This is what I did, hopefully no mistakes along the way!
Okay so, we have:
2HCl + Ba(OH)2 ----> BaCl2 + 2H20
If we remove the spectator ions, we end up with: H+(aq) + OH-(aq) ---> H20(l)
Now if we find the mole we have of each, we can see that n(OH-)= 2*0.04*0.431= 0.03448mol (which is limiting as it is less than the n(H+)
Now since 1mol of reaction = 56.2kJ of energy
0.03448mol = x
Cross multiply and you get a total of 1.9378kJ of energy released. Since we are dealing with a calibration factor with the units J/degree Celsius we have to convert this to J, so multiply by 1000 = 1937.8J of energy.
Pop this into out calorimeter rule thingo
C.F = E/Change in temp (CT) ------------> 453 = (1937. 8 )/(CT)
So then we solve and see that change in temp is 4.278 degrees celsius. Add this to our initial temperature and the final temperature is hopefully 24.8 degrees celsius.