How Many Moles of Methane (CH4) Are Required to Produce 22g of Carbon Dioxide (CO2) After Combustion?

Methane (CH4) is a common fuel source, and understanding how it behaves during combustion is crucial for various applications, including energy production and chemical manufacturing. This article delves into the precise calculation required to determine the amount of methane needed to produce a specific amount of carbon dioxide (CO2) through the process of combustion.

Stoichiometric Equation for Methane Combustion

The balanced chemical equation for the complete combustion of methane is as follows:

CH4 2O2 → CO2 2H2O

This equation indicates that one mole of methane (CH4) reacts with two moles of dioxygen (O2) to produce one mole of carbon dioxide (CO2) and two moles of water (H2O).

Moles of Carbon Dioxide and Methane Relationship

From the equation, we can see that the molar ratio of methane to carbon dioxide is 1:1. Therefore, if 1 mole of CH4 produces 1 mole of CO2, the same is true for any quantity of CH4. To determine the number of moles of methane needed to produce 22 grams of CO2, we must first convert the mass of CO2 to moles.

Mass to Molar Conversion of CO2

The molar mass of CO2 is calculated as follows:

Molar mass of CO2 12 g/mol (for carbon) 2 × 16 g/mol (for oxygen) 44 g/mol

To find the moles of CO2 in 22 grams, we use the formula:

Moles of CO2 Mass of CO2 / Molar mass of CO2 22 g / 44 g/mol

This simplifies to:

Moles of CO2 0.5 moles

Calculating Moles of Methane Required

Since the molar ratio between methane and carbon dioxide is 1:1, the moles of methane required to produce 0.5 moles of CO2 is also 0.5 moles.

The molar mass of methane (CH4) is 16 g/mol. To find the mass of methane required, we again use the molar mass and the number of moles:

Mass of CH4 Moles of CH4 × Molar mass of CH4 0.5 moles × 16 g/mol

This results in:

Mass of CH4 8 grams

Verifying the Calculation with a Balanced Equation

Let's verify this calculation using the balanced equation:

CH4 2O2 → CO2 2H2O

We can see that:

1 mole of CH4 produces 1 mole of CO2

Therefore, 0.5 moles of CH4 will produce 0.5 moles of CO2, which is equivalent to 22 grams of CO2.

Thus, the required mass of methane to produce 22 grams of CO2 is 8 grams.

By understanding and applying these stoichiometric relationships, we can accurately calculate the amount of methane needed in various chemical and industrial processes, ensuring efficiency and precision.