A1.00 g sample of nh4no3 is decomposed in a bomb calorimeter. the temperature increases by 6.12°c. what is the molar heat of decomposition for ammonium nitrate?

First, you have to know that this is an exothermic reaction as the heat increased as a product of the reaction.

then, we need to get the heat change q = M*C*ΔT 

                                                                    = 1 g * 1.23 KJ/C-1 * 6.12

                                                                    = 7.5 KJ

and because of this is an exothermic reaction so,
the heat of decomposition ΔH = - 7.5 KJ

after that, we need to get the moles of NH4NO3:

moles = mass / molar mass

when the molar mass of NH4NO3 = 80.043 g/mol

∴ moles of NH4NO3 = 1g / 80.043 g/mol 

                                   = 0.0125 moles

So the decomposition then will be = ΔH / moles NH4NO3

                                                           = -7.5 KJ / 0.0125 moles

                                                           = -600 KJ.mol-1