Determine the number of atoms in 2.00 mL of mercury. The density of mercury is 13.5 g/mL.
The correct answer and explanation is:
To determine the number of atoms in 2.00 mL of mercury, we need to follow a few steps, starting with the mass of mercury and converting it into the number of atoms.
- Calculate the mass of mercury:
The density of mercury is given as 13.5 g/mL. Density is defined as mass per unit volume, so the mass of mercury in 2.00 mL can be calculated using the formula: Mass=Density×Volume\text{Mass} = \text{Density} \times \text{Volume} Substituting the known values: Mass=13.5 g/mL×2.00 mL=27.0 g\text{Mass} = 13.5 \, \text{g/mL} \times 2.00 \, \text{mL} = 27.0 \, \text{g} - Determine the number of moles of mercury:
To find the number of moles of mercury, we use the molar mass of mercury. The molar mass of mercury (Hg) is 200.59 g/mol. The number of moles is calculated by dividing the mass of mercury by its molar mass: Moles of mercury=MassMolar Mass=27.0 g200.59 g/mol≈0.134 mol\text{Moles of mercury} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{27.0 \, \text{g}}{200.59 \, \text{g/mol}} \approx 0.134 \, \text{mol} - Calculate the number of atoms:
Avogadro’s number is 6.022×10236.022 \times 10^{23} atoms per mole. To find the number of atoms in the given amount of mercury, we multiply the number of moles by Avogadro’s number: Number of atoms=0.134 mol×6.022×1023 atoms/mol\text{Number of atoms} = 0.134 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} Number of atoms≈8.06×1022 atoms\text{Number of atoms} \approx 8.06 \times 10^{22} \, \text{atoms}
Thus, the number of atoms in 2.00 mL of mercury is approximately 8.06×10228.06 \times 10^{22} atoms.