1.50g of titanium at -5.0 °C was placed into a calorimeter with an initial temperature of 21.3; calculate the heat capacity of the calorimeter if the thermal equilibrium, between the titanium and the calorimeter was reached at 15.0°C. The specific heat capacity of titanium is 0.523 J/g°C.

The answer given was c=2.5 J/°C

here heat lost = heat gained
heat is gained by titanium which can be calculated using the following formula
q= mc delta t --(1)
m = 1.50 g
c= 0.523 J/g°C.
delta t = 15-(-5) deg C
heat is lost by calorimetry
here
q = c delta t --(2)
so delta t = 21.3- 15
and q is the amount of heat gained
plug in the value of heat gained from eq 1 and delta t and calculate c