When 85g of CH4 are mixed with 85g of O2 according to this equation:
CH4 + 2O2 - cO2 + 2H2O
What is the theoretical yield in gams of CO2?
What is the percent yield if 45.7g of CO2 are produced?
Please explain!
This is a limiting reagent (LR) problem; you know that because amounts are given for BOTH reactants. This is worked just like two simple stoichiometry problems.
CH4 + 2O2 - cO2 + 2H2O
mols CH4 = grams/molar mass = ?
mols O2 = grams/molar mass = ?
Using the coefficients in the balanced equation, convert mols CH4 to mols CO2.
Do the same to convert mols O2 t mnols CO2.
It is likely these two values for mols CO2 will not agree; the correct value in LR problems is ALWAYS the smaller value and the reagent responsible for that number is the LR.
Using the smaller value, convert to g CO2. g = mols CO2 x molar mass CO2. This is the theoretical yield (TY). The actual yield (AY) is 45.7g.
%yield = (AY/TY)*100 = ?
To find the theoretical yield of CO2, we need to calculate the amount of CH4 that will react completely with O2 based on the given equation.
1. Start by converting the mass of CH4 and O2 into moles using their respective molar masses.
- The molar mass of CH4 (methane) is 16.04 g/mol (1 carbon + 4 hydrogens).
- The molar mass of O2 (oxygen gas) is 32.00 g/mol (2 oxygens).
Moles of CH4 = Mass of CH4 / Molar mass of CH4
Moles of CH4 = 85 g / 16.04 g/mol ≈ 5.298 mol
Moles of O2 = Mass of O2 / Molar mass of O2
Moles of O2 = 85 g / 32.00 g/mol ≈ 2.656 mol
2. Based on the balanced chemical equation, the stoichiometric ratio between CH4 and CO2 is 1:1. This means that for every mole of CH4, we will produce one mole of CO2.
Moles of CO2 = Moles of CH4 = 5.298 mol
3. To convert moles of CO2 to grams, we can use its molar mass. The molar mass of CO2 (carbon dioxide) is 44.01 g/mol (1 carbon + 2 oxygens).
Mass of CO2 = Moles of CO2 × Molar mass of CO2
Mass of CO2 = 5.298 mol × 44.01 g/mol ≈ 233.9 g
Therefore, the theoretical yield of CO2 is approximately 233.9 grams.
To calculate the percent yield, we need the actual yield of CO2, which is given as 45.7 grams.
Percent yield = (Actual yield / Theoretical yield) × 100
Percent yield = (45.7 g / 233.9 g) × 100 ≈ 19.52%
The percent yield is approximately 19.52%.