# Case Study: Thermodynamics of ATP

Adenosine triphosphate (ATP) is an organic molecule which stores energy used to carry out life processes. ATP is made of an adenine nucleoside, ribose sugar, and three phosphate groups. The high energy bonds between phosphate groups are broken when hydrolyzed, thus releasing energy in the system. Either one or two phosphate groups can break off, releasing Gibb's free energy, which can then be used to drive other reactions.

### Introduction

ATP can be formed from bonding either adenosine monophosphate (AMP) and two inorganic phosphate groups (PPi) together or by bonding adenosine diphosphate (ADP) and one inorganic phosphate group (Pi) together. Energy is required to bond the adenosine to the phosphate groups, making it an endergonic reaction. The energy used to bond the two molecules together is then stored within covalent bonds between phosphate groups in ATP. ATP can be formed through two different endergonic processes, either through substrate-level phosphorylation or chemiosmosis.

Figure 1: The molecular structure of ATP which is formed from a adenine nucleoside, ribose sugar, and three phosphate groups

When ATP is hydrolyzed, energy is released from the breaking of the covalent bonds between phosphate groups, making it an exergonic reaction. The energy released can then be used to drive other endergonic reactions.

ATP + H2O → ADP + Pi               Releases -30.5 kJ/mol= ΔG˚     (when one phosphate group breaks off)

ATP + H2O → AMP + PPi           Releases -45.6 kJ/mol= ΔG˚     (when two phosphate groups break off)

### Gibb's Free Energy and ATP

The Gibb's free energy at equilibrium shown above can be derived from the experimental values under standard conditions. Recall that the formula for standard Gibb's free energy at equilibrium is:

$\Delta G^0 = -RT \ln K_{eq}$

Keq, the equilibrium constant, can be determined from reactions involving the hydrolysis of ATP.

From the reactions: ATP + Glucose → ADP + Glucose-Phosphate where Keq1 is 870 and
Glucose-6-phosphate + H2O → Glucose + Phosphate where Keq2 is 254.

The summation of the two equations is: ATP + H2→ ADP + Pi

The equilibrium constant of the third reaction (Keq3) can be found by using the equation

$K_{eq}=\dfrac{[products]}{[reactants]}=\dfrac{[ADP][P_i]}{[ATP][H_2O]}$

and realizing that $$K_{eq3}=K_{eq1} \times K_{eq2}$$

Thus the solution for $$K_{eq3} = 870 \times 254 = 221,000$$

Under standard conditions the amount of Gibb's free energy can be found. R is the gas constant $$R=8.314 \dfrac{J}{K \times mol}$$, T is the standard temperature T=298.15 K, and Keq = 240,300 is experimentally determined and calculated from the data above.

$\Delta G^0 = -(8.314) \dfrac {J}{K \times mol} \times \dfrac{1kJ}{1000J} \times 298.15 K \times ln (221,000) \approx -30.5 kJ/mol$

Figure 2: The energy diagram representing the exergonic reaction of the hydrolysis of ATP.

As noted previously, the covalent bonds linking the phosphates groups together in ATP are referred to as "high energy" bonds. "High energy" bonds refers to the fact that a large amount of energy is released when such bonds are broken, meaning ΔG (Gibb's free energy) is large and negative. The phosphate groups are slightly negatively charged which repel one another but the bonds are strong enough to hold the phosphate groups together. When ATP is hydrolyzed, the stress of the unfavorable reaction is relieved and the products are at a more favorable lower energy state. During this process, the electrostatic energy that was stored by bonding phosphate groups is released.

### ATP is Formed Through Endergonic Reactions

ATP can be made through two different endergonic reactions, meaning that energy is required to form ATP. In substrate level phosphorylation, an inorganic phosphate group is directly added to adenosine triphosphate (ADP). An intermediate compound is used to add the phosphate group to ADP. An example of this is in the last step of glycolysis. Two molecules of phosphoenolpyruvate (PEP) donates a phosphate group onto ADP to form ATP.

ATP is also formed through a process called chemiosmosis in which a proton gradient is formed between a semi-permeable cell membrane. This process requires an enzyme, ATP synthase, to harvest the kinetic energy of moving protons to attach a free floating phosphate group onto ADP. Overall, these endergonic reactions require 30.5kJ of energy to form ATP from ADP. Note that the in the transferring of energy, energy is conserved, following the first law of thermodynamics.

### Why is ATP Thermodynamics So Important?

The question of why the thermodynamics of ATP is necessary to drive life's processes often comes up regularly. Plainly put, ATP is an energy carrier. Without it, organisms could not store the large amount of energy that is released from breaking down fuel molecules. For example, glucose is a high source of energy and in the process of glycolysis, a molecule of glucose is broken down. The break down of one glucose molecule releases an enormous amount of energy (approximately 2872.1448 kJ per glucose molecule!) . This amount of energy is simply too large for living systems to use. Therefore, as an energy carrier, multiple molecules of ATP can capture the energy released and transfer that energy to perform endergonic reactions in living systems.

### References

1. Stefano Iotti, Antonio Sabatini, Alberto Vacca. Chemical and Biochemical Thermodynamics: From ATP Hydrolysis to a General Reassessment. The Journal of Physical Chemistry B 2010 114 (5), 1985-1993
2. Sarang S. Nath, Sunil Nath. Energy Transfer from Adenosine Triphosphate: Quantitative Analysis and Mechanistic Insights. The Journal of Physical Chemistry B 2009 113 (5), 1533-1537

### Contributors

• Renee Leong (UC Davis)

Viewing 2 of 2 comments: view all
Problem

The previous derivation of $$\Delta G^0$$ was based off of standard conditions. Recall the Nernst formula when conditions are not under standard conditions:

$E = E^o - \dfrac{RT}{nF} \ln Q$

where $$Q$$ represents the reaction quotient,

$Q=\dfrac{[\text{products}]}{[\text{reactants}]}$

However, in living organisms, both temperature conditions as well as pH may vary from standard conditions and affect the energy that is released when ATP is hydrolyzed to ADP.

What is the amount of Gibb's free energy released in the human body (assume body temperature is 37 ˚C) when ATP is hydrolyzed to ADP given that the concentration of [ATP]=0.09 M, [ADP]=0.001M, and [Pi]=0.011M.
Solution

$\Delta G = -30.5 \dfrac{kJ}{mol} + RT \ln \dfrac{[ADP][Pi]}{[ATP]}$

$\Delta G= \left (-30.5 \dfrac{kJ}{mol}\right) \times \left(\dfrac{1kJ}{1000J}\right) +8.314 \dfrac{J}{mol} \times (37+273.15) K \times \ln \dfrac{[0.001][0.011]}{[0.09]} =-23,262.7 \dfrac{J}{mol}$

$\left(-23,262.7 \dfrac{J}{mol}\right) \times \left(\dfrac{1kJ}{1000J}\right)=-23.263 \dfrac{kJ}{mol}$
Posted 10:13, 5 Jun 2014
http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/49039.html
Posted 08:58, 26 Jul 2014
Viewing 2 of 2 comments: view all
10:13, 5 Jun 2014

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This material is based upon work supported by the National Science Foundation under Grant Number 1246120