Final answer:
To find the number of carbon atoms in 41.3 mL of pentane, first calculate the mass of pentane using its volume and density, convert the mass to moles using the molar mass of pentane, and then determine the number of carbon atoms using Avogadro's number.
Step-by-step explanation:
To find out how many carbon atoms are present in 41.3 mL of pentane (C5H12), we must first calculate the mass of pentane and then convert it to moles. Since the density of pentane is 0.626 g/mL, the mass of pentane is found by multiplying the volume by the density:
Mass = Volume × Density = 41.3 mL × 0.626 g/mL = 25.8538 g
To convert the mass of pentane to moles, we need the molar mass of pentane. Pentane's molar mass, as given by its molecular formula C5H12, is (5 × 12.01 g/mol for carbon) + (12 × 1.008 g/mol for hydrogen) = 72.15 g/mol for pentane.
Number of moles of pentane = Mass / Molar Mass = 25.8538 g / 72.15 g/mol ≈ 0.3583 moles
Now that we have the moles of pentane, we can find the number of moles of carbon atoms. Since each molecule of pentane contains 5 carbon atoms, the total moles of carbon atoms is 0.3583 moles × 5 = 1.7915 moles of carbon.
Finally, to find the number of carbon atoms, we use Avogadro's number, which is 6.02 × 10²³ atoms/mol:
Number of carbon atoms = Moles of carbon × Avogadro's number = 1.7915 moles × 6.02 × 10²³ atoms/mol ≈ 1.078 × 10²µ carbon atoms.