ShmoopTube

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And here's your Shmoop du jour, brought to you by free energy.

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It’s like a free lunch, except, you know, it actually exists. [Girl approaches pizza store]

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Okay, here's our question.

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For ?G to have a negative value 100% of the time, ?H

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and ?S should be which of the following, respectively?

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And here are our potential answers.

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All right, well, the change in Gibbs free energy, or ?G, tells us whether

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or not a chemical reaction is spontaneous. [Scientists working in a lab]

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Not in the romantic way.

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In the science way.

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Though flowers are always a nice gesture…take notes, chemical reactions… [Scientist holding bunch of flowers]

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If ?G is negative, the reaction is spontaneous.

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If it’s positive, the reaction is not spontaneous and we have to add energy to get the reaction

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to proceed. [Man holding glassware of chemical and goes up in flames]

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We’re sure there’s a message about optimism in there somewhere.

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Anyway, this question is asking us for the signs on ?H and ?S so that ?G is always negative,

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and the reaction is always spontaneous.

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So, what in the world are ?H and ?S, and what do they have to do with free energy?

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No, it’s not hours and seconds, and no, free energy is not a sports drink. [Man holding energy on a track]

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?H and ?S are thermodynamic quantities, and for this problem we care about how they relate

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to ?G.

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What we have to do is recall the Gibbs free energy equation.

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We want to know when ?G is negative.

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What do we have here?

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This looks like a complex inequality. [Complex inequality example]

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…No?

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Not ringing a bell?

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Go read up on complex inequalities. [Man reading a book]

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We’ll be sitting here, waiting patiently.

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Now let’s think about the necessary signs of ?H and ?S in order for this inequality

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to always be true.

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Add T?S to both sides to simplify the inequality.

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Inequality – easy to simplify in science, not so much in life.

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When using the Kelvin temperature scale, we know T is always positive. [temperature thermometer increases]

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Multiplying by T won’t change the sign of the right hand side, so we can simply consider

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the signs of ?H and ?S.

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What signs on these variables make this inequality always true? [Girl standing with mathematical signs]

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Let’s look at our options.

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Let's check out A, for example.

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If ?H and ?S are both positive, is the inequality always true?

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If you can think of a scenario to disprove the inequality, then your answer is no.

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The only scenario that can’t be disproven is choice (D).

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The left hand side of the inequality is always negative, and the right hand side is always

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positive, meaning the inequality is always true.

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Because, you know, a positive number is always greater than a negative number. [Guys holding positive and negative number signs]

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And there’s our message about optimism.

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And now you know a little bit more about Gibbs free energy.

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And if you happen to come across a free lunch, please… let us know. [People cue outside a store for free lunch]

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