Problem 9 - Biology

Question

Which of the following reactions could be coupled to an endergonic reaction with \(\Delta G=+3.56 \mathrm{kJ} / \mathrm{mol} ?\) (a) \(\mathrm{A} \longrightarrow \mathrm{B}\), \(\Delta G=+6.08 \mathrm{kJ} / \mathrm{mol}\) (b) \(\mathrm{C} \longrightarrow \mathrm{D}, \Delta G=+3.56 \mathrm{kJ} / \mathrm{mol}\) (c) \(\mathrm{E} \longrightarrow \mathrm{F}, \Delta G=0 \mathrm{kJ} / \mathrm{mol}\) (d) \(\mathrm{G} \longrightarrow \mathrm{H}, \Delta \mathrm{G}=-1.22 \mathrm{k} \mathrm{J} /\) mol (e) \(\mathrm{I} \longrightarrow \mathrm{J}, \Delta G=-5.91 \mathrm{kJ} / \mathrm{mol}\).

Step-by-Step Solution

Answer

Reaction (e) can be coupled with the endergonic reaction.

Step 1: Understanding Coupling Mechanism

In biochemistry, a reaction with a positive \( \Delta G \) (endergonic) can be driven by coupling it with a reaction that has a larger negative \( \Delta G \) (exergonic). The total \( \Delta G \) of the coupled reactions must be negative for the overall process to be spontaneous.

Step 2: Identify Candidates for Coupling

To drive the endergonic reaction with \( \Delta G = +3.56 \, \text{kJ/mol} \), we need an exergonic reaction with a \( \Delta G \) more negative than \(-3.56 \, \text{kJ/mol} \). Thus, we look for reactions with \( \Delta G \leq -3.56 \, \text{kJ/mol} \).

Step 3: Analyze Each Given Reaction

(a) \( \Delta G = +6.08 \, \text{kJ/mol} \) is endergonic, cannot couple.(b) \( \Delta G = +3.56 \, \text{kJ/mol} \) is endergonic, cannot couple.(c) \( \Delta G = 0 \, \text{kJ/mol} \) is neither endergonic nor exergonic, cannot couple.(d) \( \Delta G = -1.22 \, \text{kJ/mol} \) is exergonic, but not negative enough.(e) \( \Delta G = -5.91 \, \text{kJ/mol} \) is exergonic and sufficiently negative.

Step 4: Select the Reaction for Coupling

Reaction (e) \( I \longrightarrow J \) with \( \Delta G = -5.91 \, \text{kJ/mol} \) can be coupled to the endergonic reaction, as it provides enough energy to make the overall process spontaneous with \( \Delta G = -2.35 \, \text{kJ/mol} \) when totalled.

Key Concepts

Endergonic Reactions

Endergonic reactions are processes where the change in Gibbs free energy \( \Delta G \) is positive. This means that the reaction absorbs energy from its surroundings to proceed. These reactions are not self-sustaining and cannot occur on their own without an input of energy.
One common example of an endergonic reaction is photosynthesis, where plants use sunlight to convert carbon dioxide and water into glucose. The process requires an energy input to make it happen, which is provided by the sun.
Key characteristics of endergonic reactions include:

• \( \Delta G > 0 \)
• Energy required
• Non-spontaneous

In cells, endergonic reactions are often coupled with exergonic reactions to ensure they occur. This coupling is essential in biochemical pathways to maintain cell function.

Exergonic Reactions

Exergonic reactions are processes that release energy, often in the form of heat or light, and have a negative change in Gibbs free energy \( \Delta G \). This signifies that the reaction can occur spontaneously, as it loses energy to the surroundings.
Combustion, a process where fuel burns to produce carbon dioxide, water, and energy, is a practical example of an exergonic reaction. This type of reaction is essential for providing the energy required for endergonic reactions when coupled.
Important features of exergonic reactions include:

• \( \Delta G < 0 \)
• Energy-releasing
• Spontaneous

An understanding of exergonic reactions is crucial in fields like biochemistry, where they facilitate energy transfer necessary for metabolic pathways. ATP hydrolysis in cells is a well-known exergonic reaction that helps power various cellular activities.

Spontaneous Reactions

Spontaneous reactions are those that occur without the need for additional energy once initiated. They have a negative Gibbs free energy \( \Delta G \), indicating that the energy released is enough to drive the process forward naturally.
The second law of thermodynamics states that spontaneous reactions increase the entropy, or disorder, of the universe. This law helps explain why reactions with a negative \( \Delta G \) are spontaneous—they occur because they lead to greater overall entropy.
Characteristics of spontaneous reactions are:

• \( \Delta G < 0 \)
• No energy input required once started
• Increase in entropy

In the context of coupled reactions, an exergonic reaction can be combined with an endergonic reaction to create a spontaneous overall process. This is fundamental in biochemistry, allowing cells to perform work like muscle contraction and nerve impulse propagation efficiently.