One mole of H₂O(l) is super cooled to −3.75°C at 1 bar pressure. The freezing temperature of water at this pressure is 0.00°C. The transformation H₂O(l) → H₂O(s) is suddenly observed to occur. By calculating ΔS, ΔS _surroundings , and ΔS _total , verify that this transformation is spontaneous at −3.75°C. The heat capacities are given by C_P,m(H₂O(l)) = 75.3 J K^-1 mol^-1 and C_P,m(H₂O(s)) 37.7 J K^-1 mol^-1 ,  and ΔH _fusion = 6.008 kJ mol^–1 at 0.00°C. Assume that the surroundings are at −3.75°C. [Consider the two pathways at 1 bar:

a. H₂O(l, − 3.75°C) → H₂O(s, − 3.75°C)

b. H₂O(l,−3.75°C) → H₂O(l, 0.00°C) → H₂O(s, 0.00°C) → H₂O(s,−3.75°C). Because S is a state function, ΔS must be the same for both pathways.]