[meghan]

I appreciate your help.  I've read other posts on Hess's Law and have attempted to solve the problem accordingly.  Can you tell me if I am correct?  If not, can you help me understand my error?

The question is:

Use Hess's Law to determine  :delta:H_f for CaO:  Ca (s) + 1/2O₂ (g)  CaO (g)

Ca (s) + 2H⁺ (aq)  Ca²⁺ (aq) + H₂ (g)     :delta:H = 1925.9 kJ/mol

2H₂ (g) + O₂  2H₂O (l)                          :delta:H = -571.68 kJ/mol

CaO (s) + 2H⁺ (aq)  Ca²⁺ (aq) + H₂O (l)        :delta:H = 2275.2 kJ/mol

I think the answer is:

2CaO (s) + 4H⁺ (aq)  2Ca²⁺ (aq) + 2H₂O (l)   :delta:H = 3629.42 kJ/mol

Thanks for your help and time.  I really appreciate it!

[UG]

Hi meghan,
What you have to do here is to rearrange your equations so that you end up with the one you want. Let me show you what I mean, your task was to find ΔH_f for CaO:  Ca (s) + 1/2O₂ (g)   CaO (g)*

*By the way, I think that is a typo, it should be CaO (s)

So what you need to do is to rearrange the three equations you have and then add up all of their ΔH's
Firstly rearrange the bottom one so you get CaO (s) on the other side.

Ca²⁺ (aq) + H₂O (l)   CaO (s) + 2H⁺ (aq)         ΔH = -2275.2 kJ/mol
Notice that the ΔH sign also changes

Next you half the second equation, so you only have 1/2O₂

H₂ (g) + 1/2O₂   H₂O (l)                          ΔH = -285.84 kJ/mol
Notice that ΔH halves

Finally, the first equation remains the same because Ca(s) is on the left hand side

Ca (s) + 2H⁺ (aq)   Ca²⁺ (aq) + H₂ (g)     ΔH = 1925.9 kJ/mol

What is the point of doing all this? I hear you ask   well, now all of the equations will cancel out to give you the one you want, which is Ca (s) + 1/2O₂ (g)   CaO (s). Like this:

  Ca (s) + 2H⁺ (aq) Ca²⁺ (aq) + H₂ (g)     ΔH = 1925.9 kJ/mol
     H₂ (g) + 1/2O₂ H₂O (l)                     ΔH = -285.84 kJ/mol
Ca²⁺ (aq) + H₂O (l) CaO (s) + 2H⁺ (aq)    ΔH = -2275.2 kJ/mol

So all that you're left with is: Ca (s) + 1/2O₂ (g)   CaO (s)
Now to work out the ΔH_f, you simply add up all of the numbers, 1925.9 + (-285.84) + (-2275.2) = -635.14 kJ/mol

[meghan]

Thank you, UG!  I understand this now.