δ S values into the equation, we determined the spontaneity of the reaction at that temperature. The correct answer choice is C: Δ G = 18 kJ/mol .
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Answered by Anonymous | 2025-07-04