Question

Identify the following processes as either spontaneous or not spontaneous. (a) Ice melts when placed in a flask containing water at \(5^{\circ} \mathrm{C}.\) (b) Hydrogen iodide molecules decompose at \(400 \mathrm{K}\) to give a mixture of \(\mathrm{H}_{2}, \mathrm{I}_{2},\) and \(\mathrm{HI}\) (c) Ethanol and water are mixed to form a solution. (d) Slightly soluble \(\mathrm{PbCl}_{2}\left(K_{\mathrm{sp}}=1.7 \times 10^{-5}\right)\) dissolves in water to form a saturated solution.

Short answer

(a) Spontaneous, (b) Non-spontaneous (depends on conditions), (c) Spontaneous, (d) Non-spontaneous.

Step-by-step solution

Understanding Spontaneity

A process is considered spontaneous if it occurs naturally without any external input of energy. Spontaneity is influenced by the Gibbs Free Energy (ΔG), where a negative ΔG indicates a spontaneous process.

Evaluate Process (a) - Ice Melting at 5°C

Ice melts at temperatures above 0°C. Since 5°C is greater than 0°C, the ice melts spontaneously as heat naturally flows from the surroundings to the ice.

Evaluate Process (b) - HI Decomposition at 400K

Hydrogen iodide decomposes into its elements (H₂ and I₂) when heated to high temperatures like 400K. However, this decomposition is usually thermodynamically unfavorable but may be kinetically controlled. In general, additional information like Gibbs energy details are needed for precise assessment, but decomposition due to added heat can imply a non-spontaneous nature depending on equilibrium constants.

Evaluate Process (c) - Mixing Ethanol and Water

When ethanol and water are mixed, they form a homogeneous solution spontaneously, as the mixing increases entropy.

Evaluate Process (d) - Dissolution of PbCl₂

PbCl₂ is slightly soluble, and forms a saturated solution overall. The dissolution of such sparingly soluble salts is considered non-spontaneous under ordinary circumstances without drivers like ion pairing or equilibrium shifts (common ion effect). The small solubility product (Ksp) indicates its low solubility.

Key concepts

Gibbs Free Energy

When it comes to determining if a chemical process is spontaneous, Gibbs Free Energy (\(\Delta G\)) is the key factor. This concept helps us evaluate the feasibility of a reaction under constant temperature and pressure.

• If \(\Delta G < 0\), the process is spontaneous and energy is released.
• If \(\Delta G > 0\), the process is non-spontaneous and requires an input of energy.
• If \(\Delta G = 0\), the system is at equilibrium, showing no net change over time.

Gibbs Free Energy combines enthalpy (\(H\)), entropy (\(S\)), and temperature (\(T\)) and is given by the equation: \[ \Delta G = \Delta H - T \Delta S \]Understanding this equation helps predict whether a given process will self-proceed without external influence or intervention.

Entropy in Chemistry

Entropy (\(S\)) measures the disorder or randomness in a system. In chemistry, it's crucial because it indicates how energy is distributed among particles.
During spontaneous processes, the overall entropy of the universe (system plus surroundings) tends to increase. This is often summed up by the second law of thermodynamics.

• An increase in entropy (\(\Delta S > 0\)) means more disorder and a tendency towards spontaneous processes.
• A decrease in entropy (\(\Delta S < 0\)) indicates less disorder, often requiring energy input to proceed.

For example, when mixing ethanol and water, the increase in entropy due to molecular dispersion is a favorable driver for spontaneous solution formation. Understanding entropy helps explain why certain reactions or phase changes occur naturally.

Thermodynamics

Thermodynamics provides the framework to understand energy transfer within physical and chemical processes. It's centered around several laws that govern these energy changes.
The first law of thermodynamics, known as the law of energy conservation, states that energy cannot be created or destroyed, only transferred or transformed.

• This principle implies that total energy before and after any process remains constant—migrating between kinetic, potential, chemical, or thermal forms.
• In processes like ice melting, heat transfers to the ice, causing a state change due to energy absorption.

Furthermore, thermodynamics relates directly to spontaneity via the concept of Gibbs Free Energy. It harmonizes with the second law, favoring processes that result in maximum entropy increase. By grasping these concepts, we can deduce and predict the direction and extent of reactions and physical transformations.

Chemical Equilibrium

Chemical equilibrium occurs when the forward and reverse reactions proceed at equal rates, maintaining constant concentrations of reactants and products. At equilibrium, the Gibbs Free Energy change (\(\Delta G\)) of the system is zero.
Even at equilibrium, reactions aren't static; rather, they dynamically maintain balance.

• This dynamic nature is aptly described by the concept of reaction quotient (\(Q\)) and the equilibrium constant (\(K\)).
• If \(Q < K\), the forward reaction is favored until equilibrium is reached.
• Conversely, if \(Q > K\), the reverse reaction gains favor.

For example, the decomposition of hydrogen iodide at 400K depends on thermodynamic favorability. Even if the products tend to form under certain conditions, the position of equilibrium, dictated by \(K\), significantly influences the final outcome. Studying equilibrium provides insights into reaction conditions and the reversibility of chemical processes.