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Description:

This is a question about Gibbs free energy. You'd better act fast though. Otherwise, you may have to pay the normal sticker price of $99.99.

Language:
English Language

Transcript

00:03

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

00:06

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

00:10

Okay, here's our question.

00:12

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

00:18

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

00:23

And here are our potential answers.

00:25

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

00:30

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

00:31

Not in the romantic way.

00:34

In the science way.

00:35

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

00:40

If ?G is negative, the reaction is spontaneous.

00:44

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

00:49

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

00:50

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

00:54

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

01:02

and the reaction is always spontaneous.

01:05

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

01:09

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

01:13

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

01:19

to ?G.

01:21

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

01:24

We want to know when ?G is negative.

01:27

What do we have here?

01:28

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

01:30

…No?

01:31

Not ringing a bell?

01:33

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

01:35

We’ll be sitting here, waiting patiently.

01:38

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

01:43

to always be true.

01:45

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

01:47

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

01:49

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

01:53

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

01:58

the signs of ?H and ?S.

02:01

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

02:05

Let’s look at our options.

02:06

Let's check out A, for example.

02:07

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

02:12

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

02:17

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

02:21

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

02:26

positive, meaning the inequality is always true.

02:30

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

02:34

And there’s our message about optimism.

02:36

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

02:39

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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