Final answer:
To find the total number of atoms in a 10.0 mL ethanol sample with a density of 0.889 g/mL, calculate the mass of ethanol, determine the number of moles using the molar mass, and then use Avogadro's number to find the number of ethanol molecules, and finally multiply this by 9 to get the total number of atoms.
Step-by-step explanation:
The question asks how many atoms are in a 10.0 mL sample of ethanol (C2H6O) with a density of 0.889 g/mL. To find the total number of atoms, we need to calculate the mass of ethanol, determine the number of moles, and then use Avogadro's number to find the number of molecules and subsequently the total number of atoms.
First, calculate the mass of ethanol by multiplying the volume by the density:
Mass of ethanol = Volume × Density
\(Mass = 10.0 mL × 0.889 g/mL = 8.89 g\)
Next, we need to find the number of moles of ethanol using its molar mass. The molar mass of ethanol (C2H6O) is approximately 46.07 g/mol. So:
\(Moles of ethanol = \frac{Mass}{Molar Mass}\)
\(Moles = \frac{8.89 g}{46.07 g/mol} = 0.193 moles\)
Now, using Avogadro's number (6.022 × 10^23 molecules/mol), we can find the number of molecules in 0.193 moles of ethanol.
\(Number of molecules = Moles × Avogadro's number\)
\(Number of molecules = 0.193 moles × 6.022 × 10^23 molecules/mol\)
As each molecule of ethanol has 9 atoms (2 carbon, 6 hydrogen, 1 oxygen), we can then calculate the total number of atoms:
\(Total number of atoms = Number of molecules × Atoms per molecule\)
\(Total number of atoms = Number of molecules × 9\)
Finally, we multiply the number of ethanol molecules by 9 to find the total number of atoms.