A student wants to measure the heat of crystallization of sodium acetate trihydrate. The student takes 50 g of sodium acetate trihydrate and dissolves it in 100 ml of water at 70°C. The solution is then allowed to cool to 20°C, during which the sodium acetate trihydrate crystallizes out. The student measures the temperature change during this process and finds that the temperature drops to 45°C. What is the heat of crystallization of sodium acetate trihydrate in kJ/mol?

Question

A student wants to measure the heat of crystallization of sodium acetate trihydrate. The student takes 50 g of sodium acetate trihydrate and dissolves it in 100 ml of water at 70°C. The solution is then allowed to cool to 20°C, during which the sodium acetate trihydrate crystallizes out. The student measures the temperature change during this process and finds that the temperature drops

Answer 1

To calculate the heat of crystallization of sodium acetate trihydrate, we need to first determine the amount of heat released during the crystallization process. We can do this using the formula:q = mcTwhere q is the heat released, m is the mass of the solution, c is the specific heat capacity of the solution, and T is the change in temperature.The mass of the solution  m  can be calculated by adding the mass of sodium acetate trihydrate  50 g  to the mass of water  100 g . The specific heat capacity of water  c  is 4.18 J/gC.m = 50 g + 100 g = 150 gT = 45C - 20C = 25CNow we can calculate the heat released  q :q =  150 g  4.18 J/gC  25C  = 15675 JNext, we need to determine the number of moles of sodium acetate trihydrate in the 50 g sample. The molar mass of sodium acetate trihydrate  NaC2H3O23H2O  is:Na: 22.99 g/molC: 12.01 g/molH: 1.01 g/molO: 16.00 g/molMolar mass =  1  22.99  +  2  12.01  +  3  1.01  +  2  16.00  +  3  2  1.01  +  3  16.00  = 82.03 + 36.03 + 18.00 = 136.06 g/molNow we can calculate the number of moles of sodium acetate trihydrate:moles = mass / molar mass = 50 g / 136.06 g/mol = 0.367 molFinally, we can calculate the heat of crystallization per mole of sodium acetate trihydrate:Heat of crystallization = q / moles = 15675 J / 0.367 mol = 42710 J/molSince we want the answer in kJ/mol, we need to convert J/mol to kJ/mol:Heat of crystallization = 42710 J/mol   1 kJ / 1000 J  = 42.71 kJ/molSo, the heat of crystallization of sodium acetate trihydrate is approximately 42.71 kJ/mol.