Expert: ScienceAdviser - 3/18/2009

Question
QUESTION: OK - here is the set - up.  Question is way at the bottom but you need this set-up to understand my question.  
ΔHf methane is represented by the equation:

C(s) + H2(g) CH4 (g)

This equation can be constructed using the equations for combustion of the reactants (carbon and hydrogen) and the product (methane)
C(s) + O2(g) CO2(g)    -394kj    enthalpy 1
         
H2(g) + 1/2O2(g) H2O(l)    -242kj    enthalpy 2

   multiply this equation by 2 to get

       
         
2H2(g) + O2(g) 2H2O(l)    -484kj    enthalpy 3

   Add the first and third equation together to get:

       
C(s) + 2O2(g) + 2H2(g) CO2(g) + 2H2O(l)    -878kj    enthalpy (1 + 3) = 4

   Now take away the equation for the combustion of methane

       
CH4 (g) + 2O2(g) CO2(g) + 2H2O(l)    -891kj    enthalpy 5
         

   And after rearrangement ( take the CH4 to the right hand side) the result is the equation for the formation of methane

       
C(s) + H2(g) CH4 (g)    +13kj    enthalpy ( 4 - 5)
         
I cannot figure out why I have to multiply H2(g) + 1/2O2(g) H2O(l) by two?  And why do I start with 1/2 O2 rather than just using O2.  THANKS!

ANSWER: Hi there, you usually multiply because you need the equiblrium between the number of atoms that you have in each site. If you use the 1/2 of oxyen you are not able to get one mole of CH4. If you go back and use only 1/2 of oxygen, you will notice that it won't add up to methan that you are looking for.

Please get back to me if my answer is not very clear and you would like me to go back and explain it step by step. I will do that for you.

Best,
Gloria

---------- FOLLOW-UP ----------

QUESTION: Hi Gloria, THANKS.  I think I am getting it.  The only thing I am still confused about is why I have to start with only 1/2 oxygen rather than using 1 O2 for the combustion of H2 in the first place?  How do I know that I have to start by using 1/2 O2?  Thank you so much.

Answer
Hi there, You are very welcome. I think it is becasue, again, you have to equiblirate your equation. Honestly, most of the time, we were told to use O2 instead of 1/2O2. but if you think about it:

H2 + O2 ---> H2O, you just need one molecular of oxygen in the water, so you go with 1/2 rather than doubling every thing. you get one mole of H2, but you require only 1/2 of oxygen for that.

That is the only reason that came to my mind.

Let me know if you have any more question or it is still not clear to you.
Best
Gloria