Hey guys, in this new video, we're going to take a look at the calculations behind Gibbs
Free Energy.
If we take a look at example one, it says the reduction of iron (III) oxide with hydrogen
produces iron metal and can be written as follows, so we have one mole of iron (III)
oxide solid reacting with three moles of hydrogen gas to give us two moles of iron solid plus
three moles of water vapor.
I give you the delta H or enthalpy value and the delta S entropy value.
The question says is this reaction spontaneous under standard-state conditions at 25 degrees
Celsius.
If not, at what temperature will it become spontaneous.
This is a two part question.
So they're asking us if it's spontaneous or not.
Remember the best variable to calculate spontaneity is delta G. I gave you delta H. I gave you
delta S. And we have temperature.
So we can use delta G zero equals delta H zero minus T delta S zero.
We know we should use this version because I'm saying standard-state conditions.
We're supposed to use delta G with a zero.
What we need to do next is we have to make sure that our delta H and our delta S values
agree in units.
Here, delta H uses kilojoules, but delta S uses joules.
Kilojoules are the default type of units for these types of questions, so let's just convert
the delta S to kilojoules as well.
Remember, we're going to say for every 1,000 joules, there's one kilojoule.
This is equivalent to 0.1415 kilojoules over K.
We're going to plug in the 98.8 kilojoules minus temperature has to be in Kelvin as well,
so I add 273.15 to 25.
That gives us 298.15 Kelvin times the delta S value we just calculated.
The Kelvins will cancel out, so it will be kilojoules minus kilojoules.
When we do that we get an answer of 56.633 kilojoules.
Remember if delta G is negative, then it's going to be spontaneous.
The fact that we got a positive answer means that this reaction is not spontaneous.
Now it's up to us to figure out what temperature will it become spontaneous.
Anytime they ask you at what temperature does it become spontaneous, that means you assume
that delta G zero is equal to zero.
We're going to use the same exact equation here, except now delta G is zero.
That still equals the same value for delta H, the same value for delta S. Here we're
not going to know what temperature is.
That's what we're trying to solve.
So zero equals 98.8 kilojoules minus T times 0.1415 kilojoules over K. What we're going
to do first, we're going to subtract out the 98.8 kilojoules.
That equals negative T times 0.1415 kilojoules over K.
We need to isolate temperature by itself, so we're going to divide out negative 0.1415
kilojoules over K on both sides.
This cancels out with this and the negative sign also cancels out.
So we have a negative being divided by another negative.
Kilojoules cancel out, so we'll be in Kelvin.
Temperature here equals 698.233 temperature.
Technically, if we take that number and plug it back in, then delta G will equal zero.
Remember when delta G equals zero, we're at equilibrium.
We're technically still not spontaneous.
What you would say is temperatures above this answer would give you a spontaneous reaction.
We're going to say temperatures above this answer would be spontaneous.
Temperatures below would be non-spontaneous.
Make careful sure when you're looking at your exam, what exactly are they asking you in
terms of temperature.
Are they looking for an exact answer or are they asking at what temperature will it be
spontaneous?
Just remember when you work it out, the temperature you get, that's technically a temperature
at equilibrium.
All you have to say is any temperature above that, whether it be 0.0001 degrees higher,
it's still going to be spontaneous.
It will just be a little bit spontaneous.
Remember the answer you get, temperatures above that answer will make your reaction
spontaneous.
Now that we've done example one together, I want you guys to attempt to do practice
one.
Here we're saying if delta G is small and positive, which of the following statements
is true.
I'll give you guys a huge hint, remember we have to think of delta G in three situations,
when it's less than zero, equal to zero or greater than zero.
What do each of those mean?
What do I mean by the word small?
Also, remember if you're spontaneous one way, then you'll be non-spontaneous the other way.
Just because delta G is positive, doesn't mean it can't be spontaneous period.
It would be non-spontaneous in the forward, but what about the reverse?
Ask yourself these questions and you'll be able to answer this question really quickly.
Good luck guys.