Question

Which of the following reactions is (are) spontaneous at standard conditions? (a) \(2 \mathrm{NO}_{3}^{-}(a q)+8 \mathrm{H}^{+}(a q)+6 \mathrm{Cl}^{-}(a q) \longrightarrow\) \(2 \mathrm{NO}(g)+4 \mathrm{H}_{2} \mathrm{O}+3 \mathrm{Cl}_{2}(g)\) (b) \(\mathrm{O}_{2}(g)+4 \mathrm{H}^{+}(a q)+4 \mathrm{Cl}^{-}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{Cl}_{2}(g)\) (c) \(3 \mathrm{Fe}(s)+2 \mathrm{AuCl}_{4}^{-}(a q) \longrightarrow 2 \mathrm{Au}(s)+8 \mathrm{Cl}^{-}(a q)+3 \mathrm{Fe}^{2+}(a q)\)

Short answer

Provide the calculated ∆G° values for each reaction to support your answer.

Step-by-step solution

(a) Calculate ∆G° for reaction (a)

Using the standard Gibbs free energy values from a table, find the ∆G° values for the reactants and products of reaction (a). Subtract the sum of the reactant ∆G° values from the sum of the product ∆G° values to find the ∆G° for the reaction.

(b) Calculate ∆G° for reaction (b)

Repeat step (a) for the reactants and products of reaction (b).

(c) Calculate ∆G° for reaction (c)

Repeat step (a) for the reactants and products of reaction (c). Step 2: Determine if each reaction is spontaneous

(a) Determine spontaneity for reaction (a)

If the calculated ∆G° for reaction (a) is negative, then the reaction is spontaneous. If the ∆G° is positive or zero, the reaction is non-spontaneous or reaches equilibrium, respectively.

(b) Determine spontaneity for reaction (b)

Repeat step (a) for the calculated ∆G° of reaction (b).

(c) Determine spontaneity for reaction (c)

Repeat step (a) for the calculated ∆G° of reaction (c). Step 3: Conclusion

Conclusion

Based on the calculated ∆G° values and the spontaneity determinations, list which of the reactions (a), (b), and (c) are spontaneous at standard conditions.

Key concepts

Understanding Spontaneous Reactions

In the world of chemistry, a reaction is considered **spontaneous** if it can proceed without any external energy input. This doesn't necessarily mean that the reaction occurs instantly but rather that it is thermodynamically favorable.
For a reaction to be spontaneous under standard conditions, the Gibbs free energy change, denoted by \( \Delta G^\circ \), must be less than zero. The formula for calculating \( \Delta G^\circ \) is:

• \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \)

where \( \Delta H^\circ \) is the change in enthalpy, \( \Delta S^\circ \) is the change in entropy, and \( T \) is the temperature in Kelvin.
In simpler terms, a negative \( \Delta G^\circ \) indicates a release of energy, making the reaction favorable, similar to a stone naturally rolling downhill due to gravity.However, even with a negative \( \Delta G^\circ \), other factors like activation energy might influence the rate at which the reaction actually appears to proceed. But in terms of potential, such reactions are ready to go.

Standard Conditions in Chemistry

**Standard conditions** are a set of specific parameters under which reactions are studied to allow for consistency and comparison. These conditions ensure that scientists across the world can accurately compare results and predict the feasibility of reactions. Standard conditions often include:

• Temperature set at 298 K (25°C)
• Pressure of 1 atm
• Concentrations of 1 M for all solutions

When stating that a reaction is spontaneous "at standard conditions," it implies that these factors are strictly maintained. By keeping these variables constant, we reduce the complexity involved in predicting reaction spontaneity, allowing the focus to remain on the inherent properties of the reactants and products.
This enables scientists to tabulate and use standard Gibbs free energy values across various chemical processes for easier and practical calculations.

The Role of Thermodynamics in Chemical Reactions

**Thermodynamics** is a branch of physical chemistry concerned with energy changes in a system. In the context of chemical reactions, it helps determine whether a reaction will occur spontaneously under set conditions. Three major laws govern thermodynamics:

• The First Law, or the law of energy conservation, states that energy can neither be created nor destroyed, only transferred or transformed.
• The Second Law introduces entropy, suggesting that in an isolated system, natural processes increase overall entropy, or disorder.
• The Third Law states that as a system reaches absolute zero, the entropy approaches a constant minimum.

Gibbs free energy is directly connected to these laws. Through thermodynamics, we derive concepts like \( \Delta G^\circ \) to predict reaction spontaneity.
Our understanding of these principles allows scientists to break down complex reactions into manageable calculations, offering insight into how and why reactions behave as they do, whether they release or consume energy, and whether they are reversible or irreversible in nature.