Problem 70 - General Chemistry: Principles and Modern Applications

Question

The synthesis of glutamine from glutamic acid is given by Glu \(^{-}+\mathrm{NH}_{4}^{+} \longrightarrow \mathrm{Gln}+\mathrm{H}_{2} \mathrm{O}\). The Gibbs energy for this reaction at \(\mathrm{pH}=7\) and \(T=310 \mathrm{K}\) is \(\Delta G^{\circ \prime}=14.8 \mathrm{kJ} \mathrm{mol}^{-1} .\) Will this reaction be sponta- neous if coupled with the hydrolysis of ATP? \(\mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{ADP}+\mathrm{P}\) $$\Delta G^{\circ \prime}=-31.5 \mathrm{kJ} \mathrm{mol}-1$$

Step-by-Step Solution

Answer

Yes, the total reaction will be spontaneous since its Gibbs energy is negative (-16.7 kJ/mol).

Step 1: Understanding Gibbs Energy

The Gibbs energy (or Gibbs free energy) of a reaction is a thermodynamic potential that measures the maximum reversible work that an isothermal, isobaric system can do. In other words, it can be thought of as the 'useful' work obtainable from the system. A reaction is spontaneous if ΔG is negative, and it is non-spontaneous if ΔG is positive.

Step 2: Calculation

To check if the total reaction (consisting of the synthesis of glutamine from glutamic acid and the hydrolysis of ATP) is spontaneous, the Gibbs energies for the two individual reactions should be added together. The given ΔG for the glutamine synthesis is +14.8 kJ/mol, and for the ATP hydrolysis, it is -31.5 kJ/mol. Adding these up, the total ΔG is \(+14.8 + (-31.5) = -16.7 \, kJ/mol\). This is a negative value.

Step 3: Interpretation

Since the total ΔG is negative, the total reaction (which includes both the synthesis of glutamine from glutamic acid and the hydrolysis of ATP) will be spontaneous.

Key Concepts

Chemical Spontaneity

Chemical spontaneity refers to whether a chemical reaction will occur without the need for external input. In thermodynamic terms, a reaction's spontaneity is determined by its Gibbs Free Energy, denoted as \( \Delta G \). A spontaneous reaction has a negative \( \Delta G \) value, which means it releases free energy and can perform work.

The Gibbs Free Energy equation is given by \( \Delta G = \Delta H - T\Delta S \), where \( \Delta H \) is the change in enthalpy (heat content), \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy (disorder). Both enthalpy and entropy play crucial roles in determining the spontaneity of a process. For example, a process may be spontaneous due to a large decrease in enthalpy (\( \Delta H < 0 \) is exothermic) or a significant increase in entropy (\( \Delta S > 0 \) shows greater disorder).

When the conditions, such as temperature or concentration, change, the spontaneity of a reaction can also change. This adaptability is vital in complex systems like those in biochemistry where reactions must be tightly controlled and regulated for the organism to function properly.

ATP Hydrolysis

ATP hydrolysis is a fundamental reaction in biochemistry that involves the conversion of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and an inorganic phosphate (\( P_i \) or sometimes abbreviated as \( P \)). The reaction can be represented as \( ATP + H_2O \rightarrow ADP + P_i \).

Why is ATP Hydrolysis Exergonic?

ATP hydrolysis is an exergonic reaction, meaning it releases energy (\( \Delta G < 0 \) ). This energy release happens because the phosphate groups in ATP are negatively charged, and repulsion between them is relieved upon hydrolysis. Additionally, the products (ADP and \( P_i \) ) are more stable and have lower energy than ATP, contributing to a negative \( \Delta G \) value. The actual free energy change (\( \Delta G \) ) for ATP hydrolysis in cellular conditions is approximately -30 to -35 kJ/mol, which varies with conditions such as pH and magnesium concentration.

ATP hydrolysis is a crucial provider of energy for many cellular processes, including muscle contraction, active transport across membranes, and synthesis reactions such as that of glutamine from glutamic acid.

Glutamine Synthesis

Glutamine synthesis is a biosynthetic process where glutamine is produced from glutamic acid through the involvement of ammonia (\( NH_4^+ \) ). The reaction \( Glu^- + NH_4^+ \rightarrow Gln + H_2O \) is crucial for nitrogen metabolism in cells.

This reaction, under standard biochemical conditions (\( pH = 7 \) and \( T = 310 \, K \) or approximately 37°C, which mimics the human body temperature), is not spontaneous due to its positive \( \Delta G \) value. However, in the body, this process occurs efficiently because it is often coupled with ATP hydrolysis, which drives the overall series of reactions forward.

Glutamine itself serves as an amino acid important for protein synthesis, acting as a nitrogen donor in various biosynthetic reactions, and plays a key role in maintaining the acid-base balance in the body by acting as a buffer.

Thermodynamics in Biochemistry

Thermodynamics in biochemistry is the study of energy changes and transfers within biological systems. It is essential for understanding how organisms obtain and use energy to drive life processes.

Application of Thermodynamics:

In biochemistry, thermodynamics helps explain the feasibility of metabolic pathways and their regulation. The Gibbs Free Energy concept is particularly important since it predicts the direction of chemical reactions in a cell. Enzymes, the biological catalysts, often facilitate the reactions to proceed at a faster rate without affecting the direction predicted by \( \Delta G \).

Moreover, thermodynamics is not only about energy but also about the order within the system. The concept of entropy (\( \Delta S \)) is a measure of the randomness or disorder in a system. In biological processes, an increase in entropy often accompanies energy release. However, living systems are unique because they maintain a high level of order and complexity, partly accomplished through the constant input of energy, such as via ATP hydrolysis, to build complex molecules and structures from simpler ones.