Instant cold packs, often used to ice athletic injuries on the field, contain am
ID: 938687 • 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: NH_4 NO_3 (s) rightarrow NH_4^+ (aq) + NO_3^- (aq). The enthalpy change for this reaction is called the heat of solution for ammonium nitrate. In order to measure this, 7.41 g of NH_4 NO_3 is dissolved in enough water to make 47.08 mL of solution. The initial temperature is 27.80 degree C and the final temperature (after the solid dissolves) is 23.20 0 degree C. Calculate the enthalpy of solution ammonium nitrate in kJ/mol. (Use 1.000 g/mL as the density of the solution and 4.184 J/g degree C as the specific heat capacity.)Explanation / Answer
Heat of system = -Heat of surrounding
Enthalpy of solution = -Q
Q = m*Cp*dT
mtotal = 7.41+47.08 = 54.49
dT = 23.20-27.8 = -4.6°C (its cooling)
C = 4.184
then
Q = 54.49*4.184*(-4.6) = -1048.736336 J
Enthalpy of solution = -Q
Hsoln = 1048.736336 J
per unit mol
mol = mass/MW = 7.41/80.0434 = 0.09257 mol
then
Hsoln = 1048.736336/0.09257 = 11329.1167333J/mol
Hsln = 11.329 kJ/mol
it must be positive since it is taking energy from surrounding, i.e. it is endothermic