Science, Tech, Math Science Free Energy and Reaction Spontaneity Example Problem Using Changes in Free Energy to Determine if a Reaction is Spontaneous Share Flipboard Email Print Gibbs free energy may be used to determine whether or not a reaction will occur spontaneously. Steve McAlister, Getty Images Science Chemistry Basics Chemical Laws Molecules Periodic Table Projects & Experiments Scientific Method Biochemistry Physical Chemistry Medical Chemistry Chemistry in Everyday Life Famous Chemists Activities for Kids Abbreviations & Acronyms Biology Physics Geology Astronomy Weather & Climate by Todd Helmenstine Updated February 14, 2018 This example problem demonstrates how to calculate and use changes in free energy to determine a reaction's spontaneity.ProblemUsing the following values for ΔH, ΔS, and T, determine the change in free energy and if the reaction is spontaneous or nonspontaneous.I) ΔH = 40 kJ, ΔS = 300 J/K, T = 130 KII) ΔH = 40 kJ, ΔS = 300 J/K, T = 150 KIII) ΔH = 40 kJ, ΔS = -300 J/K, T = 150 KSolutionThe free energy of a system can be used to determine if a reaction is spontaneous or nonspontaneous. Free energy is calculated with the formulaΔG = ΔH - TΔSwhereΔG is the change in free energyΔH is the change in enthalpyΔS is the change in entropyT is the absolute temperatureA reaction will be spontaneous if the change in free energy is negative. It will not be spontaneous if the total entropy change is positive.**Watch your units! ΔH and ΔS must share the same energy units.**System IΔG = ΔH - TΔSΔG = 40 kJ - 130 K x (300 J/K x 1 kJ/1000 J)ΔG = 40 kJ - 130 K x 0.300 kJ/KΔG = 40 kJ - 39 kJΔG = +1 kJΔG is positive, therefore the reaction will not be spontaneous.System IIΔG = ΔH - TΔSΔG = 40 kJ - 150 K x (300 J/K x 1 kJ/1000 J)ΔG = 40 kJ - 150 K x 0.300 kJ/KΔG = 40 kJ - 45 kJΔG = -5 kJΔG is negative, therefore the reaction will be spontaneous.System IIIΔG = ΔH - TΔSΔG = 40 kJ - 150 K x (-300 J/K x 1 kJ/1000 J)ΔG = 40 kJ - 150 K x -0.300 kJ/KΔG = 40 kJ + 45 kJΔG = +85 kJΔG is positive, therefore the reaction will not be spontaneous. AnswerA reaction in system I would be nonspontaneous.A reaction in system II would be spontaneous.A reaction in system III would be nonspontaneous. citecite this article Format mla apa chicago Your Citation Helmenstine, Todd. "Free Energy and Reaction Spontaneity Example Problem." ThoughtCo, Feb. 14, 2018, thoughtco.com/free-energy-and-reaction-spontaneity-problem-609492. Helmenstine, Todd. (2018, February 14). Free Energy and Reaction Spontaneity Example Problem. Retrieved from https://www.thoughtco.com/free-energy-and-reaction-spontaneity-problem-609492 Helmenstine, Todd. "Free Energy and Reaction Spontaneity Example Problem." ThoughtCo. https://www.thoughtco.com/free-energy-and-reaction-spontaneity-problem-609492 (accessed April 22, 2018). copy citation Continue Reading