Question

Use the balanced equation for the combustion of ethane to complete the table. \begin{tabular}{|l|l|l|l|l|} \hline \multicolumn{5}{|c|}{\(2 \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})+7 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)} \\ \hline Initially mixed & \(0.260 \mathrm{~g}\) & \(1.00 \mathrm{~g}\) & \(0.00 \mathrm{~g}\) & \(0.00 \mathrm{~g}\) \\ \hline How much reacts & & & \(-\) & \(-\) \\ \hline Composition of final mixture & & & & \\ \hline \end{tabular}

Short answer

The amounts that react are \(0.260 g\) of \(C_2H_6\) and \(0.96656 g\) of \(O_2\). The final composition of the mixture is \(0.03344 g\) of \(O_2\), \(0.68636 g\) of \(CO_2\), and \(0.46318 g\) of \(H_2O\).

Step-by-step solution

Figure out the amount of moles for each reactant

First, convert the given grams of each reactant to moles. The molar mass of \(C_2H_6\) is roughly 30.07 g/mol and for \(O_2\) it's 32.00 g/mol. Thus, there are \((0.260 g)/(30.07 g/mol) = 0.00863 mol\) of \(C_2H_6\) and \((1.00 g)/(32.00 g/mol) = 0.03125 mol\) of \(O_2\).

Calculate the limiting reactant

Next, determine the limiting reactant. This is done by comparing the ratio of the moles of the reactants with the stoichiometric coefficients in the balanced equation. The ratio for \(C_2H_6\) is \(0.00863/2 = 0.004315\) and for \(O_2\) it's \(0.03125/7 = 0.004464\). Since the ratio for \(C_2H_6\) is smaller, \(C_2H_6\) is the limiting reactant. This means that \(0.260 g\) of \(C_2H_6\) reacts.

Compute the amount of \(O_2\)

Using stoichiometry, calculate the amount of \(O_2\) that reacts with \(C_2H_6\). For every 2 moles of \(C_2H_6\), 7 moles of \(O_2\) are required. Therefore, \(0.00863 * (7/2) = 0.030205 mol\) or \(0.96656 g\) of \(O_2\) reacts.

Determine the composition of final mixture

Understand that is left of the reactants and formed from the products. After the reaction, \(1.00 g - 0.96656 g = 0.03344 g\) of \(O_2\) is left. From the products, for every 2 moles of \(C_2H_6\) that reacts, 4 moles of \(CO_2\) and 6 moles of \(H_2O\) are produced. Therefore, \(0.00863 mol *2 = 0.01726 mol\) or \(0.68636 g\) of \(CO_2\) and \(0.00863 mol * 3 = 0.02589 mol\) or \(0.46318 g\) of \(H_2O\) are produced.

Key concepts

Limiting Reactants

In a chemical reaction, a limiting reactant is the substance that is completely consumed first and thereby limits the amount of product that can be formed. Imagine you're baking cookies and you run out of sugar - even if you have more than enough of other ingredients, you can't make more cookies. A similar concept applies to chemical reactions. The limiting reactant dictates how much product can be formed because the reaction cannot proceed once it is entirely used up.

To identify a limiting reactant, follow these steps:

• First, find the moles of each reactant by using their given mass and molar mass.
• Then, compare the mole ratios of the reactants to their coefficients in the balanced chemical equation.
• The reactant that has the smaller ratio is the limiting reactant.

It is crucial to identify the limiting reactant to accurately predict how much product will form, as any excess reactant will be left unreacted.

Mole Calculations

Moles are a measurement unit that allows chemists to count particles, like atoms or molecules, in a given mass of a substance. It's akin to a dozen representing 12 items and is fundamental in stoichiometry, which helps calculate the quantities of reactants and products in a chemical reaction.

To perform mole calculations effectively,:

• Use the molar mass of each substance, usually found on the periodic table, which tells you the mass of a mole of a substance in grams.
• Convert between mass and moles using the equation: \[moles = \frac{mass (g)}{molar\ mass (g/mol)}\]
• This conversion is crucial to relate the quantities of different substances participating in a reaction based on the balanced chemical equation.

By understanding how to calculate moles, you can efficiently determine the proportions of substances required for a reaction and those produced.

Combustion Reactions

Combustion reactions are a type of chemical reaction where a substance combines with oxygen and releases energy. This usually results in the production of hot gases, light, or heat, and is a crucial process in engines and power generation.

Key characteristics of combustion reactions include:

• They typically involve a hydrocarbon reacting with oxygen to produce carbon dioxide and water.
• They are exothermic, meaning they release energy.
• They are used in everyday life, such as burning fuels in vehicles or heating homes.

In the combustion of ethane (\(\text{C}_2\text{H}_6\)), it reacts with oxygen (\(\text{O}_2\)) to produce carbon dioxide (\(\text{CO}_2\)) and water (\(\text{H}_2\text{O}\)). Understanding the proportions and reactants involved in this reaction is essential for predicting the outcome, ensuring efficiency, and minimizing waste.