Answer:
Yes, this reaction will be spontaneous.
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 = <em>-21,3 kJ/mol</em>
As ΔG<0, <em>this reaction will be spontaneous</em>
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I hope it helps!