Problem 29 - Chemistry in 30 days

Question

The standard state Gibb's free energy change for the i. cis-2-pentene = 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 (a) more cis-2-pentene is formed (b) equilibrium shifts in the forward direction (c) equilibrium remains unaltered (d) more trans-2-pentene is produced

Step-by-Step Solution

Answer

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

Step 1: Identify the Reaction Direction

The given standard Gibbs free energy change for the reaction \( \text{cis-2-pentene} \rightarrow \text{trans-2-pentene} \) is \( \Delta G^\circ = -3.67 \text{ kJ/mol} \). Since \( \Delta G^\circ \) is negative, this indicates that at standard conditions, the reaction favors the formation of trans-2-pentene (forward direction).

Step 2: Apply Le Chatelier's Principle

According to Le Chatelier's Principle, if more trans-2-pentene is added to the system at equilibrium, the system will shift to counteract this change, which means the equilibrium will shift towards the reverse reaction, forming more cis-2-pentene.

Step 3: Determine the Correct Option

Given that adding more trans-2-pentene will shift the equilibrium towards the formation of cis-2-pentene, option (a) more cis-2-pentene is formed, is the correct choice.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that explains how a system at equilibrium responds to changes in concentration, temperature, or pressure. This principle helps us predict the direction in which a reaction will shift to restore equilibrium.

When a change occurs in a system at equilibrium, such as adding more reactants or products:

• The system will shift in the direction that opposes this change.
• If more products are added, the equilibrium will shift towards the reactants.
• If more reactants are added, the equilibrium will shift towards the products.

In the context of the cis-2-pentene and trans-2-pentene reaction, adding more trans-2-pentene causes the system to shift to the left, producing more cis-2-pentene.

Reaction Equilibrium

Reaction equilibrium refers to the state where the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant over time.

In a chemical equation like cis-2-pentene \( \leftrightarrow \) trans-2-pentene:

• The reaction has reached equilibrium when the amounts of cis-2-pentene and trans-2-pentene stay steady.
• No further net change in concentrations will occur unless the system is disturbed.

Understanding reaction equilibrium is crucial for predicting the behavior of a system under different conditions, especially in combination with principles like Le Chatelier's.

Thermodynamics

Thermodynamics is the study of energy and its transformations. In the realm of chemical reactions, it explores concepts like Gibbs free energy, enthalpy, and entropy.

Gibbs Free Energy
Gibbs free energy \( (\Delta G) \) is used to determine the spontaneity of a reaction:

• If \( \Delta G \) is negative, the reaction is spontaneous under the given conditions.
• If \( \Delta G \) is positive, the reaction is non-spontaneous.

In the provided example, a negative standard Gibbs free energy change \( (\Delta G^\circ = -3.67 \text{ kJ/mol}) \) indicates that the formation of trans-2-pentene is spontaneous.

Standard State Conditions

Standard state conditions are a set of established conventions in thermodynamics to provide a reference point for measuring properties of substances.

Under standard state conditions:

• The pressure is typically \( 1 \text{ atm} \).
• The temperature is usually \( 298.15 \text{ K} \) (or \( 25 ^\circ \text{C} \)).
• Solutions are at a concentration of \( 1 \text{ M} \).

Using standard state conditions, chemists can calculate properties like Gibbs free energy and determine how reactions will behave under typical laboratory settings. In our example, knowing the standard state Gibbs free energy helps us understand the reaction tendency when the temperature deviates to \( 400 \text{ K} \).