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

Short answer

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

Step-by-step solution

Understand the Reaction

The reaction given is an isomerization reaction between cis-2-pentene and trans-2-pentene. The standard Gibbs free energy change, \( \Delta G^{\circ} \), is \(-3.67 \, \text{kJ/mol}\), which indicates that the reaction is spontaneous under standard conditions towards the formation of trans-2-pentene.

Analyze Le Châtelier's Principle

Le Châtelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will shift to counteract the change. Adding more trans-2-pentene to the system will initially increase its concentration.

Predict the Equilibrium Shift

According to Le Châtelier's principle, increasing the concentration of trans-2-pentene will shift the equilibrium to the left to reduce the concentration of the trans-2-pentene. This means more cis-2-pentene will be formed in response to the addition.

Conclusion

Based on the above analysis, the system will respond to the added trans-2-pentene by producing more cis-2-pentene, shifting the equilibrium towards the formation of cis-2-pentene.

Key concepts

Isomerization Reaction

An isomerization reaction involves the conversion of one isomer into another. In this exercise, the focus is on the isomerization of cis-2-pentene to trans-2-pentene, two isomers of pentene. Isomers are molecules that have the same molecular formula but different structural arrangements. This reaction keeps the molecular makeup the same, but changes how the atoms are connected or oriented in space.
In these reactions, the transformation happens without breaking major chemical bonds, except for those dictating the spatial arrangement of the atoms. The isomerization from cis to trans (or vice versa) often affects physical properties like boiling point and stability. In our case, this process is spontaneous under standard conditions, tending to produce more of the trans isomer due to its lower energy state.

Le Châtelier's Principle

Le Châtelier's Principle is a fundamental concept in chemistry that helps predict the behavior of a reaction upon a disturbance. It asserts that if a dynamic equilibrium is disturbed by changing conditions such as concentration, pressure, or temperature, the system will adjust itself to counteract the effect of the disturbance.
This principle is crucial in determining how the system will behave when conditions change. For instance, in the isomerization of cis-2-pentene and trans-2-pentene, if the concentration of trans-2-pentene is increased by adding more to the reaction vessel, the system will try to minimize this increase. It will shift the equilibrium towards the formation of more cis-2-pentene, in order to restore balance.

Equilibrium Shift

An equilibrium shift refers to the movement of a reaction system's balance point in response to changes in conditions. This can occur due to adjustments in concentration, temperature, or pressure, in accordance with Le Châtelier's Principle. The equilibrium can shift in the forward direction (towards more products) or the reverse direction (towards more reactants).
In the context of the isomerization reaction between cis- and trans-2-pentene, adding more trans-2-pentene causes a shift in equilibrium. This shift occurs because the system reacts to the increase in trans-2-pentene by favoring the production of more cis-2-pentene. As a result, the position of equilibrium moves to the left, increasing the concentration of the less initially abundant cis-2-pentene.

Standard State Conditions

Standard state conditions serve as a reference point for scientists, ensuring that measurements are consistent and comparable. These conditions typically involve a pressure of 1 bar, a temperature of 298 K, and each substance at a concentration of 1 M. However, it's important to note that in our exercise, the temperature is specified as 400 K rather than the usual 298 K.
Gibbs free energy changes, such as the \( \Delta G^{\circ} \) given for the reaction, are calculated under these standard conditions. They are essential for understanding the spontaneity and direction of a reaction. A negative Gibbs free energy change, as observed here at 400 K, suggests that the isomerization from cis-2-pentene to trans-2-pentene is spontaneous under these conditions.