[minestrypta]

Hey guys so here is a question from a practice test we were given:

"A student decides to investigate the enthalpy of reaction of solid magnesium and a solution of hydrochloric acid for an open inquiry heat laws systems laboratory exercise. Her objective is to determine ∆H for the reaction.
She weighs a 0.158-gram sample of magnesium and adds it to enough hydrochloric acid solution to make 100.0 mL of solution in a coffee-cup calorimeter. The acid is sufficiently concentrated so that the magnesium completely reacts. The temperature of the solution changes from 25.6°C to 32.8°C.
She made the assumption that the solution had the same density and specific heat as liquid water. Use her data to determine ∆H for the reaction, and then write the thermochemical equation for the reaction"

We are given the answer as: Mg(s) + 2 HCl(aq) → MgCl₂(aq) + H₂(g) + 4.6 × 10^5 J
I thought that if I took the mass of the Mg and calculated stoichiometrically the moles of HCl and both products and then used the heat of fusion (∆H°f) of each product and each reactant for the equation ∆H = (n * ∆H°f)products - (n * ∆H°f)reactants. My calculation looks like:

((-641.5 kJ *.00649) + (0 kJ *.00649)) - ((∆Hf of Mg(s) =0) + (-167.2 kJ *.01299))

Then I got
-4.16 kJ - 2.17kJ = -1.99 kJ = 1990 J or 1.9 x 10^2 J

Obviously not right. I tried it without the moles because they were clearly causing my numbers to be too small. I got:
(-641.5 kJ) - (-167.2 kJ) = 474.3 kJ = 4.7 x 10^5

Which seems very close to the actual answer...but it isn't. I'm not quite sure where to go, especially since I was given several other variables which are unused in this first attempt. I have been trying to think about it now as the heat flow q, in particular, qreaction + qsoln + qcalorimeter = 0 , but this approach has yielded no results as of yet. Can anyone please assist me in understanding this problem?

[Borek]

You are overcomplicating it. It is just a plain, old q=mcΔT. Once you know q, just convert it to molar.