Problem 17 - Chemistry: An Atoms-Focused Approach

Question

How many moles of water vapor are produced for every mole of methane consumed in the combustion reaction \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) ?\)

Step-by-Step Solution

Answer

Answer: The ratio of moles of water vapor produced to moles of methane consumed is 2:1.

Step 1: Identify the given balanced equation

We are given the balanced chemical equation for the combustion of methane: \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

Step 2: Analyze the stoichiometry of the reaction

Looking at the balanced chemical equation, we can understand the stoichiometry of the reaction. The coefficients of the reactants and products represent the molar ratios in which they participate in the reaction. In this equation, we can see that 1 mole of methane (\(\mathrm{CH}_4\)) reacts with 2 moles of oxygen (\(\mathrm{O}_2\)) to produce 1 mole of carbon dioxide (\(\mathrm{CO}_2\)) and 2 moles of water vapor (\(\mathrm{H}_2\mathrm{O}\)).

Step 3: Determine the ratio of moles of water vapor produced to moles of methane consumed

From the stoichiometry of the balanced chemical equation, we know that for every 1 mole of methane consumed, 2 moles of water vapor are produced. Therefore, the ratio of moles of water vapor produced to moles of methane consumed is 2:1. So, 2 moles of water vapor are produced for every mole of methane consumed in the combustion reaction.

Key Concepts

Understanding Combustion Reactions

Combustion reactions are a type of chemical reaction where a substance combines with oxygen to release energy in the form of heat and light. This energy often manifests through flames. In the case of methane combustion, methane (\(\text{CH}_4\)) reacts with oxygen (\(\text{O}_2\)) in the air. This reaction is common in residential heating and cooking.
When methane burns, it forms carbon dioxide (\(\text{CO}_2\)) and water vapor (\(\text{H}_2\text{O}\)). Evolving gases, such as water vapor, is a characteristic of combustion reactions. These reactions play a critical role in the carbon cycle due to their involvement in producing carbon dioxide.
Some typical features of combustion reactions:

• Oxygen is always a reactant.
• They often release large amounts of energy.
• The products usually include oxides, like \(\text{CO}_2\) and water vapor.

Balancing a Chemical Equation

A chemical equation represents a chemical reaction using symbols and formulas. It shows the reactants and products along with their quantities through coefficients. Balancing a chemical equation is crucial because it abides by the law of conservation of mass. This means the quantity of atoms for each element remains constant throughout the reaction.
When balancing the equation for methane combustion:\[\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(g)\]The coefficients—1 for \(\text{CH}_4\), 2 for \(\text{O}_2\), 1 for \(\text{CO}_2\), and 2 for \(\text{H}_2\text{O}\)—ensure that the same number of each atom is present on both sides of the equation.
Key points to remember while balancing:

• Only coefficients, never subscripts, should be altered to balance an equation.
• Check each element sequentially to ensure balance across the reaction.
• Start by balancing elements that appear in only one reactant and one product.

Understanding Molar Ratios in Reactions

The concept of molar ratios is integral to stoichiometry in chemistry. It refers to the proportion in which reactants react and products form in a given chemical reaction. These ratios are derived from the balanced chemical equation.
For the combustion of methane, the balanced equation tells us:\[\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(g)\]From this, we determine that 1 mole of methane reacts with 2 moles of oxygen to yield 1 mole of carbon dioxide and 2 moles of water vapor.
Essential aspects of molar ratios:

• Molar ratios guide calculations in chemical reactions, predicting amounts of products from known quantities of reactants.
• They help us understand the stoichiometric coefficients in balanced equations.
• In the given reaction, the molar ratio for methane to water vapor is 1:2.

These ratios are instrumental in chemical calculations, such as finding the yield of reactions and proportional quantities used or produced.