A 2.760 g sample of carbon was burned, yielding 10.120g of carbon dioxide. How many grams of oxygen was taken up by the reaction? What ofrmula would I use to solve this problem?
C + O2 ==> CO2
Convert 10.120 g CO2 to mols.
Convert mols CO2 to mols O2.
Convert mols O2 to grams O2.
Post your work if you get stuck.
(As it turns out, the 2.760 g C was apparently pure C so the same process could have been used with the 2.760 g C but the problem doesn't say pure C so the SURE way is to do it the way I outlined.)
To solve this problem, you need to use the concept of stoichiometry. Stoichiometry is the calculation of quantitative relationships between reactants and products in a chemical reaction.
First, we need to write down the balanced chemical equation for the combustion of carbon:
C + O2 → CO2
From the balanced equation, we can see that for every 1 mole of carbon burned, 1 mole of carbon dioxide is produced. And since we have the mass of the carbon dioxide produced (10.120 g), we can calculate the moles of carbon dioxide using its molar mass.
The molar mass of carbon dioxide (CO2) is calculated by adding the atomic masses of carbon (C) and oxygen (O), which are approximately 12.01 g/mol and 16.00 g/mol, respectively.
Molar mass of CO2 = (12.01 g/mol) + 2(16.00 g/mol) = 44.01 g/mol
Now, we can calculate the moles of carbon dioxide:
Moles of CO2 = Mass of CO2 / Molar mass of CO2
= 10.120 g / 44.01 g/mol
≈ 0.23 mol
Since the balanced equation shows a 1:1 mole ratio between carbon and carbon dioxide, we can conclude that 0.23 mol of carbon was burned in the reaction.
Now, to find the number of moles of oxygen used in the reaction, we compare the mole ratio from the balanced equation.
From the balanced equation, we can see that for every 1 mole of carbon burned, 1 mole of oxygen is consumed. Therefore, the number of moles of oxygen used is also 0.23 mol.
Finally, to find the mass of oxygen used, we multiply the number of moles of oxygen by its molar mass.
Mass of oxygen = Moles of oxygen × Molar mass of oxygen
The molar mass of oxygen (O2) is approximately 32.00 g/mol (since O2 is a diatomic molecule).
Mass of oxygen = 0.23 mol × 32.00 g/mol ≈ 7.36 g
Therefore, approximately 7.36 grams of oxygen were consumed in the reaction.
To summarize, to solve this problem, we used the concept of stoichiometry and the balanced chemical equation to calculate the moles of carbon dioxide produced. Then, by comparing the mole ratio from the balanced equation, we determined the moles of oxygen consumed in the reaction. Finally, by multiplying the moles of oxygen by its molar mass, we found the mass of oxygen consumed.