Question

Ethene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) reacts with halogens \(\left(\mathrm{X}_{2}\right)\) by the following reaction: $$\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{X}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}(g)$$ The following figures represent the concentrations at equilibrium at the same temperature when \(\mathrm{X}_{2}\) is \(\mathrm{Cl}_{2}\) (green), \(\mathrm{Br}_{2}\) (brown), and \(\mathrm{I}_{2}\) (purple). List the equilibria from smallest to largest equilibrium constant. [Section 15.3\(]\)

Short answer

The order of equilibrium constants for the given reaction with different halogens is: Cl2 (green) < Br2 (brown) < I2 (purple). This order is determined by analyzing the graphical representations of concentrations at equilibrium, indicating the largest constant for I2 (purple) and the smallest constant for Cl2 (green).

Step-by-step solution

Step 1. Understanding the reaction and equilibrium constant

The given chemical reaction is an addition reaction between Ethene (C2H4) and a halogen (X2) to form C2H4X2. The reaction is reversible, which means it reaches equilibrium when the forward and reverse reactions are occurring at the same rate. The equilibrium constant (K) for this reaction can be represented as: \[ K = \frac{[C_{2}H_{4}X_{2}]}{[C_{2}H_{4}][X_{2}]}\] Where [C2H4X2] is the equilibrium concentration of the product and [C2H4] and [X2] are the equilibrium concentrations of the reactants. The larger the equilibrium constant, the more the reaction forms the product. In contrast, a smaller equilibrium constant means that the concentrations of reactants are higher at equilibrium.

Step 2. Analyze the graphical representation of equilibrium concentrations

The exercise provides us with figures showing the equilibrium concentrations of reactants and products for each halogen (Cl2, Br2, I2). The colors representing the halogens are: - Green: Cl2 - Brown: Br2 - Purple: I2 The figures show the relative concentrations of Ethene (C2H4), the halogens (X2), and the product (C2H4X2) at equilibrium. From the graphs, we can infer the equilibrium constants for each halogen reaction.

Step 3. Determine the order of equilibrium constants

Now, using the equilibrium constant formula and the information from the graphs: 1. For Cl2 (green), the graph has a relatively higher concentration of [C2H4] and [Cl2] compared to [C2H4Cl2]. This indicates a smaller K, as the reaction leans more towards the reactants. 2. For Br2 (brown), the graph shows a moderate concentration of [C2H4] and [Br2] and an increased concentration of [C2H4Br2]. So, the equilibrium constant K will be larger than for Cl2. 3. For I2 (purple), the graph has a very small concentration of [C2H4] and [I2] and much larger concentration of [C2H4I2]. The equilibrium constant K for I2 will be the largest among the three halogens. Based on the analysis, the order of equilibrium constants will be: Cl2 (green) < Br2 (brown) < I2 (purple)

Key concepts

Equilibrium Constant

The equilibrium constant, often denoted as \( K \), is a numerical value that describes the ratio of the concentrations of products to reactants at equilibrium for a given chemical reaction.
This concept comes into play when dealing with reversible reactions, which are reactions that can proceed both in the forward and reverse directions.

The equilibrium constant is significant because it gives insight into the extent of a reaction at equilibrium.

• A large \( K \) (much greater than 1) suggests that products are favored at equilibrium, indicating a larger concentration of reaction products.
• A small \( K \) (much less than 1) indicates that reactants are favored at equilibrium, meaning that the reaction barely progresses forward.

In this exercise, the equilibrium constant for each reaction between ethene and halogens can be calculated using:
\[ K = \frac{[C_{2}H_{4}X_{2}]}{[C_{2}H_{4}][X_{2}]} \]
This expression shows how the concentration of the product \([C_{2}H_{4}X_{2}]\) compares to the reactants \([C_{2}H_{4}]\) and \([X_{2}]\), providing meaningful insight into the system's behavior at equilibrium.

Reversible Reactions

Reversible reactions are reactions that do not go to complete conversion to products but instead reach a point where both reactants and products are present without further noticeable change in their concentrations.
This point is known as chemical equilibrium.

For the addition reaction of ethene with a halogen, the reversibility implies that the system can achieve equality in the rates of the forward and reverse reactions.
This balance of reaction rates ensures that the concentrations of reactants and products remain constant over time. The chemical equation for this reversible reaction is:
\[ \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{X}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}(g) \]
Here, ethene and the halogen can react to form a halogenated product but can also break back down to the original reactants.

• This indicates a dynamic equilibrium, where the transformations continue to occur yet the concentrations remain unchanged.
• Understanding reversible reactions is crucial for predicting how changes in conditions affect the system's equilibrium position, as described by Le Chatelier's Principle.

Addition Reaction

An addition reaction is a type of chemical reaction in which two or more reactants combine to form a single new product.
In the case of ethene reacting with halogens, an addition reaction occurs because the ethene molecule adds the halogen across its carbon-carbon double bond.

The formula for this specific type of reaction is:
\[ \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{X}_{2}(g) \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}(g) \]
Here the double bond in ethene opens up, allowing the halogen atoms to attach to each carbon atom.
This process leads to the formation of a dihalogenated alkane.

• Addition reactions are crucial in organic chemistry for synthesizing complex molecules from simpler ones.
• They are typically characterized by the disappearance of a double bond, which is replaced by single bonds to new substituents.

Understanding how addition reactions work is essential for predicting the products of reactions involving alkenes and other unsaturated compounds.

Halogens

Halogens are a group of non-metal elements found in Group 17 of the periodic table.
They include fluorine, chlorine, bromine, iodine, and astatine, each characterized by their high reactivity, especially with alkenes such as ethene.

The role of halogens in the context of this exercise emphasizes their ability to participate in addition reactions, where they add across the double bonds of alkenes.
This can be illustrated in the general reaction:
\[ \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{X}_{2}(g) \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}(g) \]
Chlorine, bromine, and iodine are the halogens involved in the exercise. Their varying reactivity influences the equilibrium constant for each reaction with ethene.

• Chlorine (\( \mathrm{Cl}_{2} \)) is highly reactive, influencing the equilibrium proportions of reactants and products.
• Bromine (\( \mathrm{Br}_{2} \)), while less reactive than chlorine, still participates readily in addition reactions.
• Iodine (\( \mathrm{I}_{2} \)), being the least reactive, tends to form the most product at equilibrium.

The understanding of how halogens interact with alkenes helps in predicting product distribution and reaction conditions appropriate for each halogen.