Final answer:
A person weighing 78 kg with 18% carbon by mass has 14.04 kg or 14040 grams of carbon. Using the average molar mass of carbon (12.011 g/mol), this mass corresponds to approximately 1169 moles of carbon.
Step-by-step explanation:
To calculate the mass of carbon in a person who weighs 78 kg and is approximately 18% carbon by mass, we first find the mass of carbon as a percentage of the total body mass:
Mass of carbon = 0.18 × 78 kg = 14.04 kg
Since 1 kg = 1000 g, we convert this mass into grams:
Mass of carbon in grams = 14.04 kg × 1000 g/kg = 14040 g
To find the number of moles of carbon, we use the molar mass of carbon. The average molar mass of carbon is 12.011 g/mol as carbon naturally occurs as a mixture of isotopes, mainly carbon-12, carbon-13, and a trace of carbon-14. One mole of carbon is 6.022 × 1023 carbon atoms.
Number of moles = Mass of carbon in grams ÷ Molar mass of carbon
Number of moles = 14040 g ÷ 12.011 g/mol ≈ 1169 moles