Question

Use the balanced equation for the combustion of ethane to complete the table. \begin{tabular}{|l|c|c|c|c|} \hline \multicolumn{5}{|c|}{\(2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)} \\ \hline Initially mixed & 6 molecules & 18 molecules & 0 molecules & 0 molecules \\ \hline How much reacts & & & \(-\) & \(-\) \\ \hline Composition of final mixture & & & & \\ \hline \end{tabular}

Short answer

The amount that reacts is 6 molecules of ethane (C2H6), and 18 molecules of oxygen (O2). The composition of the final mixture is 12 molecules of carbon dioxide (CO2) and 18 molecules of water (H2O).

Step-by-step solution

Identify Reactants and Products

From the given balanced equation, ethane (C2H6) and oxygen (O2) are the reactants, while carbon dioxide (CO2) and water (H2O) are the products.

Determine the Amount of Reacted Molecules

Using the stoichiometric coefficients, for every 2 molecules of ethane, 7 molecules of oxygen react to yield 4 molecules of carbon dioxide and 6 molecules of water. Given that we initially mixed 6 molecules of C2H6 and 18 molecules of O2, we have 3 sets of reactions according to he stoichiometric ratios. Therefore, all given quantities of reactants will be completely converted into products.

Determine the Composition of the Final Mixture

Since all the reactants are completely converted into products, the final mixture will have 12 molecules of CO2 and 18 molecules of H2O resulting from the 6 molecules of C2H6 and 18 molecules of O2 initially mixed.

Key concepts

Stoichiometric Coefficients

Stoichiometric coefficients are numbers that appear in front of molecules in a chemical equation. Their main job is to ensure that the same number of atoms of each element is present on both sides of the equation. In a combustion reaction like burning ethane, these coefficients help us understand how many molecules of each substance react and are formed.
To see how this works, look at the balanced equation: \[2 \mathrm{C}_{2}\mathrm{H}_{6}(g) + 7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g) + 6 \mathrm{H}_{2}\mathrm{O}(g)\]

• The coefficient '2' before \(\mathrm{C}_{2}\mathrm{H}_{6}\) means that 2 molecules of ethane are needed.
• The '7' before \(\mathrm{O}_{2}\) indicates 7 molecules of oxygen gas are required.
• On the product side, '4' shows 4 molecules of carbon dioxide are produced.
• '6' means the reaction produces 6 molecules of water.

Understanding these numbers helps you calculate how much of each substance you'd need and how much you'd get in a reaction.

Reactants and Products

In a chemical reaction, reactants are the starting substances that undergo change, while products are the new substances formed. In our ethane combustion example:
- **Ethane (\(\mathrm{C}_{2}\mathrm{H}_{6}\))** and **Oxygen (\(\mathrm{O}_{2}\))** are the reactants. These are the substances you start with, and they will be transformed in the reaction.
- The **Products** are the results of the chemical reaction. In this case, they are **Carbon Dioxide (\(\mathrm{CO}_{2}\))** and **Water (\(\mathrm{H}_{2}\mathrm{O}\))**. These substances are generated after the reactants undergo a transformation.
Reactants and products are crucial to study because they give insights into the chemical processes and how elements and compounds interact. By knowing the reactants and products, you can determine the amount of energy released (using a concept called enthalpy), as well as calculate how much of each product is made from a given amount of reactants.

Balanced Chemical Equation

A balanced chemical equation accurately represents the conservation of mass during a chemical reaction. In simple terms, it ensures that the number of each type of atom is the same before and after the reaction. For instance, the balanced equation \[2 \mathrm{C}_{2} \mathrm{H}_{6}(g) + 7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g) + 6 \mathrm{H}_{2} \mathrm{O}(g)\]is an example of such a balance. It ensures that the same number of carbon, hydrogen, and oxygen atoms we started with are present in the products.
To check if an equation is balanced:

• Count the number of atoms of each element on both sides.
• Make sure each type of atom has the same count on both reactant and product sides.
• If not, adjust the coefficients accordingly until the equation balances.

The balancing process sometimes might require iterations. However, once balanced, the equation will give you the exact proportions in which reactants react and products form, making it a reliable guide for predicting the outcome of a chemical reaction.