Basically, Hess's law requires that you manipulate the equations (either by multiplying or dividing by a factor) and add (or subtract) the equations, such that terms in the final combined equation cancel out on either side to leave you with the equation you are trying to end up with.
Whenver you operate on a single equation (say, multiply by 2), you need to multiply the value of delta H by 2.
For your problem above, you would need the value of delta h in the final problem. From what I can see, you would need to do the following:
1. Multiply the entire first equation by two (2) which would leave you with 2H2 (g) + O2 (g) -------> 2H2O and delta H = -571.6 kJ
2. Reverse the third equation, which would leave you with
3CO2 + 4H2O ----------> C3H8 + 5O2 and delta H = (the negative of whatever the omitted value is i.e. if it is -300, then it should be 300 and vice versa).
3. Add equation 2 to the results obtained from (1) and (2) above. You will see that species cancel out to give you
C3H4(g)+2H2(g) ----> C3H8(g)
the delta H value of this equation is then -571.6 + (-1937) + (********) kJ
3CH4(g)->C3H8(g)+2H2(g)
Calculate change in G at 298 k if the reaction mixture consists of 41atm of CH4 , 0.010 atm of CH3, and 2.3×10−2 atm of H2.
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