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We know that the products are all in the liquid state, so now we consider the states of the reactants needed to make those products. For example, we get liquid H2O from O2 and H2. Both of these diatomic elements are in the gaseous state because elements like to be in the most stable phase at 1 atm and 25 C. For oxygen and hydrogen, the most stable state is the gas phase. For methanol which has Carbon, the most stable state is (gr) which means solid graphite. You use this logic to assume what the states of the reactants are for the rest of the problem. But be aware, that not all diatomic elements have the most stability in the gaseous state.
For part a, that's what I thought, but the solutions manual said that water is in gas form so you have to use the enthalpy of vaporization equation to find the enthalpy of the liquid state. So are we supposed to know that H2 gas and O2 gas make H2O gas. And for the rest of the parts, are we assuming that the product is in gas phase as well, if not, how do we tell?
From what I understand, we should probably memorize the most stable states of common compounds and elements such as carbon. Otherwise you would just need to guess which state the product is, though it may often be easy to assume; for example in part a, both H2 and O2 are in the gas phase, so it would be logical for H2O to be in the gas phase. We cannot simply assume that all the products are in the gas phase for the other parts though.
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