Final answer:
To find the number of moles of carbon in the ethanol sample, first calculate the total mass of ethanol using the mass of hydrogen. Then, divide the total mass of ethanol by the molar mass to get the moles of ethanol, which equals the moles of carbon since each ethanol molecule contains two carbon atoms.
Step-by-step explanation:
The question is asking how to calculate the number of moles of carbon in a sample of ethanol (C2H5OH or C2H6O) given that there are 3.024 grams of hydrogen in the sample. The molar mass of ethanol is provided as 46.07 grams per mole.
First, we need to calculate the total mass of the ethanol sample using the mass of hydrogen. Since ethanol contains 6 hydrogen atoms (with each hydrogen atom having an approximate atomic mass of 1 g/mol), we can say that 6 moles of hydrogen have a mass of 6 grams. Therefore, we can calculate the total sample mass using proportions:
Total mass of ethanol = (Total mass of hydrogen / Mass of hydrogen in one mole of ethanol) * Molar mass of ethanol
Total mass of ethanol = (3.024 g / 6 g/mol) * 46.07 g/mol = 23.24 grams of ethanol
Next, we calculate the moles of ethanol in the sample, and since ethanol has two carbon atoms, this will give us the moles of carbon directly:
Moles of ethanol = Total mass of ethanol / Molar mass of ethanol
Moles of ethanol = 23.24 g / 46.07 g/mol ≈ 0.504 moles of ethanol
Since there are two moles of carbon in every mole of ethanol:
Moles of carbon = Moles of ethanol * 2
Moles of carbon ≈ 0.504 * 2 ≈ 1.008 moles of carbon