During the metabolism of glucose, glyceraldehyde 3-phosphate is converted to dihydroxyacetone phosphate by a process that involves two keto-enol tautomerizations. Draw a stepwise mechanism for this reaction in the presence of acid.
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In the metabolism of glucose, the first step is the conversion of glucose to glucose 6 -phosphate: glucose $+\mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow$ glucose 6 -phosphate $+\mathrm{H}_{2} \mathrm{O}$ $$ \Delta G^{\circ}=13.4 \mathrm{~kJ} / \mathrm{mol} $$ Because $\Delta G^{\circ}$ is positive, this reaction does not favor the formation of products. Show how this reaction can be made to proceed by coupling it with the hydrolysis of ATP. Write an equation for the coupled reaction and estimate the equilibrium constant for the coupled process.
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