Question

Calculate the volume of oxygen necessary to burn completely 1000 cubic feet of butane gas according to the equation \(2 \mathrm{C}_{4} \mathrm{H}_{10}+13 \mathrm{O}_{2} \rightarrow 8 \mathrm{CO}_{2}+10 \mathrm{H}_{2} \mathrm{O}\)

Short answer

The volume of oxygen required to completely burn 1000 cubic feet of butane gas is 6500 cubic feet, according to the stoichiometry and the Law of Combining Volumes.

Step-by-step solution

Interpret the balanced chemical equation

The balanced equation for the combustion of butane gas is given as: \(2C_4H_{10} + 13O_2 \rightarrow 8CO_2 + 10H_2O\) This equation indicates that 2 moles of butane (C4H10) react with 13 moles of oxygen (O2) to produce 8 moles of carbon dioxide (CO2) and 10 moles of water (H2O).

Determine the molar ratio between butane and oxygen

From the balanced chemical equation, the molar ratio between butane gas (C4H10) and oxygen gas (O2) is 2:13. It means that for every 2 moles of butane, 13 moles of oxygen are required for the complete combustion.

Use the Law of Combining Volumes

The Law of Combining Volumes states that the ratio of the volumes of reacting gases is directly proportional to the ratio of moles of the gases involved in the reaction, provided that the pressure and temperature conditions are the same for all gases. In this case, we are looking for the volume of oxygen (O2) required to completely burn 1000 cubic feet of butane gas (C4H10). Using the ratio from Step 2, we can set up the following proportion: \( \frac{V_{O_2}}{V_{C_{4}H_{10}}} = \frac{13}{2}\)

Calculate the volume of oxygen gas required

Plug in the given volume of butane gas (1000 cubic feet) into the proportion, and solve for the volume of oxygen gas (V_O2): \( \frac{V_{O_2}}{1000\,\text{cubic feet}} = \frac{13}{2}\) Multiply both sides by 1000 cubic feet to solve for the volume of oxygen gas: \( V_{O_2} = 1000\,\text{cubic feet} × \frac{13}{2} \) \( V_{O_2} = 6500\,\text{cubic feet} \) So, 6500 cubic feet of oxygen gas (O2) is necessary to burn completely 1000 cubic feet of butane gas (C4H10).

Key concepts

Combustion Reaction

A combustion reaction is a type of chemical reaction where a substance combines with oxygen to produce heat and light. In simple terms, it's what happens when something burns. For the case of butane, a combustion reaction occurs when butane gas combines with oxygen gas. As a result, this reaction produces carbon dioxide and water.

• Essential components: Fuel (like butane), oxygen, and a source of heat.
• Products formed: Typically involves carbon dioxide and water in hydrocarbon combustion.
• Exothermic nature: Releases energy as heat and light.

Understanding combustion reactions is pivotal as they are foundational to many processes, like powering engines and generating electricity. It also shows the dependence on a balance of reactants to ensure complete combustion.

Balanced Chemical Equation

A balanced chemical equation represents a chemical reaction with an equal number of atoms for each element on both sides of the equation. In the context of the combustion of butane, the formula is:
\[2 C_4H_{10} + 13 O_2 \rightarrow 8 CO_2 + 10 H_2O\]

• Balancing act: Ensures there are the same number of each type of atom on both sides.
• Maintains mass conservation: Matter doesn't disappear; it just changes forms.
• Coefficients: Numbers in front of formulas indicate moles needed for balance.

Getting the balance right is crucial in stoichiometry, which involves calculating the amounts of reactants and products in a chemical reaction.

Molar Ratio

In chemical reactions, a molar ratio shows the ratio of the amounts in moles of any two components involved in a reaction. For butane's combustion, the balanced equation reveals a molar ratio of 2:13 between butane and oxygen.

• Interpretation: For every 2 moles of butane, 13 moles of oxygen are needed.
• Crucial for calculations: Essential in determining how much of a reactant is consumed or a product formed.
• Ratios arise from coefficients in a balanced equation.

Utilizing the molar ratio helps chemists and engineers figure out exact quantities needed to achieve reactions with no excess of reactants left behind.

Law of Combining Volumes

The Law of Combining Volumes, a principle discovered by Gay-Lussac, states that under the same conditions of temperature and pressure, the volumes of gaseous reactants and products of a reaction are in simple numerical ratios.
For the combustion of butane:

• Volume correspondence: The molar ratio reflects directly onto volume ratios since butane and oxygen are gases.
• Calculation: Given 1000 cubic feet of butane, you need 6500 cubic feet of oxygen, respecting the 2:13 ratio.
• Importance: Simplifies calculations in gaseous reactions.

By applying this law, it's straightforward to predict the volumes of gases involved in reactions, making it invaluable for chemical engineering and industrial applications.