Problem 88 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

The enthalpy and entropy change for a chemical reaction are \(-2500 \mathrm{cal}\) and \(+7.4 \mathrm{cal} / \mathrm{K}\), respectively. The nature of reaction at \(298 \mathrm{~K}\) is (a) Spontaneous (b) Reversible (c) Irreversible (d) Non-spontaneous

Step-by-Step Solution

Answer

The reaction is spontaneous at 298 K.

Step 1: Understanding Gibbs Free Energy

The spontaneity of a chemical reaction can often be determined using Gibbs Free Energy, given by the equation \[\Delta G = \Delta H - T\Delta S\] where \(\Delta G\) is the change in Gibbs Free Energy, \(\Delta H\) is the enthalpy change, \(T\) is the temperature in Kelvin, and \(\Delta S\) is the entropy change. A negative \(\Delta G\) indicates a spontaneous reaction.

Step 2: Calculate Gibbs Free Energy

Using the given enthalpy change \(\Delta H = -2500 \mathrm{cal}\) and entropy change \(\Delta S = +7.4 \mathrm{cal/K}\) at T = 298 K, calculate the Gibbs Free Energy. Plug the values into the equation: \[\Delta G = (-2500 \mathrm{cal}) - (298 \mathrm{K})\times (+7.4 \mathrm{cal/K})\]

Step 3: Evaluate the Sign of Gibbs Free Energy

Perform the calculation from Step 2 to determine the sign of \(\Delta G\): \[\Delta G = (-2500 \mathrm{cal}) - (298 \mathrm{K})\times (7.4 \mathrm{cal/K})\] Simplify the terms to get the numerical value of \(\Delta G\). The sign of this value will indicate whether the reaction is spontaneous (negative) or non-spontaneous (positive).

Key Concepts

Chemical Reaction Spontaneity

Understanding whether a chemical reaction will occur spontaneously is a foundational concept in chemistry. Spontaneity does not imply that a reaction will happen fast, only that it will proceed without external energy input. A spontaneous reaction means that once started, it will continue by itself without any need for continuous outside help.

The spontaneous nature of a reaction is determined by Gibbs Free Energy (Delta G), a thermodynamic property that combines enthalpy (Delta H) and entropy (Delta S) with the temperature (T) of the system. If Delta G is negative, the reaction is spontaneous; if it's positive, the reaction is not spontaneous and requires energy input. In the given exercise, calculating Delta G allows us to predict the reaction's spontaneity at 298 K.

Enthalpy Change

Enthalpy change (Delta H) is a measure of the total heat content in a chemical system under constant pressure. It is a key component in determining the energy difference between the products and reactants involved in a reaction. A negative Delta H signifies that the reaction releases heat, classifying it as exothermic. Conversely, a positive Delta H indicates that the reaction absorbs heat, making it endothermic.

In the provided exercise, the enthalpy change is -2500 cal, which means the reaction is exothermic. This heat release often contributes to the spontaneous nature of chemical reactions. However, enthalpy alone cannot predict spontaneity; entropy changes must also be considered.

Entropy Change

Entropy (S) represents the degree of disorder or randomness in a system. In thermodynamics, the change in entropy (Delta S) during a reaction indicates the change in dispersal of energy and matter. A positive Delta S means that the disorder is increasing in the course of the reaction, which is a sign that the reaction could be spontaneous. However, whether the increase in entropy will result in a spontaneous process also depends on the temperature and the enthalpy change.

The exercise mentions that the entropy change is +7.4 cal/K, a positive value, suggesting the system's disorder is increasing. Alongside the negative enthalpy change, this supports the tendency toward a spontaneous reaction, but we need to calculate Delta G to be sure.

Thermodynamics

Thermodynamics is a branch of physics and chemistry that describes the relationships and conversions between heat energy and other forms of energy and how these influence matter. The laws of thermodynamics provide a framework to understand how systems reach equilibrium and how energy transformations determine the direction and spontaneity of chemical reactions.

In this context, using the Gibbs Free Energy formula, a marriage of enthalpy, entropy, and temperature, we can apply thermodynamic principles to predict the spontaneity of a chemical reaction. The formula acknowledges that both energy and entropy considerations must be balanced to determine the feasibility of a reaction under certain conditions.