What mass of carbon dioxide is produced from the complete combustion of 2.10×10−3g of methane?
Express your answer with the appropriate units.
To calculate the mass of carbon dioxide produced from the complete combustion of methane, we need to use the balanced chemical equation for the reaction.
The balanced equation is:
CH4 + 2O2 → CO2 + 2H2O
From the equation, we can see that one molecule of methane (CH4) produces one molecule of carbon dioxide (CO2).
To calculate the mass of carbon dioxide produced, we need to convert the given mass of methane to moles, and then use the mole ratio from the balanced equation to convert moles of methane to moles of carbon dioxide, and finally convert back to mass.
1. Convert the given mass of methane to moles:
The molar mass of methane (CH4) is:
1 carbon (12.01 g/mol) + 4 hydrogen (1.01 g/mol each) = 16.05 g/mol
Number of moles of methane = given mass / molar mass
Number of moles of methane = 2.10×10−3g / 16.05 g/mol
2. Use the mole ratio from the balanced equation:
From the balanced equation, we can see that for every 1 mole of methane (CH4) combusted, 1 mole of carbon dioxide (CO2) is produced.
3. Convert moles of methane to moles of carbon dioxide:
Number of moles of carbon dioxide = number of moles of methane
4. Convert moles of carbon dioxide to mass:
Multiply the number of moles of carbon dioxide by its molar mass to get the mass of carbon dioxide.
The molar mass of carbon dioxide (CO2) is:
1 carbon (12.01 g/mol) + 2 oxygen (16.00 g/mol each) = 44.01 g/mol
Mass of carbon dioxide = number of moles of carbon dioxide * molar mass of carbon dioxide
Now, let's perform the calculations:
Number of moles of methane = 2.10×10−3g / 16.05 g/mol = 1.30868×10−4 mol
Number of moles of carbon dioxide = number of moles of methane = 1.30868×10−4 mol
Mass of carbon dioxide = number of moles of carbon dioxide * molar mass of carbon dioxide
Mass of carbon dioxide = 1.30868×10−4 mol * 44.01 g/mol ≈ 0.00575 g
Therefore, the mass of carbon dioxide produced from the complete combustion of 2.10×10−3g of methane is approximately 0.00575 grams.