Problem 53 - A Complete Resource Book in Chemistry for JEE Main

Question

Standard state Gibbs free energy change for isomerization reaction, cis-2-pentene \rightleftharpoons- trans-2-pentene is \(-3.67 \mathrm{~kJ} / \mathrm{mol}\) at \(400 \mathrm{~K}\). if more trans-2-pentene is added to the reaction vessel, then (a) more cis-2-pentene is formed (b) additional trans-2-pentene is formed (c) equilibrium remains unaffected (d) equilibrium is shifted in the forward direction

Step-by-Step Solution

Answer

(a) More cis-2-pentene is formed.

Step 1: Understand the Reaction

The reaction given is cis-2-pentene \(\rightleftharpoons\) trans-2-pentene. This indicates an isomerization process where the cis form converts to the trans form and vice versa.

Step 2: Analyze Gibbs Free Energy

The standard Gibbs free energy change for the reaction is given as \(-3.67\, \mathrm{kJ/mol}\) at \(400\, \mathrm{K}\). A negative \(\Delta G^0\) implies that the trans-2-pentene is more stable than cis-2-pentene under standard conditons, making the forward reaction (cis to trans) favorable.

Step 3: Apply Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is disturbed, the system will adjust to minimize the disturbance. Adding more trans-2-pentene disturbs the equilibrium by increasing its concentration.

Step 4: Predict Direction of Shift

When trans-2-pentene is added, the equilibrium will shift towards the reactant (left) to decrease the concentration of trans- and increase the concentration of cis-2-pentene. More cis-2-pentene will be formed until a new equilibrium is reached.

Key Concepts

Isomerization Reactions

Isomerization reactions involve the transformation of a molecule into one of its isomers. An isomer is a molecule that has the same molecular formula as another molecule but a different arrangement of atoms. In the exercise, we examine the isomerization between cis-2-pentene and trans-2-pentene.
In cis-trans isomerism, the two isomers differ in the relative positioning of their atoms. Specifically, cis-2-pentene and trans-2-pentene have different spatial arrangements around the double bond in the pentene chain. The cis form has similar groups on the same side of the double bond, whereas the trans form has them on opposite sides. This distinct arrangement affects the stability and properties of the isomers.
Factors like temperature and pressure can influence isomerization reactions. In our case, the Gibbs free energy alters the direction and favorability of the reaction. Understanding the stability of different isomers helps predict how the reaction will proceed.

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemical equilibrium. It states that if a system at equilibrium experiences a change in concentration, temperature, or pressure, the equilibrium will shift to counteract the imposed change.
For the isomerization reaction between cis-2-pentene and trans-2-pentene, adding more trans-2-pentene increases its concentration in the system. According to Le Chatelier's Principle, the system tries to reduce this disturbance by shifting the equilibrium position to the left.
This shift means more cis-2-pentene is formed to restore balance. The principle is a powerful tool for predicting how reactions will respond to external stresses and is widely applied in both chemical engineering and everyday scenarios.

Chemical Equilibrium

Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the backward reaction. At this point, the concentrations of reactants and products remain constant.
In the isomerization reaction provided, equilibrium is reached when the conversion rates from cis- to trans-2-pentene and vice versa are equal. However, the introduction of additional trans-2-pentene disrupts this balance.
The system adapts by shifting the equilibrium to favor the reverse reaction, allowing more cis-2-pentene to form. This shift continues until the new equilibrium establishes a balance of concentrations. Understanding chemical equilibrium involves recognizing that it is dynamic, not static, with continuous reactions occurring at the molecular level.