Answer:
Yes, this reaction will be spontaneous.
Step-by-step explanation:
A reaction is spontaneous if ΔG < 0.
The coupling of glycerol to glycerol-3-phospate with ATP gives:
glycerol + HPO₄²⁻ ⟶ glycerol-3-phosphate + H₂O ΔG = +9,2 kJ/mol
ATP + H₂O ⟶ ADP + HPO₄²⁻ ΔG = -30,5 kJ/mol
glycerol + ATP ⟶ ADP + glycerol-3-phosphate
ΔG = +9,2 kJ/mol - 30,5 kJ/mol = -21,3 kJ/mol
As ΔG<0, this reaction will be spontaneous
I hope it helps!