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)-->NH4 ^+(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 degrees C and the final temperature (after the solid dissolves) is 21.9 degrees C. Calculate the change in enthalpy for the reaction. (Use 1.0g/mL as the density of the solution and 4.18 J/g . degrees C as the specific heat capacity.

Answer 1

Answer:

ΔH = +26.08 kJ/mol

Explanation:

The change in enthalpy (ΔH) is given in J/mol, and can be calculated for  dissolution by the equation:

ΔH = m(water)*Cp*ΔT/n(solute)

The mass of water is the density multiplied by the volume

m = 1g/mL * 25.0mL = 25.0 g

The number of the moles is the mass divided by the molar mass. Knowing the molar masses of the elements:

N = 14 g/mol x 2 = 28

H = 1 g/mol x 4 = 4

O = 16 g/mol x 3 = 48

NH₄NO₃ = 80 g/mol

n = 1.25/80 = 0.015625 mol

So,  

ΔH = 25*4.18*(25.8 - 21.9)/0.015625

ΔH = 26,083.2 J/mol

ΔH = +26.08 kJ/mol