Question

Instant cold packs 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 endothermic reaction: NH4NO3 (s) --> NH4+ (aq) + NO3- (aq) 1.85g ammonium nitrate is added to water in a calorimeter. The total solution (water and ammonium nitrate) is 25.0g. The heat capacity of the calorimeter is Ccal=45.0 J/k. The initial temperature of the solution is 21.1C. The final temperature of the solution is 17.0C. Assume cs of the solution is 4.20 J/(g K) What is ΔHrxn per mol of the reaction?

Answer 1

The enthalpy of the reaction is 18.616 kJ/mol.

Step-by-step explanation:

Heat released by the solution = Q

Mass of the solution = 25.0 g

Heat capacity of the solution = c = 4.20 J/g K

Initial temperature of the solution ,
`T_1= 21.1 ^oC = 294.25 K`

Final temperature of the solution,
`T_2 = 17.0^oC=290.15 K`

Change in temperature of the solution = ΔT =

`\Delta T=T_2-T_1=290.15 K-294.25 K=-4.1 K`

`Q=mc\Delta T=25 g* 4.20 J/g K* (-4.1 K)=-430.5 J`

Heat gained during the reaction of ammonium nitrate = Q'

Q' = -Q (energy remained conserved)

Q'= -(-430.5 J)=430.5 J

Mass of ammonium nitrate added in water = 1.85 g

Moles of ammonium nitrate added in water =
`(1.85 g)/(80 g/mol)=0.02312 mol`

0.02312 moles of ammonium nitrate absorbs 430.5 Joules of energy. the 1 mole will absorb:

`(Q')/(0.02312 mol)=(430.5 J)/(0.02312 mol)=18,616.21 J=18.616 kJ/mol`

The enthalpy of the reaction is 18.616 kJ/mol.