Question

In a human cell, \(32 \mathrm{~mol}\) of ATP \(^{4-}\) are formed from \(\mathrm{ADP}^{3-}\) every time one mole of glucose is oxidized to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O} .\) (a) Write the overall reaction and calculate \(\Delta G^{\circ}\). (b) Is the reaction spontaneous or nonspontaneous?

Short answer

(a) \( \Delta G^{\circ} = -1894 \, \text{kJ/mol} \); (b) The reaction is spontaneous.

Step-by-step solution

Write the Overall Reaction

The overall reaction for the oxidation of glucose can be written as follows: \[ \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} + 32\,\text{ATP} \] This reaction indicates that one glucose molecule reacts with oxygen to produce carbon dioxide, water, and ATP.

Calculate the Standard Free Energy for ATP Formation

The free energy change for the formation of ATP from ADP is approximately \( \Delta G^{\circ} = +30.5 \, \text{kJ/mol} \). Thus, for the formation of 32 moles of ATP:\[ \Delta G^{\circ} (\text{ATP}) = 32 \times 30.5 \, \text{kJ/mol} = 976 \, \text{kJ/mol} \]

Determine the Standard Free Energy of Glucose Oxidation

The standard free energy change for glucose oxidation is known to be approximately:\[ \Delta G^{\circ} (\text{glucose oxidation}) = -2870 \, \text{kJ/mol} \]

Calculate the Overall Reaction's Free Energy Change

We calculate the total standard free energy change for the overall reaction by summing the energy changes: \[ \Delta G^{\circ}_{\text{overall}} = \Delta G^{\circ} (\text{glucose oxidation}) + \Delta G^{\circ} (\text{ATP}) = -2870 \, \text{kJ/mol} + 976 \, \text{kJ/mol} = -1894 \, \text{kJ/mol} \]

Evaluate Reaction Spontaneity

Since the overall \( \Delta G^{\circ} \) is negative \(-1894 \, \text{kJ/mol}\), the reaction is spontaneous under standard conditions. A negative \( \Delta G^{\circ} \) indicates that the reaction can proceed without the input of energy.

Key concepts

ATP Synthesis

ATP, or Adenosine Triphosphate, is often referred to as the "energy currency" of the cell because it plays a critical role in storing and transferring energy within cells. ATP synthesis is the process through which ATP is produced, primarily in a cell's mitochondria, during cellular respiration. This involves the conversion of chemical energy from food molecules, like glucose, into usable energy in the form of ATP.

• ATP is formed with a condensation reaction that combines an adenosine diphosphate (ADP) molecule and an inorganic phosphate group ( Pi) resulting in ATP.
• The reaction is written as: ADP + Pi → ATP, releasing approximately +30.5 kJ/mol of energy per mole of ATP synthesized.
• In the context of cellular respiration, the energy necessary for ATP synthesis is provided by the oxidation of glucose, which releases a large amount of energy.

The formation of ATP from ADP is crucial for many cellular functions, including muscle contraction, molecule transport, and chemical synthesis. The energy provided by ATP breakdown fuels these processes, essentially powering various biological activities in the organism.

Glucose Oxidation

Glucose oxidation is a critical metabolic pathway in cellular respiration that breaks down glucose to generate ATP. It involves a series of complex reactions where glucose is fully oxidized to carbon dioxide and water. Through this process, high-energy electrons are harvested and used to generate ATP.

• Glucose ( C_6H_{12}O_6) is combined with oxygen ( O_2) in the reaction: C_6H_{12}O_6 + 6O_2 → 6CO_2 + 6H_2O.
• This reaction releases a significant amount of energy, with a standard free energy change of approximately -2870 kJ/mol.
• The energy from glucose oxidation is captured through the electron transport chain and used to add a phosphate group to ADP, creating ATP.

The process of glucose oxidation is vital because it provides the bulk of the energy required for ATP production in aerobic organisms. It's an efficient means of converting the chemical energy stored in glucose into a form that can be readily used by cells.

Spontaneous Reactions

A spontaneous reaction is one that occurs naturally under given conditions without needing an external energy source. In chemistry, spontaneity is related to the Gibbs free energy change ( ΔG) of a reaction. If ΔG is negative, the process is spontaneous, indicating it can proceed on its own with a net release of energy.

• For a reaction to be spontaneous, the change in free energy ( ΔG^{ ext{°}}) must be negative.
• In cellular respiration, the overall reaction involving glucose oxidation and ATP production has a ΔG^{ ext{°}} of -1894 kJ/mol.
• This negative value signifies that the process is energetically favorable and occurs spontaneously under standard conditions.

Understanding spontaneous reactions is crucial in biochemistry because it explains how cells efficiently harness energy. By coupling endergonic reactions (like ATP formation) with exergonic reactions (like glucose oxidation), cells ensure efficient energy use and sustain the processes necessary for life.