Hess's law from Kaplan

[joonkimdds]

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Given the reaction and thermodynamic data, calculate the delta Hf for C6H5OH in kcal/mol.

C6H5OH + 7O2 => 6CO2 + 3H2O = 729.8
C + O2 => CO2 = 94.4
2H2 + O2 => 2H2O = 136.8


delta H = (sum of all product) - (sum of all reactant)
729.8kcal = 6(delta Hf CO2) + 3(delta Hf H2O) - (delta Hf C6H5OH)
729.8kcal = 6(94.4)+3(136.8)-(delta Hf C6H5OH)
this is how the solution found the delta Hf C6H5OH.


I understand that we put 6 in front of CO2 because the product has 6CO2 even though the reactant only had 1.


but I don't understand why we put 3 in front of H2O.
I mean it's true that there will be 3H2O in the product side
but 3 x 126.8 means 3 (delta Hf 2H2O not H2O) and it will make 6H2O instead of 3H2O.


and I don't understand why we don't need to subtract (delta Hf 7O2).
The solution says its in standard state but I am having hard time understanding this.

 

[UNMPDS]

Given the reaction and thermodynamic data, calculate the delta Hf for C6H5OH in kcal/mol.

C6H5OH + 7O2 => 6CO2 + C = 729.8
C + O2 => CO2 = 94.4
2H2 + O2 => 2H2O = 136.8


delta H = (sum of all product) - (sum of all reactant)
729.8kcal = 6(delta Hf CO2) + 3(delta Hf H2O) - (delta Hf C6H5OH)
729.8kcal = 6(94.4)+3(136.8)-(delta Hf C6H5OH)
this is how the solution found the delta Hf C6H5OH.


I understand that we put 6 in front of CO2 because the product has 6CO2 even though the reactant only had 1.


but I don't understand why we put 3 in front of H2O.
I mean it's true that there will be 3H2O in the product side
but 3 x 126.8 means 3 (delta Hf 2H2O not H2O) and it will make 6H2O instead of 3H2O.


and I don't understand why we don't need to subtract (delta Hf 7O2).
The solution says its in standard state but I am having hard time understanding this.

Divide the 2H2 + O2 => 2H2O = 136.8 by 2 to get 1 mole of everything and 1/2 0f 136.8, then plug this new amount into 3H2O. Make sense?

 

[joonkimdds]

Divide the 2H2 + O2 => 2H2O = 136.8 by 2 to get 1 mole of everything and 1/2 0f 136.8, then plug this new amount into 3H2O. Make sense?

that's what I was thinking.
136.8/2 = 68.4
and then 3 x 68.4 = 205.2 is what I thought 3H2O should be.
but Kaplan used 136.8 x 3 = 410.4 for 3H2O.