Question

Use the balanced equation for the combustion of butane to complete the table. \begin{tabular}{|l|c|c|c|c|} \hline \multicolumn{5}{|c|}{\(2 \mathrm{C}_{4} \mathrm{H}_{1 u}(g)+13 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)\)} \\ \hline Initially mixed & \(0.500\) \(\mathrm{~mol}\) & \(3.50\) \(\mathrm{~mol}\) & \(0.00\) \(\mathrm{~mol}\) & \(0.00\) \(\mathrm{~mol}\) \\ \hline How much reacts & & & \(-\) & \(-\) \\ \hline Composition of final mixture & & & & \\ \hline \end{tabular}

Short answer

In the given reaction, all 3.50 moles of oxygen react with 0.269 moles of butane. The final composition of the mixture is 0.231 moles of butane, 2.15 moles of carbon dioxide, and 2.69 moles of water.

Step-by-step solution

Identify the Limiting Reactant

First, the limiting reactant is determined. This is the reactant that gets used up first, thus it will determine how much of the products can be formed. The balanced equation tells us that the molar ratio of butane to oxygen should be 2:13. So, for every mole of butane, we should have 6.5 moles of oxygen. Given that we start with 0.5 moles of butane and 3.50 moles of oxygen, it's clear that we have more than enough butane (since 0.5*6.5 = 3.25), but insufficient oxygen. Therefore, oxygen is the limiting reactant.

Calculate How Much Reacts

Since oxygen is the limiting factor, all the oxygen will react. From the balanced chemical equation, we can see that 2 moles of butane react with 13 moles of oxygen, so we can calculate how much butane reacts with 3.5 moles of oxygen. This is done by using the ratios from the balanced equation, giving \(0.5 \times 2/13 = 0.269\) moles of butane that reacts.

Determine the Final Composition

So, all 3.50 moles of oxygen react, using up 0.269 moles of butane. That leaves \(0.5 - 0.269 = 0.231\) moles of butane unreacted. Also, for each mole of oxygen that reacted, 8/13 moles of carbon dioxide and 10/13 moles of water are produced. Thus, we have \(3.50 \times 8/13 = 2.15\) moles of carbon dioxide and \(3.50 \times 10/13 = 2.69\) moles of water.

Key concepts

Chemical Reactions

Chemical reactions are processes where substances, called reactants, transform into different substances, known as products. This transformation involves the breaking and forming of chemical bonds. Understanding chemical reactions is key to grasping chemical principles.

In a balanced chemical reaction, such as the combustion of butane, represented by \[2 ext{C}_4 ext{H}_{10(g)} + 13 ext{O}_{2(g)} \rightarrow 8 ext{CO}_{2(g)} + 10 ext{H}_2 ext{O}_{(g)},\]we see that butane (\( ext{C}_4 ext{H}_{10}\)) reacts with oxygen (\( ext{O}_2\)) to produce carbon dioxide (\( ext{CO}_2\)) and water (\( ext{H}_2 ext{O}\)).

• The reactants, butane and oxygen, are consumed during the reaction.
• New products, carbon dioxide and water, are formed.
• The balanced equation ensures that the number of atoms for each element is the same on both sides.

By balancing the equation, we ensure the conservation of mass, which is fundamental in chemical reactions.

Molar Ratio

Molar ratios are essential for understanding how much of each reactant and product is involved in a chemical reaction. These ratios come directly from the coefficients in a balanced chemical equation. In our butane combustion reaction example, the molar ratio between butane and oxygen is 2:13, meaning:

• For every 2 moles of butane, 13 moles of oxygen are required.

Using molar ratios, we can determine the limiting reactant, which is the substance that runs out first and thus limits the reaction's progress. Knowing the limiting reactant is key to calculating the amount of products formed.

Here's how it works in practice:

• Start with the given initial amounts: 0.5 moles of butane and 3.5 moles of oxygen.
• Calculate needed proportions: 0.5 moles of butane would ideally react with 3.25 moles of oxygen (by multiplying 0.5 by the molar ratio \(13/2\)).
• Since we have 3.5 moles of oxygen available, a bit more than needed, oxygen becomes the limiting reactant.

Understanding these ratios helps predict and calculate amounts in complex chemical processes.

Combustion Reaction

A combustion reaction is a type of chemical reaction where a substance combines with oxygen and releases energy. Combustion reactions are essential because they release energy that is harnessed in many industrial and everyday applications.

The butane combustion reaction is typical and involves hydrocarbons. When hydrocarbons like butane (\( ext{C}_4 ext{H}_{10}\)) combust, they usually produce carbon dioxide and water, along with energy:

• The general formula is: \( ext{Hydrocarbon} + ext{O}_2 \rightarrow ext{CO}_2 + ext{H}_2 ext{O}\)
• These reactions are exothermic, meaning they release heat.

By understanding combustion reactions, we see how energy is generated from fuel and why careful control is important to minimize pollutants like carbon dioxide, which contribute to environmental issues.