Problem 91 - Chemistry Matter and Change

Question

Gaseous methane \(\left(CH_{4}\right)\) undergoes complete combustion by reacting with oxygen gas to form carbon dioxide and water vapor. a. Write a balanced equation for this reaction. b. What is the volume ratio of methane to water in this reaction?

Step-by-Step Solution

Answer

The balanced equation for the combustion of methane is \(CH_{4} + 2O_{2} \rightarrow CO_{2} + 2H_{2}O\) and the volume ratio of methane to water is 1:2.

Step 1: Unbalanced Chemical Equation

The unbalanced chemical equation for the combustion of methane can be written as: \(CH_{4} + O_{2} \rightarrow CO_{2} + H_{2}O\) Step 2: Balance the chemical equation

Step 2: Balancing the Chemical Equation

Now, let's balance the equation by adjusting the coefficients of the reactants and products. Start by balancing the carbon atoms, then the hydrogen atoms, and finally, the oxygen atoms. \(CH_{4} + 2O_{2} \rightarrow CO_{2} + 2H_{2}O\) Here, we have adjusted the coefficients for oxygen gas and water molecules as 2, and now the equation is balanced. Step 3: Determine the volume ratio of methane to water

Step 3: Volume Ratio of Methane to Water

In the balanced chemical equation: \(CH_{4} + 2O_{2} \rightarrow CO_{2} + 2H_{2}O\) For every 1 mole of methane, 2 moles of water vapor are produced. Since gases at the same temperature and pressure occupy the same volume per mole, the volume ratio of methane to water can be obtained directly from the mole ratio. The volume ratio of methane to water is 1:2. Thus, the balanced equation for the combustion of methane is \(CH_{4} + 2O_{2} \rightarrow CO_{2} + 2H_{2}O\) and the volume ratio of methane to water is 1:2.

Key Concepts

Combustion Reaction

In a combustion reaction, a substance reacts with oxygen gas to produce energy in the form of heat and light. Combustion reactions are a type of chemical reaction that usually involve hydrocarbons, like methane. This type of reaction is essential due to its widespread applications in heating, engines, and power generation.
When methane combusts completely, it reacts with oxygen to form carbon dioxide and water vapor. Complete combustion occurs when there is enough oxygen for methane to fully react.
Key points in combustion reaction:

• It releases energy.
• Hydrocarbons like methane are common fuels.
• It involves the production of carbon dioxide and water.

Knowing how to write and balance these reactions is crucial for understanding energy production.

Volume Ratio

Volume ratio in chemistry refers to the ratio of the volumes of gases involved in a chemical reaction. This concept is derived from Avogadro's law, which states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules.
In the case of the methane combustion, we can use the balanced chemical equation to determine the volume ratio. For the reaction:

• 1 mole of methane produces 1 mole of carbon dioxide.
• The same reaction produces 2 moles of water vapor.

Since each mole of gas occupies the same volume, the volume ratio of methane to water vapor is directly 1:2. This means for every unit volume of methane consumed, two unit volumes of water vapor are produced.

Balancing Equations

Balancing equations is an essential step in any chemical reaction to obey the law of conservation of mass. This law states that matter cannot be created or destroyed in an isolated system. Therefore, the number of each type of atom must be the same on both sides of the reaction equation.
In the combustion of methane, we start with carbon atoms: there is 1 carbon atom in methane and 1 in carbon dioxide, so they are balanced.
Next, we look at hydrogen: 4 hydrogen atoms in methane corresponds to 2 water molecules. Finally, balance the oxygen atoms, 4 oxygen atoms in total are needed for CO2 and H2O.
The balanced equation for the combustion of methane is:

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