Commercial cold packs consist of solid ammonium nitrate and water. NH4NO3 absorb

Question

Commercial cold packs consist of solid ammonium nitrate and water. NH4NO3 absorbs 25.69kJ of heat per mole dissolved in water. In a coffee cup calorimeter 5.60g of NH4NO3 is dissolved in 100g of water at 22 degrees celsius. What is the final temperature of the solution?

**** Isnt 22 celsius the initial temp so we do Final - initial = change in temperature? so X - 22 = change in T??? I've seen this problem done the opposite way where its solved with Tinitial - t final? which makes no sense to me... so they do 22-x = change in temperature. Which is the correct way please help solve. ****

a. 11.6 C

b. 26.1 C

c. 17..9 C

d. -54.8 C

e. 0 C

Explanation / Answer

Here ammonium nitrate absorbs heat when it is dissolved in water. That means the final temperature of solution in the calorimetry will be less than 22 °C.

Moles of ammonium nitrate = 5.60 g /80.043 = 0.0687 moles

Heat absorbed = 25.69 kJ /mol x 0.0687 mol == 1.764 kJ

Final temperature of water is calculate using following formula :

100 g x 4.18 J/g C x (22-T) = 1764

22- T = 4.2

T = 17.8 C

So, the correct option is (c)

Here we using 22-T because , ammonium nitrate absorbs heat from solution making water much colder

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