Question

The equation for the combustion of ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) is $$ 2 \mathrm{C}_{2} \mathrm{H}_{6}+7 \mathrm{O}_{2} \longrightarrow 4 \mathrm{CO}_{2}+6 \mathrm{H}_{2} \mathrm{O} $$ Explain why it is unlikely that this equation also represents the elementary step for the reaction.

Short answer

This equation is unlikely to represent an elementary step due to the improbability of nine reactant molecules colliding simultaneously to form the product molecules.

Step-by-step solution

Understand the Reaction

Firstly, you need to understand the given reaction. Ethane (\(C_{2}H_{6}\)) is combusted with oxygen (\(O_{2}\)) to produce carbon dioxide (\(CO_{2}\)) and water (\(H_{2}O\)). As per the reaction, 2 molecules of ethane and 7 molecules of oxygen are combining to get 4 molecules of carbon dioxide and 6 molecules of water.

Identify the number of molecules taking part in the reaction

Next, identify the total number of molecules involved in the reaction. Here, a total of 9 molecules (2 ethane and 7 oxygen) are combining to give 10 molecules (4 carbon dioxide and 6 water).

Analyze the likelihood of this being an elementary step

An elementary reaction involves a single molecular event happening, i.e., the reactant molecules colliding and immediately forming the product molecules. Since in our case there needs to be collision between 9 molecules simultaneously, it is statistically improbable. Hence, it is unlikely that this equation also represents the elementary step for the reaction.

Key concepts

Elementary Reaction

In chemistry, an elementary reaction is a basic step where reactants are directly converted into products in a single collision event. Such reactions happen without any intermediate steps or stages. This is like a single action or move that transforms the reactants into the desired products immediately. Elementary reactions are known for:

• Having only one transition state or energetic hurdle to overcome.
• Involving either one molecule breaking up, or two molecules colliding to form products.

Moreover, they are generally simple and involve simple equations. In the context of our given problem, the combustion of ethane involves many molecules reacting together. This requires a simultaneous collision of all these molecules. The chances of so many molecules colliding at the same exact place and time are extremely slim, making it unlikely for the reaction to be elementary in nature. Such large-scale coordination is typical in multi-step reactions, not elementary ones.

Chemical Equation

A chemical equation represents a chemical reaction where the reactants and products are expressed in terms of their chemical formulas. It showcases how the atoms of each element are conserved in a reaction. An important feature of such equations is that they obey the law of conservation of mass, meaning that the number of atoms for each element involved must be equal on both sides of the equation. For instance, in our ethane combustion equation:\[2 \mathrm{C}_{2} \mathrm{H}_{6} + 7 \mathrm{O}_{2} \rightarrow 4 \mathrm{CO}_{2} + 6 \mathrm{H}_{2} \mathrm{O}\]

• Reactants include 2 molecules of ethane and 7 molecules of oxygen.
• Products formed are 4 molecules of carbon dioxide and 6 molecules of water.

Each side of the equation holds an equal number of each type of atom, illustrating their mass conservation principle. Additionally, while this equation provides a complete picture of what enters and exits the reaction, it does not illustrate how the reaction occurs, i.e., it doesn’t describe the individual steps or mechanisms involved. Thus, it is different from the notion of an elementary reaction.

Reaction Mechanism

A reaction mechanism is a detailed step-by-step description of how a reaction occurs at the molecular level. It delineates the path from reactants to products, including all the intermediate stages and molecular interactions. These mechanisms are an integral part of understanding chemical reactions, particularly for complex transformations. The combustion reaction in question is an example of such complexity. Reasons a reaction mechanism is significant include:

• Revealing all the intermediate stages through which the reactants pass to become products.
• Helping to elucidate the rate-determining step—the slowest step governing the overall reaction rate.
• Allowing chemists to predict and control the outcomes of reactions more effectively.

For the ethane combustion, a simple combustion equation does not show these intermediary steps or how the necessary energy thresholds are surpassed. The real-life mechanism would involve multiple stages with temporary intermediates, completely aligning with the improbable scenario of involving several molecules in a singular direct clash.