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You should be able to change the equations so that you can cancel things. For example, you could reverse the direction of one equation. Or you could multiply an equation's coefficients by 2. These changes would make it possible to cancel something that needs to be cancelled. I do not think there will be a situation where you are completely unable to cancel anything. But I could be wrong.
If you choose to reverse the reaction or multiply by coefficients then you would have to change the enthalpy of the reaction as well. If the reaction is reversed, you multiply the enthalpy by -1 or by the coefficient that you multiplied the equation by.
In regards to multiplying by 1.5 to cancel out the reactants, you can do this because enthalpy is a state function, which means it is additive. By multiplying the coefficients in the equation you must also multiply the delta H by the same equation. Doing this makes the equation still the same, just a larger multiple of the base equation, and therefore helpful for us in the problem. Reflect on Chem 14A when we did this to make net equations as well.
The only situation in which you wouldn't be able to cancel out intermediate compounds is if you haven't fixed the coefficients at all or there was a mathematical mistake in doing so. Otherwise, you can be confident in knowing that a Hess's Law problem is solvable. Be sure to double check coefficients if you're having trouble as not all problems will require a simple 'multiply the equation by 2'. You may need more complex fractions in order to make intermediate steps cancel out, like the problem Prof. Lavelle did in lecture requiring a factor of 3/2.
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