Question

Fill in the blanks. The number of oxygen molecules required for the complete combustion of 5 moles of methane is

Short answer

Answer: 10 moles of oxygen molecules are required for the complete combustion of 5 moles of methane.

Step-by-step solution

Write down a balanced chemical equation for the combustion of methane

The balanced chemical equation for the combustion of methane is given by: CH₄ + 2O₂ → CO₂ + 2H₂O

Identify the mole ratio of methane to oxygen in the balanced chemical equation

From the balanced chemical equation in step 1, we can observe that 1 mole of methane (CH₄) reacts with 2 moles of oxygen (O₂). This mole ratio can be written as: 1 CH₄ : 2 O₂

Calculate the number of moles of oxygen required for the combustion of 5 moles of methane

Using the mole ratio from step 2, we can calculate the number of moles of oxygen (O₂) reqiured for the complete combustion of 5 moles of methane (CH₄) as follows: Number of moles of O₂ = (Number of moles of CH₄ × 2 moles of O₂) / 1 mole of CH₄ Number of moles of O₂ = (5 moles of CH₄ × 2 moles of O₂) / 1 mole of CH₄ Number of moles of O₂ = 10 moles of O₂ In conclusion, 10 moles of oxygen molecules are required for the complete combustion of 5 moles of methane.

Key concepts

Balanced Chemical Equation

Understanding the balanced chemical equation is crucial when investigating reactions such as the combustion of methane. In chemical reactions, a balanced equation ensures that the same number of atoms for each element is present on both the reactant and product sides. For the combustion of methane, the equation is written as \( CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \).

To achieve balance, there must be an equal number of atoms for each element involved in the reaction. For methane combustion, this means one carbon atom from \( CH_4 \) becomes one carbon atom in \( CO_2 \), four hydrogen atoms from \( CH_4 \) become four hydrogen atoms in two molecules of \( H_2O \), and four oxygen atoms from two molecules of \( O_2 \) are distributed between one \( CO_2 \) and two \( H_2O \) molecules. Balancing chemical equations allows chemists to understand how different molecules react and predict the products of a reaction.

Mole Ratio

The mole ratio is derived from the coefficients of the reactants and products in a balanced chemical equation. It is a guiding number that tells us how many moles of each reactant and product participate in the reaction. In the context of the methane combustion equation, \( 1 CH_4 : 2 O_2 \) indicates that one mole of methane reacts with two moles of oxygen to yield products according to the equation.

This mole ratio is essential for converting moles of one substance into moles of another. For example, if a student knows the amount of methane available, the mole ratio can be used to calculate the exact amount of oxygen needed for complete combustion. This concept ensures that chemical reactions are carried out with the correct proportions of reactants, thus preventing waste or insufficient reactions.

Stoichiometry

Stoichiometry is the quantitative relationship between the reactants and products in a chemical reaction. It involves calculations based on the balanced chemical equation and mole ratios to determine the amount of substances consumed or produced. In the example provided, the stoichiometry of the combustion of five moles of methane involves using the mole ratio of \(1 CH_4 : 2 O_2\) to calculate that ten moles of oxygen are required for complete combustion.

By mastering stoichiometry, students can predict the amounts of substances needed for chemical reactions in real-world applications, such as industrial synthesis, pharmaceuticals, or environmental processes. It is a foundational concept in chemistry that supports the understanding of material conservation and the efficient use of resources.