Problem 69 - General Chemistry: Principles and Modern Applications

Question

In biochemical reactions the phosphorylation of amino acids is an important step. Consider the following two reactions and determine whether the phosphorylation of arginine with ATP is spontaneous. $$\begin{array}{c} \mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{ADP}+\mathrm{P} \quad \Delta G^{\circ \prime}=-31.5 \mathrm{kJ} \mathrm{mol}^{-1} \\ \text {arginine }+\mathrm{P} \longrightarrow \text { phosphorarginine }+\mathrm{H}_{2} \mathrm{O} \\ \Delta G^{\circ \prime}=33.2 \mathrm{kJ} \mathrm{mol}^{-1} \end{array}$$

Step-by-Step Solution

Answer

To determine whether the phosphorylation of arginine with ATP is spontaneous, first sum up two Gibbs free energy changes \(\Delta G^{\circ \prime}_1 = −31.5 \, kJ/mol\) and \(\Delta G^{\circ \prime}_2 = 33.2 \, kJ/mol\). The overall \(\Delta G^{\circ \prime}_{total}\) for the reaction is \(1.7 \, kJ/mol\), which is greater than zero. Therefore, the phosphorylation of arginine is not spontaneous.

Step 1: Identify the reactions

There are two reactions given: The first is the conversion of ATP to ADP with a \(\Delta G^{\circ \prime}\) of -31.5 kJ/mol. The second reaction is the phosphorylation of arginine to form phosphorarginine with a \(\Delta G^{\circ \prime}\) of 33.2 kJ/mol.

Step 2: Calculate total \(\Delta G^{\circ \prime}\) for the phosphorylation of arginine

The phosphorylation of arginine takes place in two steps: ATP to ADP (\(\Delta G^{\circ \prime}_1\)) and arginine to phosphorarginine (\(\Delta G^{\circ \prime}_2\)). To get the total change in \(\Delta G^{\circ \prime}\) for the overall reaction, these two \(\Delta G^{\circ \prime}\) values need to be added together: \(\Delta G^{\circ \prime}_{total} = \Delta G^{\circ \prime}_1 + \Delta G^{\circ \prime}_2\)

Step 3: Evaluate Spontaneity

After calculating, if \(\Delta G^{\circ \prime}_{total}\) is negative, the reaction is spontaneous. If it's positive, the reaction is not spontaneous. If it's zero, the reaction is at equilibrium.

Key Concepts

Gibbs Free Energy

Understanding Gibbs free energy (\( \triangle G \)) is crucial when analyzing biochemical reactions. It represents the maximum amount of work a thermodynamic system can perform at constant temperature and pressure. Simply put, it tells us whether a reaction can occur spontaneously. The \( \triangle G \) is given in units of energy per amount of substance (like kJ/mol), and it's calculated from the changes in enthalpy and entropy of the system during a reaction.

A negative \( \triangle G \) value indicates that a reaction releases energy and can proceed 'spontaneously' - this means it does not need any external energy input to occur. Conversely, a positive \( \triangle G \) suggests that the reaction requires energy to proceed and is not spontaneous. When \( \triangle G = 0 \), the system is at equilibrium, and no net reaction will proceed. It's essential for students to remember that 'spontaneous' in this context does not mean 'instantaneous'; even reactions that are thermodynamically favorable might take a long time to occur without a catalyst.

Spontaneous Reactions

A spontaneous reaction is a process that occurs under specific conditions without the need for continuous external energy input. In biochemical systems, whether or not a reaction is spontaneous is determined by the change in Gibbs free energy (\( \triangle G \)). This is not just about the release or absorption of heat but involves the entire energy change, including work potentially done by the system.

The concept of spontaneity is vital for students studying biochemical pathways, as many reactions in cells would not occur without being coupled to spontaneous ones. For example, the synthesis of complex molecules from simpler ones is frequently non-spontaneous and requires the input of energy from spontaneous reactions such as the hydrolysis of ATP, showcasing an intricacy of metabolic pathways.

Adenosine Triphosphate (ATP)

Adenosine triphosphate (ATP) is often referred to as the 'molecular currency' of intracellular energy transfer. This molecule plays a pivotal role in providing energy for various biochemical cellular processes. ATP stores energy in its high-energy phosphate bonds; when those bonds are broken - generally through a process called hydrolysis - energy is released to fuel cellular activities.

This release of energy is characterized by a negative Gibbs free energy change. The hydrolysis of ATP is commonly used in the cell to drive reactions that are otherwise non-spontaneous by coupling them with the hydrolysis of ATP, allowing the cell to undertake vital processes such as active transport, mechanical work, and chemical synthesis.

Amino Acid Phosphorylation

Amino acid phosphorylation is a biochemical reaction that involves the addition of a phosphate group to an amino acid, typically mediated by enzymes known as kinases. This process is integral to cell signaling and regulation of cellular activities. The phosphorylation of proteins can activate or deactivate them, alter their function, and affect their interaction with other molecules.

When considering amino acid phosphorylation thermodynamically, the process often requires energy input since adding a phosphate group can contribute to a positive change in Gibbs free energy (\( \triangle G \)). In the case of arginine phosphorylation, the reaction relies on the energy provided by ATP hydrolysis. By coupling the phosphorylation with ATP hydrolysis, even though the phosphorylation step itself might have a positive \( \triangle G \) and be non-spontaneous, the overall reaction sequence can become spontaneous.