Problem 56 - Chemistry: An Atoms-Focused Approach

Question

Use the free energies of formation from Appendix 4 to calculate the standard free-energy change for the decomposition of ammonia in the following reaction: $$2 \mathrm{NH}_{3}(g) \rightarrow \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)$$ Is the reaction spontaneous under standard conditions?

Step-by-Step Solution

Answer

Answer: The standard free-energy change for the decomposition of ammonia into nitrogen and hydrogen gases is 33.2 kJ/mol. Since the value is positive, the reaction is nonspontaneous under standard conditions.

Step 1: Identify the free energies of formation for each compound

From Appendix 4, obtain the standard free energy of formation for ammonia (NH3), nitrogen (N2), and hydrogen (H2). Values are given in kJ/mol. $$ \begin{aligned} \Delta G^{o}_{f}[\mathrm{NH_3}] &=-16.6 \\ \Delta G^{o}_{f}[\mathrm{N_2}] &=0 \\ \Delta G^{o}_{f}[\mathrm{H_2}] &=0 \end{aligned} $$

Step 2: Calculate the standard free energy change for the reaction

Use the free energies of formation to calculate the standard free-energy change for the reaction, using the following equation: $$\Delta G^{o}_{rxn}=\sum(\Delta G^{o}_{f}\cdot\nu_{products})-\sum(\Delta G^{o}_{f}\cdot\nu_{reactants})$$ Here, ν is the stoichiometric coefficient of the compound in the balanced chemical equation. Substitute the values: $$\Delta G^{o}_{rxn} = (\Delta G_f[N_2]+3\Delta G_f[H_2])-2\Delta G_f[NH_3]$$

Step 3: Solve for the standard free-energy change

Plug in the values of free energy of formation for each compound: $$\Delta G^{o}_{rxn} = ((0) + 3(0)) - 2(-16.6)$$ Do the calculations: $$\Delta G^{o}_{rxn} = 2 \times 16.6 = 33.2 \,\text{kJ/mol}$$

Step 4: Determine if the reaction is spontaneous

If the standard free-energy change is negative, the reaction is spontaneous. If it's positive, the reaction is nonspontaneous. In this case, the standard free-energy change is: $$\Delta G^{o}_{rxn} = 33.2 \,\text{kJ/mol}$$ Since it's a positive value, the reaction is not spontaneous under standard conditions. The decomposition of ammonia into nitrogen and hydrogen gases is nonspontaneous at standard conditions.

Key Concepts

Spontaneity

Understanding whether a chemical reaction is spontaneous is crucial in determining if it will occur under given conditions without external influence. Spontaneity in chemistry refers to a process that proceeds naturally. The driving force for spontaneity is Gibbs Free Energy, denoted as \( \Delta G \), analyzed under standard conditions at \( 25 ^\circ C \) and 1 atm pressure.

If \( \Delta G \) is negative, the reaction releases free energy and is spontaneous. Conversely, a positive \( \Delta G \) indicates the reaction requires energy input and is nonspontaneous. For reactions like the decomposition of ammonia, checking \( \Delta G \) helps us understand if it naturally progresses.

• Negative \( \Delta G \): Spontaneous reaction
• Positive \( \Delta G \): Nonspontaneous reaction

Therefore, knowing \( \Delta G \) gives valuable insights into the reaction's feasibility under standard conditions.

Standard Free-Energy Change

The standard free-energy change, \( \Delta G^{o}_{rxn} \), is key in evaluating the energy shift during a chemical reaction. This value is obtained from the standard free energies of formation of the reactants and products involved in the reaction. The process utilizes the well-known relationship:

\[\Delta G^{o}_{rxn} = \sum(\Delta G^{o}_{f}\cdotu_{products}) - \sum(\Delta G^{o}_{f}\cdotu_{reactants})\]

The calculation involves:

• Identifying each compound's free energy of formation from reliable datasheets or appendices
• Applying the stoichiometric coefficients from the balanced chemical equation
• Using the formula to find the total difference in energy

For the ammonia decomposition, the calculated \( \Delta G^{o}_{rxn} = 33.2 \,\text{kJ/mol} \) indicates energy input is needed, aligning with its nonspontaneous nature.

Free Energy of Formation

The free energy of formation, \( \Delta G^{o}_{f} \), is a fundamental concept in thermochemistry, representing the energy change when one mole of a compound is formed from its elements in their standard states. These values help predict reaction tendencies and can be found in standardized tables.

For instance, in the provided exercise:

• Ammonia \( (\text{NH}_3) \) has \( \Delta G^{o}_{f} = -16.6 \,\text{kJ/mol} \)
• Nitrogen \( (\text{N}_2) \) and Hydrogen \( (\text{H}_2) \) have \( \Delta G^{o}_{f} = 0 \,\text{kJ/mol} \) as they are elemental in standard states

These values are essential for calculating the standard free-energy change of reactions, thereby predicting if a reaction is likely to proceed without additional energy. Understanding them ensures accurate assessments of chemical processes.