What is the relationship of the mass of hydrogen to the moles of oxygen. The answer lies in the molecular formula of ethanol. There is a ratio of 2 molecules of carbon to every 6 molecules of hydrogen. This ratio can be extended to include for 1 mole of ethanol, there is 2 moles of carbon for every 6 moles of hydrogen. So we have the mass of a hydrogen, we need to convert this to moles and use dimensional analysis to get the moles of carbon:
3.024 g Hydrogen x ( 1 mol Hydrogen/ 1.008 g Hydrogen) x (2 mol Cabon/6 mol Hydrogen) = 1 mol Carbon
Another way to solve is that makes use of the molar mass of ethanol is as follows. In this, you will again use dimensional analysis.
3.024 g Hydrogen x (1 mol Hydrogen/ 1.008 g Hydrogen) x (1 mol ethanol/ 6 moles hydrogen) x (46.07 g/1 mol ethanol) = .23.035
23.035 g ethanol x (1 mol ethanol/ 46.07 g ethanol) x 2 mol carbon/1 mole ethanol) = 1 mole Carbon.
To be sure of the answer, ask yourself if the answer makes sense. Given that there are only three moles of hydrogen( 3.024 g Hydrogen x (1 mol Hydrogen/ 1.008 g Hydrogen)), it makes sense that since the carbon and hydrogen ratio is 1:3, carbon would have 1 mole of carbon in ethanol.