Question

Consider the combustion of butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\) $$ 2 \mathrm{C}_{4} \mathrm{H}_{10}(g)+13 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(l) $$ In a particular reaction, \(5.0 \mathrm{~mol}\) of \(\mathrm{C}_{4} \mathrm{H}_{10}\) react with an excess of \(\mathrm{O}_{2}\). Calculate the number of moles of \(\mathrm{CO}_{2}\) formed.

Short answer

20 moles of CO2 are formed.

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation for the combustion of butane is: \[ 2 \mathrm{C}_{4} \mathrm{H}_{10}(g) + 13 \mathrm{O}_{2}(g) \rightarrow 8 \mathrm{CO}_{2}(g) + 10 \mathrm{H}_{2} \mathrm{O}(l) \] This indicates the stoichiometry of the reaction.

Determine the stoichiometric ratio

From the balanced equation, notice the stoichiometric ratio between \( \mathrm{C}_{4} \mathrm{H}_{10} \) and \( \mathrm{CO}_{2} \) is 2:8, or equivalently 1:4. This means 1 mole of butane will produce 4 moles of carbon dioxide.

Calculate the moles of CO2 produced

Since we have 5.0 moles of \( \mathrm{C}_{4} \mathrm{H}_{10} \) and an excess of \( \mathrm{O}_{2} \), based on the stoichiometric ratio (1:4), \[ 5.0 \text{ moles of } \mathrm{C}_{4} \mathrm{H}_{10} \times \frac{8 \text{ moles of } \mathrm{CO}_{2}}{2 \text{ moles of } \mathrm{C}_{4} \mathrm{H}_{10}} = 20 \text{ moles of } \mathrm{CO}_{2} \]

Key concepts

Combustion Reaction

A combustion reaction is a chemical reaction in which a substance combines with oxygen to produce heat and light. Commonly, it involves organic compounds such as hydrocarbons. In the combustion of butane, \[2 \mathrm{C}_{4} \mathrm{H}_{10}(g) + 13 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g) + 10 \mathrm{H}_{2} \mathrm{O}(l)\], butane acts as the fuel that burns in the presence of oxygen to yield carbon dioxide, water, and energy. Combustion reactions release energy because new bonds are stronger than the ones broken in the process.
This reaction type is critical in everyday applications like running car engines and heating homes.

Chemical Equation

A chemical equation represents a chemical reaction where reactants transform into products. It is a symbolic way of denoting the process. For example, in the combustion of butane, the chemical equation is: \[2 \mathrm{C}_{4} \mathrm{H}_{10}(g) + 13 \mathrm{O}_{2}(g) \rightarrow 8 \mathrm{CO}_{2}(g) + 10 \mathrm{H}_{2} \mathrm{O}(l)\].
This balanced equation shows the precise number of molecules involved in the reaction, maintaining the conservation of mass, meaning atoms are neither created nor destroyed.

• Each type of atom appears on both sides in equal quantities.
• It gives insight into the ratio of reactants and products needed and formed.

Balanced chemical equations are essential for accurate stoichiometry calculations.

Mole Calculation

Mole calculation is a fundamental concept in chemistry that helps relate quantities in a chemical reaction. Using the balanced chemical equation, we can determine amounts of substances involved. In our butane combustion equation:
The stoichiometric ratio is given as 2 moles of butane to 8 moles of carbon dioxide. We can simplify this to 1 mole of butane producing 4 moles of carbon dioxide. Therefore, if 5.0 moles of butane are used, we can calculate the moles of carbon dioxide formed by multiplying:
\[5.0 \text{ moles of } \mathrm{C}_{4} \mathrm{H}_{10} \times \frac{8 \text{ moles of } \mathrm{CO}_{2}}{2 \text{ moles of } \mathrm{C}_{4} \mathrm{H}_{10}} = 20 \text{ moles of } \mathrm{CO}_{2}\]
Mole calculations allow chemists to predict product quantities based on reactant amounts.

Excess Reactant

In chemical reactions, an excess reactant is a substance that remains after the reaction is complete. It is present in a higher amount than needed according to the stoichiometry of the equation. In the combustion reaction of butane, oxygen is used in excess to ensure all of the butane combusts.
Understanding excess reactants is important because:

• It ensures the complete use of the limiting reactant, which is the substance that determines when the reaction stops once it's entirely consumed.
• Excess reactants don't limit product formation and can be beneficial in maximizing yield.

When calculating other reactants or products, knowing which reactant is in excess avoids errors in the expected outcomes of a reaction.