[yrtsimehc]

So, my question says: Consider the following reaction at 25.0 ° C : 2NO₂ (g)  N₂O₄ (g)
The values of ΔH° and ΔS° are -58.03 kJ/mol and -176.6 J/K · mol, respectively. Calculate the value of K at 25.0° C. Assuming ΔH° and ΔS° are temperature independent, estimate the value of K at 100.0 °C.

What I thought I was supposed to do is calculate ΔG using ΔG = ΔH° - TΔS° and then plug it into the equation ΔG = -RTlnK and solve for K. But, when I did that, I kept getting -6.13 for 25°C and 6.35 for 100°C

Can you please explain to me what I am doing wrong and how to solve this problem correctly?

I know what the answers are supposed to be because my teacher provides us with the answers.
For 25°C it should be K=8.84 and for 100° C it should be 0.0798

Thank you so much in advance!

[curiouscat]

Your teacher's right.

@25 C
K=exp(-(-58030+298*176.6)/8.314/298)
8.853782

@100 C
K=exp(-(-58030+373*176.6)/8.314/373)

0.07976

You didn't convert to J?
Or
You didn't convert to K?

[yrtsimehc]

Hi! Thank you! I just have a few more question about that though.
What does the exp mean? Why are you adding the -58030 to the (298 * 176.6) instead of subtracting it?  And why are you dividing the 8.314 by 298.
I'm sorry.

[curiouscat]

Hi! Thank you! I just have a few more question about that though.
What does the exp mean? Why are you adding the -58030 to the (298 * 176.6) instead of subtracting it?  And why are you dividing the 8.314 by 298.
I'm sorry.

Post your attempt / expression / solution and then I'll help you. Sorry.

[yrtsimehc]

Okay, I guess this is not right, but I was solving for ΔG as the expression by doing:
-58.03 - (-0.1766 * 298) = -5.4032 and then plugging that in.
Am I not supposed to do that?

[curiouscat]

Okay, I guess this is not right, but I was solving for ΔG as the expression by doing:
-58.03 - (-0.1766 * 298) = -5.4032 and then plugging that in.
Am I not supposed to do that?

Fine so far. Show your "plugging in".

[yrtsimehc]

This is what I plugged in:

(-5.4032(-(-58030+(298*176.6)) / (8.314*298) = -11.78

[curiouscat]

This is what I plugged in:

(-5.4032(-(-58030+(298*176.6)) / (8.314*298) = -11.78

ΔG = -RTlnK

Solve for K? Don't you need an exponentiation somewhere? I don't understand your extra -5.4032.  Otherwise you are almost there.

Why don't you systematically write down your whole working? With units. A helpful habit.

[yrtsimehc]

Okay, so let me try this again. ...By the way, I'm sorry for taking up your time.

-5.4032= -8.314(298)(lnK)
lnK= 0.0021808448
e^0.0021808448  (to get rid of the ln)   = 1.002183225=K
1.002183225(-(-58030+(298*176.6)) / (8.314*298) = 23.281

But, again that it not correct. Can you please explain to me why we are solving for K first if it doesn't fit into the equation? How do I solve for the number that goes in front of the equation using K if the 1.002183225 should not be there first?

[Dan]

Units (you have already been asked to think about them).

In your calculation, think about the units are you using for ΔG. What units are you using for R?