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A beaker contains 35.5 mL of propane (C\(_3\)H\(_8\), density is 0.500 g/mL). Determine how many C atoms this liquid contains.

Answer :

To find the number of C atoms in 35.5 mL of propane, multiply the volume by the density to get the mass, convert the mass to moles of propane, then use the molar ratio to find moles of carbon, and finally multiply by Avogadro's number to determine the number of C atoms.

To determine how many C atoms are in 35.5 mL of propane (C3H8) with a density of 0.500 g/mL, we first need to calculate the mass of propane. This can be done by multiplying the volume (35.5 mL) by the density (0.500 g/mL), giving us 17.75 grams of propane.

Next, we have to find the number of moles of propane using its molar mass. The molar mass of propane (C3H8) is 44.09 g/mol (3 carbon atoms at 12.01 g/mol each plus 8 hydrogen atoms at 1.01 g/mol each). The number of moles is calculated as the mass of propane divided by the molar mass:

Number of moles of propane = 17.75 g / 44.09 g/mol ≈ 0.402 moles

Since one mole of propane contains three moles of carbon atoms (due to the molecular formula C3H8), we multiply the number of moles of propane by three to get the total moles of carbon:

Total moles of C = 0.402 moles of propane x 3 = 1.206 moles of C

Finally, using Avogadro's number, which is 6.022 x 1023 atoms/mol, we can determine the number of carbon atoms:

Number of C atoms = 1.206 moles of C x 6.022 x 1023 atoms/mol ≈ 7.26 x 1023 C atoms

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