0:07

The question asks us to calculate the delta G at 25 degrees Celsius based on

the given information and decide whether or not the reaction is spontaneous.

We're given the balanced chemical equation.

We're given delta H of formation values and entropies of substances, but

we're not given the enthopy or the entropy of a particular reaction.

So the first thing we're going to have to do is calculate both the delta

H of formation and the delta S of the system.

Remember that when we're looking at our Gibbs free energy,

we're using the expression delta G equals delta H minus T delta S.

This is the formula we'll use to be able to calculate delta G and

determine the spontaneity of the reaction.

For our delta H value, we know we want to

have delta H of the reaction = delta

H of formation of the products- delta

H of formation of the reactants.

And since all of our coefficients are 1,

we don't have to worry about any coefficients in our calculation.

So delta H of reaction = delta H of our products, which is our COCl2.

So minus 219.1 kilojoules per mol,

and there's 1 mol of that,- (-110.5

KJ per mole for the carbon monoxide),

again x 1), because there's 1 mole.

For the chlorine, I don't need to put anything in there.

That's an element in its standard state, so it has enthalpy of formation of 0.

Then I find delta H of reaction = -108.6 kilojoules.

This is an exothermic process because the delta H value is negative, so

we're losing energy from the system.

2:12

Now I need to calculate the value of delta S of the reaction.

Just like I did with my delta H of reaction, I'm going to look at my delta S

of reaction = S of the products- S of the reactants.

So delta S of the reaction = S of my products,

which I have one product, COCl2.

So I have 283.5 joules per mol Kelvin.

2:48

And I'm going to subtract from that the entropy of

both of my reactants, so the entropy of CO,

which is 197.7 joules per mol Kelvin- the Cl2.

Entropies of pure substance or elements in there standard state is not 0,

unlike the delta H values.

And so, I have 223.1 joules per mol Kelvin.

3:17

And what I find is that the delta S of my reaction =

-137.3 joules per Kelvin.

Because each of these is 1 mol, my mols will have cancelled out as well.

So now I know my delta S of reaction.

I also know the delta H of my reaction.

Now, I can use that information with my

delta G = delta H- T delta S to solve for delta G.

And what I find is delta G =

-108.6 kilojoules- T.

I'm at 25 degrees Celsius, but I need to convert that to Kelvin.

So that's 298 Kelvin x delta S,

which is -137.3 joules per Kelvin.

But I also need to divide by 1,000 because I want to convert that to kilojoules, so

that my entropy value and my enthalpy value are both with respect to kilojoules.

Now I have delta G = -67.7 kilojoules.

And because delta G is a negative value,

this is a spontaneous process at 25 degrees Celsius.