In the classroom, we reacted

Mg(s) + 2HCl -> MgCl2(aq) + H2 (g)
(0.31 g of Mg(s), and 99.46 g of HCl)
Initial temp. = 22.5 celsius, max. temp. 36.0 celsius

and

MgO(s) + 2HCl -> MgCl2(aq) + H2(g)
(1.00 g of MgO(s) and 97.71 g of HCl)
Initial temp. 22.0 celsius, max. temp. 28.5 celsius.

Please note that the temperatures were crudely taken, so a wide range of experimental error is likely.

When calculating the deltaH for the first equation, this is what I got

Q=mcDeltaT
Q=(99.46)(4.18)(13.5)
Q=5612.5 J
Q=5.6 kJ

and the second reaction;

Q=mcDeltaT
Q=(97.71)(4.18)(6.5)
Q=2654 J
Q=2.7 kJ

My question is, how do those numbers make any sense? Or am I just confused as to what those numbers represent? Thanks in advance!

The first one is

q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
The water is what absorbed the heat generated by the reaction.
Your value of 5.6 kJ is the heat generated by 0.31 g or by (0.31/24.3) moles Mg. The usual reporting is done in kJ/mol; therefore, 5.6 kJ x (24.3/0.31) = kJ/mol.
I note that the second does NOT produce H2 gas. The reaction is
MgO + 2HCl ==> MgCl2 + H2O.

The numbers you calculated represent the heat absorbed or released during each reaction, which can be used to determine the enthalpy change (∆H) of the reaction. Enthalpy (∆H) is a measure of the heat content of a system and can be positive or negative.

In the first reaction (Mg + 2HCl -> MgCl2 + H2), you calculated that the heat change (∆H) was 5.6 kJ. This means that the reaction released 5.6 kJ of energy into the surroundings. Since the temperature increased in this case, the reaction is exothermic.

In the second reaction (MgO + 2HCl -> MgCl2 + H2), you calculated that the heat change (∆H) was 2.7 kJ. This means that the reaction released 2.7 kJ of energy into the surroundings. Similarly, since the temperature increased, this reaction is also exothermic.

The fact that the values for ∆H are different for the two reactions indicates that they have different energy changes. It is important to note that the magnitude of ∆H does not directly correlate with the amount of reactants used. Instead, ∆H is influenced by the specific stoichiometry and energy changes that occur in each reaction.

It is also worth mentioning that the experimental errors in the temperature measurements can affect the accuracy of the calculated ∆H values. Therefore, it's always necessary to include error analysis and consider a range of possible values for ∆H.

Overall, the numbers you calculated provide insight into the energy changes that occur during the reactions and help determine the exothermic or endothermic nature of the processes.