Question

One of the methods for the synthesis of dilute acetic acid from ethanol is the use of acetobacter. A dilute solution of ethanol is allowed to trickle down over beechwood shavings that have been inoculated with a culture of the bacteria. Air is forced through the vat countercurrent to the alcohol flow. The reaction can be written as \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) (aq) \(+\mathrm{O}_{2} \mathrm{CH}_{3} \mathrm{COOH}\) (aq) \(+\mathrm{H}_{2} \mathrm{O}(\ell)\) acetic acid Calculate the Gibbs Free Energy, \(\Delta \mathrm{G}^{\circ}\), for this reaction, given the following Gibbs Free Energies of Formation: Ethanol \(=-43.39 \mathrm{Kcal} / \mathrm{mole}, \mathrm{H}_{2} \mathrm{O}(\ell)=-56.69 \mathrm{Kcal} / \mathrm{mole}\), and Acetic acid \(=-95.38 \mathrm{Kcal} / \mathrm{mole} .\)

Short answer

The Gibbs Free Energy change for the given reaction, ΔG°, can be calculated using the formula: \(\Delta G^{\circ}= \sum{\Delta G^{\circ}_{products}} - \sum{\Delta G^{\circ}_{reactants}}\). Substituting the given Gibbs Free Energies of Formation and performing the calculation, the result is \(\Delta G^{\circ} = -108.68 Kcal/mol\).

Step-by-step solution

List the Given Values

Gibbs Free Energies of Formation: Ethanol = \(-43.39 Kcal/mol\) Water = \(-56.69 Kcal/mol\) Acetic Acid = \(-95.38 Kcal/mol\) Chemical reaction: \(\mathrm{ C_2H_5OH + O_2 \rightarrow CH_3COOH + H_2O }\)

Identify the Products and Reactants

Reactants: Ethanol and Oxygen Products: Acetic Acid and Water

Apply the Formula for Gibbs Free Energy Change

Use the formula: \(\Delta G^{\circ} = \sum{\Delta G^{\circ}_{products}} - \sum{\Delta G^{\circ}_{reactants}}\)

Substitute the Given Values in the Formula

\(\Delta G^{\circ} = [(1\times(-95.38) + 1\times(-56.69)) - (1\times(-43.39) + 0)]\) Here, we use 0 as the Gibbs Free Energy of Formation for an element in its standard state, such as Oxygen (O_2) in its gaseous state, is always 0.

Perform the Calculation

\(\Delta G^{\circ} = (-95.38 -56.69) -(-43.39)\) \(\Delta G^{\circ} = (-152.07) + 43.39\) \(\Delta G^{\circ} = -108.68 Kcal/mol\) The Gibbs Free Energy change for this reaction, ΔG°, is \(-108.68 Kcal/mol\).

Key concepts

Chemical Reaction

At its core, a chemical reaction involves the transformation of one set of chemical substances into another. To visualize this, think of it as a cooking recipe where reactants are like ingredients and products are the final dish. The essence is the breaking and forming of chemical bonds, leading to a change in the composition of molecules.

For instance, in the reaction where ethanol converts to acetic acid, the ethanol molecules react with oxygen to rearrange their atoms, forming acetic acid and water in the process. This type of reaction is fundamental not only in laboratory settings but also plays a critical role in many biological and industrial processes.

Enthalpy of Formation

Enthalpy of formation, denoted by \( \(\Delta H_f^\circ\) \), is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It's sort of like understanding the cost in energy to make a product from scratch. If we think about it in terms of a currency, this would tell us how much 'energy currency' is spent or released during the formation of a compound.

In our textbook example, the Gibbs Free Energies of Formation are used to calculate the overall energy change. They provide a way to gauge whether a reaction is favorable or not. A negative value suggests the reaction ‘pays off’ in energy terms, encouraging it to proceed.

Ethanol to Acetic Acid Conversion

Converting ethanol to acetic acid is fascinating as it showcases how a simple molecule like ethanol can be transformed into a more complex one like acetic acid through a biological process. This transformation involves not merely replacing one atom for another but reorganizing the molecular structure entirely.

The reaction is much more than a simple swap; it's like an assembly line where ethanol ' cars ' go in and, through several steps involving the introduction of oxygen and removal of hydrogen atoms, acetic acid ' cars ' come out. This process is exploited industrially to produce vinegar, where this chemical conversion is achieved using acetobacter bacteria.

Acetobacter Metabolism

Acetobacter metabolism is the biochemical engine driving the conversion of ethanol into acetic acid. This bacteria genre is a maestro of sorts, orchestrating the oxidation of alcohol by oxygen from the air. It's a natural chemist, facilitating the reaction efficiently without the need for high temperatures or pressures that would be typically required in a non-biological setting.

Moreover, the acetobacter's role is akin to that of a foreman in the industrial process, overseeing the proper conversion and ensuring the product quality is consistent. Understanding its metabolism not only helps in vinegar production but also provides insights into biochemical pathways and energy generation in microorganisms.