Question

Certain bacteria in the soil obtain the necessary energy for growth by oxidizing nitrites to nitrates: $$ 2 \mathrm{NO}_{2}^{-}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{3}^{-} $$ Given that the standard Gibbs free energies of formation of \(\mathrm{NO}_{2}^{-}\) and \(\mathrm{NO}_{3}^{-}\) are -34.6 and \(-110.5 \mathrm{~kJ} / \mathrm{mol}\), respectively, calculate the amount of Gibbs free energy released when 1 mole of \(\mathrm{NO}_{2}^{-}\) is oxidized to 1 mole of \(\mathrm{NO}_{3}^{-}\).

Short answer

-75.9 kJ of Gibbs free energy is released per mole of \( \mathrm{NO}_{2}^{-} \) oxidized.

Step-by-step solution

Identify the Reaction

The given reaction is the oxidation of nitrites to nitrates: \[ 2 \mathrm{NO}_{2}^{-} + \mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{3}^{-} \]. This indicates that 2 moles of \( \mathrm{NO}_{2}^{-} \) are oxidized to 2 moles of \( \mathrm{NO}_{3}^{-} \).

Write the Formation Reaction Equations

From the standard Gibbs free energies of formation, we have: \[ \text{For } \mathrm{NO}_{2}^{-}: \Delta G^0_f(\mathrm{NO}_{2}^{-}) = -34.6 \text{ kJ/mol} \] and \[ \text{For } \mathrm{NO}_{3}^{-}: \Delta G^0_f(\mathrm{NO}_{3}^{-}) = -110.5 \text{ kJ/mol} \].

Calculate the Change in Gibbs Free Energy for the Reaction

The change in Gibbs free energy for the reaction is calculated using \( \Delta G^0_{reaction} = \Sigma \Delta G^0_f(\text{products}) - \Sigma \Delta G^0_f(\text{reactants}) \). \[ \Delta G^0_{reaction} = [2(-110.5)] - [2(-34.6)] \].

Simplify the Calculation

Calculate the value: \[ \Delta G^0_{reaction} = 2(-110.5) - 2(-34.6) \]. Simplifying each term, we have: \[ 2(-110.5) = -221 \text{ kJ} \] and \[ 2(-34.6) = -69.2 \text{ kJ} \].

Compute the Reaction's Gibbs Free Energy

Substitute the calculated values: \[ \Delta G^0_{reaction} = -221 \text{ kJ} + 69.2 \text{ kJ} = -151.8 \text{ kJ/mol} \].

Calculate Gibbs Free Energy for 1 Mole

Since the reaction involves 2 moles of \( \mathrm{NO}_{2}^{-} \) to produce 2 moles of \( \mathrm{NO}_{3}^{-} \), the energy released per mole of \( \mathrm{NO}_{2}^{-} \) oxidized is half of \(-151.8 \text{ kJ/mol} \): \[ \frac{-151.8}{2} = -75.9 \text{ kJ/mol} \].

Key concepts

Nitrite Oxidation

Nitrite oxidation is a crucial biochemical process carried out by specific bacteria in the soil. In this process, nitrite ions (\( \mathrm{NO}_2^- \))are converted to nitrate ions (\( \mathrm{NO}_3^- \)). The equation for this chemical reaction is:

• 2 \( \mathrm{NO}_2^- \)
• +\( \mathrm{O}_2 \)
• \( \rightarrow \) 2 \( \mathrm{NO}_3^- \)

This process is not just a chemical change but a vital part of the nitrogen cycle in the environment. The bacteria use the energy released during this oxidation to support their growth and metabolic activities. This transformation is important because nitrates are more stable in the soil and can be utilized by plants as a nutrient.

Nitrate Formation

Nitrate formation through nitrite oxidation is what allows plants and other producers in the ecosystem to access nitrogen in a form they can use. During this reaction, oxygen combines with nitrite ions, resulting in the formation of nitrate ions. The resulting nitrate is more readily accessible to plant roots, which absorb it as a nutrient essential for growth. This conversion process is an excellent example of how chemical reactions in nature support life and maintain ecological balance. It ensures that nitrogen, an essential element found in amino acids and nucleic acids, is recycled within ecosystems.

Gibbs Free Energy Calculation

Calculating the Gibbs free energy change for a reaction is useful to determine if a reaction will occur spontaneously. For the oxidation of nitrites to nitrates, the Gibbs free energy change is calculated using the formula:\[ \Delta G^0_{\text{reaction}} = \Sigma \Delta G^0_f(\text{products}) - \Sigma \Delta G^0_f(\text{reactants}) \]In this problem, the given Gibbs free energies of formation for \( \mathrm{NO}_2^- \) and \( \mathrm{NO}_3^- \) are -34.6 kJ/mol and -110.5 kJ/mol, respectively. To find the change in Gibbs free energy:

• Multiply the formation energy of the products and reactants by their stoichiometric coefficients in the balanced equation.
• Subtract the sum of the reactants’ Gibbs free energies from the sum of the products’ Gibbs free energies.
• This results in a value of \( -151.8 \text{ kJ/mol} \) for the whole reaction.
• For 1 mole of \( \mathrm{NO}_2^- \), divide by 2.

Reaction Energetics

Reaction energetics refers to the study of energy changes that occur during chemical reactions. In the nitrite to nitrate oxidation process, the energetics are crucial to understanding how and why the reaction proceeds. Gibbs free energy, identified as\( \Delta G^0_{\text{reaction}} \), is central to this understanding, indicating whether energy is released or absorbed.

• A negative \( \Delta G^0 \) signifies that the reaction is exergonic and will proceed spontaneously, releasing energy.
• For nitrite oxidation, \( \Delta G^0 = -75.9 \text{ kJ/mol} \) per mole of nitrite clarified that the reaction releases energy, fostering bacterial growth.

Understanding this energy release helps explain why nitrite oxidation is favorable for the bacteria, as it provides energy necessary for survival and proliferation.