Question

The equation shows one mole of ethanol fuel being burned in oxygen. Convert the energy released into its equivalent mass.

C2H2OH (l) + 3 O2 (g) --> 2 CO2(g) + 3 H2O (l)

(delta/H) = -1418 kJ/mol.

Can anyone help me figure out how to solve this problem?

Answer 1

Well sense we are doing an combustion we assume that the only work done on the system is volume work and we can write up the following:
\[\Delta U=q+w\]
\[w=0\]
\[q=\Delta H\]
Here is U, the internal energy, q the process of heat, w the process of work and delta H the change in entropy.
We can here use Einstein's relation between mass and energy:
\[E=mc ^{2}\]
We isolate for the mass, m;
\[m=\frac{ E }{ c ^{2} }\]
Where:
\[E= \Delta U=\Delta H\]

Answer 2

Wait I'm very confused. Why are we finding the mass? (oh it doesn't really matter, but just for future knowledge, delta H is change in enthalpy) anyways, so if I'm finding the mass I divide -1418 kJ/mol by c2. (speed of light squared) right?

Answer 3

It say in the question: "Convert the energy released into its equivalent mass." that most be to find the mass equal to the amount of energy and the way to do that is to use Einstein's relation between energy and mass
Now, Delta H is given by kJ/mol and sense only 1 mol have been used in the reaction we can look away from the mol^-1

Basically you are right :)

Answer 4

You can try do the calculations here with the units then I can see if you are 100% right. :)

Answer 5

Or would you like me to do them?

Answer 6

Sorry about the question of the mass I didn't read my own question right :P I'm off today. Okay so c2= 9.00 x 10^16. -1418 kJ/mol / 9.00 x 10^20 = -1.2762 x10^20. Is that the final answer or do I need to convert anything?

Answer 7

I didn't type that right. -1418 / 9.00 x 10^16 = -1.2762 x 10^20

Answer 8

Lets see:
\[m=\frac{ \left| \Delta H \right| }{ c ^{2} }*n\]
\[m=\frac{ \left| -1418 kJ/mol \right| }{ 2.998*10^{8} m/s }*1mol=1.578*10^{-8} g\]

Answer 9

I sugeest you set a numerical sign as we can't have a negative mass.

Answer 10

Wait let me make sure we're on the same page. Is the c2 already squared when they give me the number 3.00 x 10^8 (that's the # in my textbook. I could use yours as well). Or do I need to square it to 9.00 x 10^16

Answer 11

sorry I forgot to square my number :P except the result is true

Answer 12

\[m=\frac{ \left| -1418 kJ/mol \right| }{ (2.998*10^{8} m/s)^{2} }*1mol=1.578*10^{-8} g\]

Answer 13

If you use 3.00 it is also fine.

Answer 14

So the answer to this question is 1.578 x 10^-8? Or do I need to recalculate that with the 3.00 x 10^8 squared? (btw, sorry for all the questions. It takes me a while for it to finally click)

Answer 15

1.578 x 10^-8 gram is the answer. The 3.00 x 10^8 m/s squared we divide with the energy which is Delta H.
I'm sorry if I'm not answering what you are asking, but I'm not sure if I fully understand what you are asking :/

Answer 16

It's okay I understand now :) I reworked it and got that answer :) thank you so much for helping. I really appreciate you working it out with me instead of just giving me the answer.

Answer 17

No problem, OpenStudy is after all a learning service and not a answer-factory :)

Answer 18

Which is awesome for me. I home school. It's really helpful to be able to come here and learn when I can't ask a teacher.

Answer 19

Strange, I've been writing a bit with the teachers from CA and they keep saying that if their students have problems they should message them. Seems like there are some connection problems after all.
But I'm glad you can get the help you need here.

Answer 20

And if you ever think I may be of help, just link me to the question and I'll do everything I can to help :)

Answer 21

Thank you so much! I really appreciate it :D