Question

Instant cold packs, often used to ice athletic injuries on the field, contain ammonium nitrate and water separated by a thin plastic divider. When the divider is broken, the ammonium nitrate dissolves according to the following endothermic reaction:

NH4NO3(s)→NH+4(aq)+NO−3(aq)

In order to measure the enthalpy change for this reaction, 1.50 g of ammonium nitrate is dissolved in enough water to make 30.0 mL of solution. The initial temperature is 23.7 ∘C and the final temperature (after the solid dissolves) is 19.6 ∘C.

Calculate the change in enthalpy for the reaction in kilojoules per mole. (Use 1.00g/mL as the density of the solution and 4.18J/g⋅∘C as the specific heat capacity.)

Answer 1

Mass of water , m = volume x density

                           = 30.0 mL x 1.00 g/mL

                          = 30.0 g

                       c = specific heat of solution = 4.18 J/g oC

                       dt = change in temperature = initial - final = 23.7 - 19.6 = 4.1 oC

So amount of heat lost by water , Q = mcdt

                                                     = 514.14 J

This amount of heat is utilized by 1.50 g of NH4NO3

The amount of heat utilized by 1 mol = 80.0 g of NH4NO3 is (80.0/1.50) x 514.14 J

                                                                                        = 27.421 x10³ J

                                                                                         = 27.421 kJ

Therefore change in enthalpy of solution , H = -27.421 kJ