If we added 25.00 mL of aqueous solution 1 to a simple calorimeter and 25.00 mL of aqueous solution 2 to the same simple calorimeter, and the solution in the calorimeter experienced an increase of 4.00 degrees Celsius during the reaction that ensued, we would predict that the calorimeter had a heat transfer (in Joules) of ____?

You had 50.00 mL. If we assume the heat capacity of the 50 mL was the same as water and that there was no loss of heat to the calorimeter or the surroundings the q would be

q = mass H2O x specific heat H2O x delta T.
q = 50g x 4.184 J/c x 4 = ?