Problem 11 - Basic Principles of Organic Chemistry

Question

Knowing that the equilibrium constant \(K_{\text {eq for formation of nonane from solid carbon and hydrogen gas is }}\) \(4.7 \times 10^{-5}\), explain why liquid nonane does not forthwith decompose into its elements.

Step-by-Step Solution

Answer

The small equilibrium constant favors the reactants, indicating nonane is stable and does not decompose easily.

Step 1: Understand the Equation

To solve this problem, let us first understand the equilibrium reaction for the formation of nonane from carbon and hydrogen. The reaction can be written as: \[9C(s) + 9H_2(g) \rightleftharpoons C_9H_{20}(l)\]Here, carbon and hydrogen are reacting to form liquid nonane. The equilibrium constant \( K_{\text{eq}} \) is \(4.7 \times 10^{-5}\).

Step 2: Interpret the Equilibrium Constant

The given equilibrium constant \( K_{\text{eq}} = 4.7 \times 10^{-5} \) is a measure of the ratio of the concentrations (or activities) of the products to the reactants at equilibrium. A small value of \( K_{\text{eq}} \) indicates that at equilibrium, the concentration of the reactants (carbon and hydrogen) is much higher than that of the products (nonane).

Step 3: Analyze Stability of Nonane

Since \( K_{\text{eq}} \) is very small, this implies that the equilibrium position favors the reactants—the solid carbon and hydrogen gas—over the product, liquid nonane. This means nonane is not thermodynamically favored to form significantly at equilibrium under standard conditions and is relatively stable against decomposition back into carbon and hydrogen.

Key Concepts

Equilibrium Constant

In the realm of chemistry, the equilibrium constant, denoted as \( K_{\text{eq}} \), plays a fundamental role in understanding chemical reactions and their tendencies. When a system reaches chemical equilibrium, the rates of the forward and reverse reactions are equal. This state is described using the equilibrium constant, which is calculated using the concentrations or activities of the reactants and products. For a general reaction: \[ aA + bB \rightleftharpoons cC + dD \] the equilibrium constant is given by: \[ K_{\text{eq}} = \frac{[C]^c[D]^d}{[A]^a[B]^b} \] A key aspect of \( K_{\text{eq}} \) is that it provides insight into the direction of the reaction. A large \( K_{\text{eq}} \) value means that products are favored at equilibrium, whereas a small value indicates that reactants are favored. In the case of the formation of nonane from carbon and hydrogen, the small \( K_{\text{eq}} \) (i.e., \( 4.7 \times 10^{-5} \)) reveals that at equilibrium, only a small amount of nonane forms because the reactants—carbon and hydrogen—are much more prevalent.

Thermodynamic Stability

Thermodynamic stability refers to the tendency of a substance to remain in its current state without spontaneously undergoing a chemical reaction to change into another state. The concept is closely linked to the equilibrium constant. A small value of \( K_{\text{eq}} \) for the formation reaction of nonane suggests that nonane is less favored to form under standard conditions, meaning it remains stable against decomposition back to carbon and hydrogen.The stability of a substance can also be inferred from Gibbs free energy (abla Gdot H-TSdot S G denoted as \( \Delta G \), which helps determine whether a reaction is spontaneous or not. If \( \Delta G \) is negative, the formation of products is spontaneous. However, a small, positive, or slightly negative \( \Delta G \) would imply that the reaction to form or decompose the substance is not significantly favored. Thus, nonane remains largely stable and does not readily decompose into its elemental forms.

Formation Reaction

A formation reaction is a specific type of chemical reaction where one mole of a compound is formed from its elements in their standard states. For the formation of nonane, the reaction involves reacting carbon in the solid state and hydrogen in the gaseous state to produce liquid nonane:\[ 9C(s) + 9H_2(g) \rightleftharpoons C_9H_{20}(l) \] Formation reactions are crucial for defining substances' thermodynamic properties, such as enthalpy and entropy changes. These reactions underpin many calculations in chemistry, helping chemists determine how a compound behaves under different conditions.During the formation reaction of nonane, the small equilibrium constant indicates that the reaction does not proceed significantly in the forward direction, meaning that the reaction reaches equilibrium with predominantly reactants present. Understanding formation reactions enables chemists and students to predict how compounds form and behave, providing insights into the energy changes involved and making sense of experimental observations.