When 0.752 g of Ca metal is added to 200.0 mL of 0.500 M HCl(aq), a temperature increase of 12.2C is observed.

Question

Assume the solution's final volume is 200.0 mL, the density is 1.00 g/mL, and the heat capacity is 4.184 J/gC.
(Note: Pay attention to significant figures. Do not round until the final answer.)
The molar heat of reaction, H rxn, for the reaction of

Ca(s) + 2H+(aq) Ca2+(aq) + H2(g)

? is kJ/mol.

for q, i got 10208.96 J, then i converted to 102 kJ.
i also got 0.01876mol Ca. However, I'm confused after that.

10,208.96 J is correct. Your conversion to kJ is not but let's not convert just yet.
The mols Ca in 0.752 g Ca is correct, also, at 0.01876 mols Ca, but I prefer to do the conversion all at once and keep all those numbers in the calculator. If you feel more comfortable working with your numbers, then 10,208.96 J/0.018763 mol = ?? J/mol.

10,208.96 J/0.752g x (40.078g/1 mol) = 544,088.70 J/mol. (You see that I haven't changed anything.). Now convert to kJ/ mol.
544,088.70 J/mol x (1 kJ/1000 J) = 544.08870 kJ/mol = 544 kJ/mol to three significant figures (3 s.f. in 12.2 and 0.752). I hope this helps.