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)→ NH + 4 (aq)+ NO − 3 (aq) In order to measure the enthalpy change for this reaction, 1.25 g of NH 4 NO 3 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. (Use 1.0 g/mL as the density of the solution and 4.18 J/(g⋅∘C) as the specific heat capacity.)

Express the enthalpy change in kilojoules per mole to two significant figures.

Answer 1

NH₄NO₃ (s)----> NH⁴⁺ (aq) + NO₃^- (aq)

q = m c ΔT

where,

m = mass of the substance,

c = specific heat capacity

ΔT = temperature drop

Mass of solution = volume x density = 25.0 mL x 1.0 g/mL = 25.0 g

q = 25.0 g x 4.18 J/g^oC x (21.9 − 25.8) ^oC

q = - 407.55 J

q = - 0.40755 kJ

Here, 'negative' sign because we know it is an endothermic reaction, causing a decrease in temperature.

Now,

this heat change is being caused by the reaction of 1.25 g of ammonium nitrate.

MW of NH₄NO₃ = 80 g/mole.

Moles of NH₄NO₃ = Mass /MW =1.25 g / 80 g/mole = 0.015625 mole

Hence,

Change in Enthalpy = 0.40755 kJ / 0.015625 mole = 26.08 kJ/mole

Answer:

Change in Enthalpy = 26 kJ/mole