Question

chemically unstable compared with its oxidation products, \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). a. What can one say about the standard free- energy change for this reaction? b. Why doesn't firewood stacked beside the fireplace undergo spontaneous combustion to its much more stable products? c. How can the activation energy be supplied to this reaction? d. Suppose you have an enzyme (firewoodase) that catalyzes the rapid conversion of firewood to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) at room temperature. How does the enzyme accomplish that in thermodynamic terms?

Short answer

\( \Delta G^\circ \) is negative for firewood combustion; high activation energy prevents spontaneous reaction; external energy or a catalyst can initiate it.

Step-by-step solution

Understanding Free-Energy Change

The standard free-energy change, denoted as \( \Delta G^\circ \), indicates the spontaneity of a reaction. Since firewood combustion leads to formation of stable products \( \text{CO}_2 \) and \( \text{H}_2\text{O} \), which are lower in energy compared to the reactants, \( \Delta G^\circ \) for this reaction is negative, signaling that the reaction is spontaneous in terms of energy.

Reason for Non-spontaneous Combustion

Though the free-energy change is negative, firewood does not combust spontaneously at room temperature due to a high activation energy barrier. This barrier prevents the reactants from transitioning to products without an initial energy input.

Overcoming Activation Energy

Activation energy can be supplied by an external energy source, such as a spark or heat, which provides the necessary energy to initiate the combustion reaction, allowing reactants to surpass the activation energy barrier.

Role of Enzyme in Catalysis

An enzyme like 'firewoodase' catalyzes the reaction by lowering the activation energy without altering the \( \Delta G^\circ \). It stabilizes the transition state, making it easier for the reaction to proceed at room temperature by requiring less external energy.

Key concepts

Free-Energy Change

In biochemistry, the term **free-energy change** refers to how energy is transferred in a chemical reaction and whether the reaction will proceed spontaneously. The concept relies heavily on Gibbs free energy, which combines enthalpy and entropy into a single value, denoted by \( \Delta G \). When a reaction results in more stable products, as is the case with the conversion of firewood to carbon dioxide \( \text{CO}_2 \) and water \( \text{H}_2\text{O} \), the system loses energy.- When \( \Delta G \) is negative, this indicates that the reaction occurs spontaneously as it releases energy.- In our exercise, since both \( \text{CO}_2 \) and \( \text{H}_2\text{O} \) are more stable than the components of firewood, the reaction possesses a negative \( \Delta G^\circ \), emphasizing its spontaneity energetically.Thus, while free-energy change gives valuable insights into the thermodynamic potential of a reaction, it doesn't provide information about the rate at which the reaction proceeds.

Activation Energy

Despite having a favorable free-energy change, many biochemical reactions do not occur spontaneously due to the presence of an energy barrier known as activation energy. This is the additional energy required to initiate a chemical reaction and reach the transition state, a high-energy state intermediating between reactants and products. - The activation energy forms a barrier that reactants must overcome in order to transform into products. It explains why firewood, though energetically favorable for combustion, does not catch fire at room temperature. However, this barrier can be overcome through the supply of external energy: - An energy source like heat or a spark can provide enough energy to allow the reactants to surpass this barrier. - Once the activation energy is overcome, the reaction can proceed swiftly towards the formation of stable products, releasing energy in the process. Understanding activation energy helps clarify why and how a seemingly spontaneous reaction needs a nudge to start.

Enzyme Catalysis

Enzymes play a crucial role in reducing the activation energy of biochemical reactions, thereby speeding up the reaction without altering the overall free-energy change (\( \Delta G^\circ \)). They serve as biological catalysts and function by stabilizing the transition state, which brings down the energy needed to initiate the reaction.- Enzymes achieve this by binding to reactants (substrates) and facilitating a different pathway with a lower activation energy.- In our scenario, an enzyme like 'firewoodase' could catalyze the conversion of firewood to \( \text{CO}_2 \) and \( \text{H}_2\text{O} \) at room temperature. - By lowering the activation energy, 'firewoodase' allows the reaction to proceed with less external energy.This ability of enzymes to reduce the required energy makes them indispensable in biochemical processes, enabling high-speed reactions at relatively low temperatures.