Determining the Moles of Methane Required for CO2 Production via Combustion

A Balanced Equation and Stoichiometry Basics

To determine the number of moles of methane (CH4) required to produce 22 grams of carbon dioxide (CO2) after combustion, we first write the balanced chemical equation for the combustion of methane:

Step 1: Write the Balanced Combustion Reaction

The balanced chemical equation for the combustion of methane is:

CH4 2O2 → CO2 2H2O

From this equation, we can see that 1 mole of methane produces 1 mole of carbon dioxide. This relationship is our fundamental starting point for solving the problem.

Calculating the Moles of CO2 Produced

Step 2: Determine the Molar Mass of CO2

The molar mass of CO2 is calculated as follows:

Molar mass of CO2 12.01 g/mol (for Carbon) 2 × 16.00 g/mol (for Oxygen) Molar mass of CO2 12.01 32.00 44.01 g/mol

Step 3: Convert Grams to Moles

Now we convert 22 grams of CO2 to moles:

Moles of CO2 (mass) / (molar mass) 22 g / 44.01 g/mol ≈ 0.50 moles

Determining the Moles of CH4 Needed

Step 4: Use Stoichiometry

Since the balanced equation shows that 1 mole of CH4 produces 1 mole of CO2, the moles of CH4 required to produce 0.50 moles of CO2 are also 0.50 moles.

Thus, 0.50 moles of methane are required to produce 22 grams of CO2 after combustion.

Additional Calculations for Verification

Step 5: Verify the Molar Masses and Grams of CH4

The gram-molecular mass of CO2 is calculated as follows:

Gram-molecular mass of CO2 12 g/mol (for Carbon) 2 × 16 g/mol (for Oxygen) Gram-molecular mass of CO2 12 32 44 g/mol

If 1 mole of CO2 is produced by 1 mole of CH4, then:

Moles of CO2 22 g / 44 g/mol 0.50 moles

Using the same stoichiometry, moles of CH4 0.50 moles.

To convert the moles of CH4 back to grams, use the molar mass of CH4 (16 g/mol):

Mass of CH4 0.50 moles × 16 g/mol 8 g of CH4

Therefore, 8 grams of CH4 are required to produce 22 grams of CO2 via complete combustion.

Additional Considerations

The balanced reaction equation and the use of stoichiometric ratios confirm the process of converting grams of CO2 to moles and back to grams of CH4. This method ensures accurate calculation and understanding of the chemical reaction dynamics.