Problem 75 - Chemistry: An Atoms-Focused Approach

Question

Renewable Energy Bacteria of the genus Metbanosarcina convert amines to methane. Their action helps make methane a renewable energy source. Determine the estandard enthalpy of the following reaction from the appropriate standard enthalpies of formation $$\left(\Delta H_{\mathrm{f}, \mathrm{CH}, \mathrm{NH}_{2}}^{\circ}=-23.0 \mathrm{kJ} / \mathrm{mol}\right)$$ $$4 \mathrm{CH}_{3} \mathrm{NH}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 3 \mathrm{CH}_{4}(g)+\mathrm{CO}_{2}(g)+4 \mathrm{NH}_{3}(g)$$

Step-by-Step Solution

Answer

Answer: The standard enthalpy change of the given reaction is -137.9 kJ/mol.

Step 1: Identify standard enthalpies of formation of reactants and products

We are given the standard enthalpy of formation of CH3NH2. We need to find the standard enthalpies of formation for all other compounds including CH4, CO2, NH3, and H2O. Standard enthalpy of formation (ΔHf, CH3NH2) = -23.0 kJ/mol Standard enthalpy of formation (ΔHf, CH4) = -74.8 kJ/mol Standard enthalpy of formation (ΔHf, CO2) = -393.5 kJ/mol Standard enthalpy of formation (ΔHf, NH3) = -45.9 kJ/mol Standard enthalpy of formation (ΔHf, H2O) = -285.8 kJ/mol

Step 2: Apply Hess's Law

Hess's Law states that the standard enthalpy change of a reaction (ΔH°) is equal to the sum of the standard enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants. ΔH° = [sum(ΔHf, products)] - [sum(ΔHf, reactants)]

Step 3: Calculate the standard enthalpy change of the reaction

Substituting the values of the standard enthalpies of formation into Hess's Law equation: ΔH° = [(3 × -74.8) + (-393.5) + (4 × -45.9)] - [(4 × -23.0) + (2 × -285.8)] ΔH° = [(-224.4) + (-393.5) + (-183.6)] - [(-92.0) + (-571.6)] ΔH° = (-801.5) - (-663.6) ΔH° = -137.9 kJ/mol The standard enthalpy change of the given reaction is -137.9 kJ/mol.

Key Concepts

Hess's Law

When studying chemical reactions, we often need to calculate the enthalpy change during a process. This is where Hess's Law becomes invaluable. Hess's Law states that the total enthalpy change for a reaction is the same, regardless of whether it occurs in one step or multiple steps. This principle is based on the fact that enthalpy is a state function, meaning its change is dependent only on the initial and final states, not the path taken.

To apply Hess's Law effectively, perform the following:

• Identify and list the standard enthalpies of formation for each reactant and product in the reaction.
• Use the formula: \( \Delta H^\circ = [\text{sum of } \Delta H_f \text{ of products}] - [\text{sum of } \Delta H_f \text{ of reactants}] \)
• Substitute the known values and compute the net enthalpy change.

This consistent method allows any unknown enthalpy changes to be evaluated accurately, using known enthalpy changes of individual components.

Standard Enthalpy of Formation

The concept of Standard Enthalpy of Formation is crucial for understanding chemical thermodynamics. It refers to the enthalpy change when one mole of a compound is formed from its elements in their standard states. This measurement is taken under standard conditions, typically 1 atm pressure and 25°C.

The standard enthalpy of formation of a pure element in its most stable form is zero. For instance:

• Standard enthalpy of formation for \( O_2(g) \) is 0.
• The formation of carbon dioxide \( \text{CO}_2 \) from carbon and oxygen gives an enthalpy of \(-393.5 \) kJ/mol.

Understanding this helps in predicting the energy changes involved when new substances form. Calculations involving standard enthalpies of formation are foundational to using Hess's Law, which relates them to the overall enthalpy change of a given reaction.

Renewable Energy Bacteria

Renewable energy bacteria are fascinating organisms that have a pivotal role in sustainable energy production. Certain bacteria, like those in the genus Methanosarcina, possess the ability to convert organic compounds, such as amines, directly into methane. Methane, being a primary component of natural gas, serves as an energy-rich fuel and can be stored or used directly as a renewable energy source.

The process of converting amines to methane via metabolic pathways is not only effective but also environmentally beneficial as it can reduce waste and produce energy simultaneously. Key benefits include:

• Producing cleaner energy compared to fossil fuels.
• Utilizing organic waste that would otherwise contribute to pollution.
• Offering a sustainable method to produce energy that can be continuously renewed.

Through understanding the chemical processes and reactions involved, researchers can optimize and harness these bacteria to enhance energy yields, further advancing the field of renewable energy sources.