Question

Cells use the hydrolysis of adenosine triphosphate, abbreviated ATP, as a source of energy. Symbolically, this reaction can be represented as

$\mathit{A}\mathit{T}\mathit{P}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathit{l}\mathbf{\right)}\mathbf{\to }\mathit{A}\mathit{D}\mathit{P}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{P}{{\mathit{O}}_{\mathbf{4}}}^{\mathbf{-}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}$

Where represents adenosine diphosphate. For this reaction

$\mathit{\Delta }\mathit{G}\mathbf{=}\mathbf{-}\mathbf{30}\mathbf{.}\mathbf{5}\mathit{k}\mathit{J}\mathbf{/}\mathit{m}\mathit{o}\mathit{l}$

1. Calculate$\mathit{K}\mathit{a}\mathit{t}{\mathbf{25}}^{\mathbf{o}}\mathit{C}$
2. If all the free energy from the metabolism of glucose${\mathit{C}}_{\mathbf{6}}{\mathit{H}}_{\mathbf{12}}{\mathit{O}}_{\mathbf{6}}\mathbf{\left(}\mathit{s}\mathbf{\right)}\mathbf{+}\mathbf{6}{\mathit{O}}_{\mathbf{2}}\mathbf{\to }\mathbf{6}\mathit{C}{\mathit{O}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}\mathbf{6}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathit{l}\mathbf{\right)}$

goes into the production ATP molecules can be produced for every molecule of glucose?

Short answer

1. The value of is $4.50\times {10}^{-6}$
2. Number of ATPs produced for every molecule of glucose is$82$

Step-by-step solution

Definition of standard free energy

The amount of energy released in the conversion of reactants to products under standard conditions is defined as standard free energy.

Calculation of

a. The reaction is $\text{ATP(aq)}+{\text{H}}_{\text{2}}\text{O(l)}\to \text{ADP(aq)}+{\text{H}}_{\text{2}}{{\text{PO}}_{\text{4}}}^{\text{-}}\text{(aq)}$

$\begin{array}{l}{\text{ΔG}}_{\text{R}}^{\text{0}}=-\text{RTlnK}\\ \text{K}={\text{e}}^{-\frac{{\text{ΔG}}_{\text{R}}^{\text{0}}}{\text{RT}}}\\ \text{K}=4.50\times {10}^{-6}\end{array}$

b.${\text{ΔG}}_{\text{R}}^{\text{0}}=-2872\text{\hspace{0.17em}kJ/mol}$

${\text{ΔG}}^{\circ }$is involved in the production of ATP$35\text{\hspace{0.17em}kJ/mol}$

${\text{ΔG}}^{\circ }$is involved in the metabolism of glucose$-2872\text{\hspace{0.17em}kJ/mol}$

Number of ATPs produced for every molecule of glucose is:

$\begin{array}{l}=\frac{2872}{35}\\ =82\end{array}$