Problem 78 - Chemistry: An Atoms-Focused Approach

Question

Methanogenic bacteria convert liquid acetic acid (CH \(_{3} \mathrm{COOH}\) ) into \(\mathrm{CO}_{2}(g)\) and \(\mathrm{CH}_{4}(g)\). a. Is this process endothermic or exothermic under standard conditions? b. Is the reaction spontaneous under standard conditions?

Step-by-Step Solution

Answer

a) The conversion process of liquid acetic acid into carbon dioxide and methane is endothermic under standard conditions. b) The conversion process of liquid acetic acid into carbon dioxide and methane is spontaneous under standard conditions.

Step 1: 1. Write the balanced chemical equation

For the given conversion process, the balanced chemical equation is: CH_3COOH (l) → CO_2 (g) + CH_4 (g)

Step 2: 2. Find the standard enthalpy change (∆H°) for the reaction

To determine if the process is endothermic or exothermic, we need to find the standard enthalpy change (∆H°) for the reaction. The ∆H° value can be calculated using the standard enthalpies of formation (∆Hf°) for the reactants and products: ∆H° = Σ n_i ∆Hf°(products) - Σ n_i ∆Hf°(reactants) Where n_i is the stoichiometric coefficient for substance i. To find ∆Hf° values for each substance, we can use standard thermodynamic tables: ∆Hf°(CH_3COOH, l) = -484.5 kJ/mol ∆Hf°(CO_2, g) = -393.5 kJ/mol ∆Hf°(CH_4, g) = -74.8 kJ/mol Now, applying the equation for ∆H°: ∆H° = [1*(-393.5) + 1*(-74.8)] - [1*(-484.5)] ∆H° = (-393.5 - 74.8) + 484.5 ∆H° = 16.2 kJ/mol Since the enthalpy change is positive (∆H° > 0), the reaction is endothermic.

Step 3: a. Answer for part (a)

The conversion process of liquid acetic acid into carbon dioxide and methane is endothermic under standard conditions.

Step 4: 3. Find the standard Gibbs free energy change (∆G°) for the reaction

To determine if the reaction is spontaneous under standard conditions, we need to find the standard Gibbs free energy change (∆G°) for the reaction. The ∆G° value can be calculated using the standard free energies of formation (∆Gf°) for the reactants and products: ∆G° = Σ n_i ∆Gf°(products) - Σ n_i ∆Gf°(reactants) To find ∆Gf° values for each substance, we can use standard thermodynamic tables: ∆Gf°(CH_3COOH, l) = -389.4 kJ/mol ∆Gf°(CO_2, g) = -394.4 kJ/mol ∆Gf°(CH_4, g) = -50.8 kJ/mol Now, applying the equation for ∆G°: ∆G° = [1*(-394.4) + 1*(-50.8)] - [1*(-389.4)] ∆G° = (-394.4 - 50.8) + 389.4 ∆G° = -55.8 kJ/mol Since the Gibbs free energy change is negative (∆G° < 0), the reaction is spontaneous.

Step 5: b. Answer for part (b)

The conversion process of liquid acetic acid into carbon dioxide and methane is spontaneous under standard conditions.

Key Concepts

Enthalpy Change

In chemistry, the enthalpy change (\(\Delta H^{\circ}\)) of a reaction tells us whether the process absorbs or releases heat under standard conditions.
Simply put, it measures the heat exchanged with the surroundings at constant pressure.
- **Positive \(\Delta H^{\circ}\)**: Endothermic process, absorbs heat- **Negative \(\Delta H^{\circ}\)**: Exothermic process, releases heatIn the exercise concerning the conversion of acetic acid to carbon dioxide and methane, the calculated enthalpy change is 16.2 \(\text{kJ/mol}\). This positive value indicates that the reaction absorbs heat from its surroundings, making it endothermic. This is essential in thermochemistry as understanding whether a reaction needs heat input or gives off heat helps predict its behavior in various conditions.

Gibbs Free Energy

The Gibbs free energy change (\(\Delta G^{\circ}\)) is crucial in determining whether a reaction will occur spontaneously under standard conditions.
It combines enthalpy, temperature, and entropy (a measure of disorder). The formula for \(\Delta G^{\circ}\) is:\[\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\]Where:- \(\Delta H^{\circ}\) is the enthalpy change - \(T\) is the temperature in Kelvin- \(\Delta S^{\circ}\) is the entropy changeIf \(\Delta G^{\circ} < 0\), the reaction is spontaneous, meaning it can occur without any additional energy input.
If \(\Delta G^{\circ} > 0\), the reaction is non-spontaneous.
In our acetic acid conversion reaction, the Gibbs free energy change is calculated to be -55.8 \(\text{kJ/mol}\). The negative sign indicates the reaction is spontaneous. It wouldn't require external energy to keep it going once it starts, which is vital for processes occurring in biological systems.

Chemical Reaction Spontaneity

Spontaneity in chemical reactions refers to the ability of a process to occur under a given set of conditions without external assistance.
This concept is all about whether a reaction moves forward naturally. Two primary energies govern this: enthalpy and Gibbs free energy.
- **Exothermic reactions** often spontaneous as they release energy (negative \(\Delta H^{\circ}\))- **Endothermic reactions** can also be spontaneous if the entropy change coupled with temperature (considered in \(\Delta G^{\circ}\)) is favorable The exercise we worked on involves checking the spontaneity through Gibbs free energy.
Despite being an endothermic process (positive \(\Delta H^{\circ}\)), our reaction was found to be spontaneous because \(\Delta G^{\circ}\) was negative.
This clearly shows how important it is not to rely solely on enthalpy changes: a negative \(\Delta G^{\circ}\) ultimately decides the spontaneity, encompassing both \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\). It's a wonderful testament to how thermodynamic variables work together to predict reaction conditions.