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Chapter 3: Problem 5

ATP hydrolysis at pH 7.0 is accompanicd by release of a hydrogen ion to the medium \\[\mathrm{ATP}^{6-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{ADP}^{3-}+\mathrm{HPO}_{4}^{2-}+\mathrm{H}^{+}\\] If the \(\Delta G^{\circ}\) for this reaction is \(-30.5 \mathrm{kJ} / \mathrm{mol}\), what is \(\Delta G^{*}\) (that is, the free energy change for the same reaction with all components, including \(\mathrm{H}^{+},\) at a standard state of \(1 \mathrm{M}\) )?

Short Answer

Expert verified
\(\Delta G^*\) for the ATP hydrolysis at pH 7 is approximately -36 kJ/mol.

Step by step solution

01

Identify given values

First, identify the given values from the problem. \(\Delta G'\) is given as -30.5 kJ/mol. The value for \(R\), the gas constant, is 0.00831 kJ/mol·K. Temperature (\(T\)) is usually 298 K at standard conditions. The concentration of hydrogen ions (\([H^{+}]\)) at pH 7 is \(10^{-7} M\). Since we are considering all components at a standard state of 1M, the concentrations of ATP, ADP and HPO4 are all 1 M.
02

Set up the equation

Now, we set up the formula \(\Delta G^* = \Delta G' + RT \cdot \ln\frac{[Products]}{[Reactants]}\). Plug the known values into the equation, \(\Delta G^* = -30.5 kJ/mol + (0.00831 kJ/mol·K)(298 K)\log_{e}(\frac{[ADP][HPO_4][H^{+}]}{[ATP][H_{2}O}])\)
03

Simplify the equation

Consider \([H_{2}O]\) in the denominator to be constant and therefore does not participate in the expression for \(\Delta G^*\). Therefore the expression for \(\Delta G^*\) simplifies to: \(\Delta G^* = -30.5 kJ/mol + (0.00831 kJ/mol·K)(298 K) \log_{e}(\frac{1M * 1M * 10^{-7} M}{1M})\).
04

Solve the equation

Solve the equation to find \(\Delta G^*\): \(\Delta G^* = -30.5 kJ/mol + (0.00831 kJ/mol·K)(298 K)\log_{e}(10^{-7})\). The value of \(\log_{e}(10^{-7})\) is -16.118, so plug this into the equation to calculate the final value of \(\Delta G^*\).

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Most popular questions from this chapter

The acyl-Co.A synthetase reaction activates fatty acids for oxidation in cells: \\[ \mathrm{R}-\mathrm{COO}^{-}+\mathrm{CaASH}+\mathrm{ATP} \longrightarrow \mathrm{R}-\mathrm{COSCOA}+\mathrm{AMP}+\text { pyrophosphate } \\] The reaction is driven forward in part by hydrolysis of ATP to AMP and pyrophosphate. However, pyrophosphate undergoes further cleavage to yield two phosphate anions. Discuss the energetics of this reaction both in the presence and absence of pyrophosphate cleavage.

Calculate the free energy of hydrolysis of ATP in a rat liver cell in which the ATP, ADP, and \(P\), concentrations are \(3.4,1.3,\) and \(4.8 \mathrm{m} M\) respectively.

Draw all possible resonance structures for creatine phosphate and discuss their possible effects on resonance stabilization of the molecule.

You are studying the various components of the venom of a poisonous lizard. One of the venom components is a protein that appears to be temperature sensitive. When heated, it denatures and is no longer toxic. The process can be described by the following simple equation: \\[ \mathbf{T}(\text { toxic }) \rightleftharpoons \mathrm{N} \text { (nontoxic) } \\] There is only enough protein from this venom to carry out two equilibrium measurements. At \(298 \mathrm{K}\), you find that \(98 \%\) of the protein is in its toxic form. However, when you raise the temperature to \(320 \mathrm{K},\) you find that only \(10 \%\) of the protein is in its toxic form. a. Calculate the equilibrium constants for the T to N conversion at these two temperatures. b. Use the data to determine the \(\Delta H^{\circ}, \Delta S^{\circ},\) and \(\Delta G^{\circ}\) for this process.

Consider carbamoyl phosphate, a precursor in the biosynthesis of pyrimidines: Based on the discussion of high-energy phosphates in this chapter, would you expect carbamoyl phosphate to possess a high free energy of hydrolysis? Provide a chemical rationale for your answer.
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