I coach U10 soccer and go through an insane amount of instant ice packs. I have

Question

I coach U10 soccer and go through an insane amount of instant ice packs. I have considered investing in magic spray, but the soccer club will pay for the ice pack and not the spray and I am super cheap. So, clearly, I was curious how they work. Turns out that most of them are a small package of ammonium nitrate (NH_4 NO_3) in water. When the inside bag is broken, the solute dissolves in the water. This dissolution requires energy and the water cools and freezes. I have done many experiments to find the best packs, and the market leader uses 300 g of the solute and 300 mL of water. It reaches a final temperature of-2 C. If I assume the dissolution process is so fast that it can be modelled as adiabatic, calculate the specific heat of solvation for ammonium nitrate in water.

Explanation / Answer

Let the initial temperature of water is 250C and Final temperature is -20C

Hence, heat lost by water during the dissolution process, q = (600) g * 4.18 J/g.C (-2-25)0C = - 67716 J

This heat is generated by mixing of 300 g of ammonium nitrate = - (-q) = q = 67716 J

q = 67716 / (300 )(27) = 8.36 J/g.C

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