Assume that you want to design a cold pack with 50. g water inside and you would

Question

Assume that you want to design a cold pack with 50. g water inside and you would like thetemperature to lower from room temperature (22 °C) to about 5 °C. Use the molar heat of solutionfor NH4NO3 and calculate how many grams of NH4NO3 should be used. Show your work below.
Hint: Assume x g of NH4NO3 being used and represent the heats involved as functions of x(heat related to NH4NO3 when dissolved and heat related to the solution that contains both waterand NH4NO3). Then try to solve x. Do not forget that it should be the mass of solution, not just thesolvent, used in calculating the heat involved for the solution.

Explanation / Answer

m = 50 gof water

dT = 5-*22 = 17 °C

C = 4.184 J/gC

Q = m*C*(Tf-Ti)

Q = 50*4.184*(-17) = -3556.4 J released

so

Qgain = -Qlost = -(-3556.4) = 3556.4 J

Q= n*HRxn

HRxn = 34.9 kJ/mol

3556.4 = n * 324.9

n = 3556.4/(324.9*1000) = 10.9461*10^-3 mol

m = mol*MW = 80.043 *10.9461/1000 = 0.876158 g of NH4NO3

note that 50 g >> 0.876158 g, no need to include NH4NO3 in calcualtions

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