Instant cold packs, often used to ice athletic injuries on the field, contain am
ID: 513586 • Letter: I
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)+NO3(aq)
In order to measure the enthalpy change for this reaction, 1.25 g of NH4NO3 is dissolved in enough water to make 25.0 mL of solution. The initial temperature is 25.8 C and the final temperature (after the solid dissolves) is 21.9 C. Calculate the change in enthalpy for the reaction in kilojoules per mole. (Use 1.0g/mL as the density of the solution and 4.18J/gC as the specific heat capacity.)
Explanation / Answer
The endothermic reaction is
NH4NO3(s)NH+4(aq)+NO3(aq)
Given that,
1.25 g of NH4NO3 is dissolved in enough water to make 25.0 mL of solution.
molar mass of NH4NO3 is 80g/mol
moles of NH4NO3 = weight of NH4NO3 / molar mass of NH4NO3
Moles of NH4NO3 = 1.25/80
moles of NH4NO3 = 0.015625 moles
The density of the solution = 1g/mL
weight of solution = density of solution * volume of solution
weight of solution = 1 * 25
weight of solution = 25 g
Temperature change (T) = final temperature - inititial temperature
Temperature change (T) = 21.9 - 25.8
Temperature change (T) = -3.90C
heat release during reaction by solution (q) = m*Cp*T
heat release during reaction by solution (q) = 25 * 4.18 * -3.9
heat release during reaction by solution (q) = -407.55 J
Enthalpy change for the reaction (H) = -heat release during reaction (q) / moles of NH4NO3
Enthalpy change for the reaction (H) = 407.55 / 0.015625
Enthalpy change for the reaction (H) = 26083.2 J/mol
Enthalpy change for the reaction (H) = 26.08332 kJ/mol