Questions on Thermodynamics

Question

Given that ΔH^o(fusion,0°C) of water is 6025 J/mol, C_p,m(ice) = 37.7 J K^–1 mol^–1, and C_p,m(water,liquid) = 75.3 J K^–1 mol^–1, calculate ΔG (in J) for the freezing of 53 moles of water at 1 atm pressure and the constant temperature T = 6.1 °C.

Hi! I end up getting a negative delta G value, and I'm not sure if this is correct because the problems says to freeze water at 6 degrees Celsius, how can it be spontaneous? Thank you!

Answer 1

Hi Hanna. I agree that the ∆G should be positive. I'll give it my best shot, but hopefully someone else will also chime in. Here goes.

∆G = ∆H - T∆S

∆H = 6025 J / mol

T = 6.1ºC + 273 = 279.1K

∆S = Cp,m(ice) - Cp,m(water,liquid)

∆S = 37.3 J / Kmol - 75.3 J / Kmol

∆S = -37.6 J / Kmol

∆G = 6025 J / mol - (279.1K)(-37.6 J / Kmol)

∆G = 6025 J / mol + 10494 J / mol

∆G = 16519 J / mol

∆G = 16519 J / mol x 53 mols = 875507 J

(Be sure to check the math. Let me know what you think)