Certainly! Let's solve this step-by-step.
1. Understanding the given values:
- The density of water is [tex]\(1.0 \, \text{g/cm}^3\)[/tex].
- The volume of the water drop is [tex]\(0.1 \, \text{cm}^3\)[/tex].
- The molar mass of water [tex]\((\text{H}_2\text{O})\)[/tex] is [tex]\(18 \, \text{g/mol}\)[/tex].
- Avogadro's number, which is the number of molecules in one mole of a substance, is [tex]\(6.022 \times 10^{23} \, \text{molecules/mol}\)[/tex].
2. Calculate the mass of the water drop:
Given the density formula [tex]\(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\)[/tex], we can rearrange to find the mass:
[tex]\[
\text{Mass} = \text{Density} \times \text{Volume}
\][/tex]
Plugging in the given values:
[tex]\[
\text{Mass} = 1.0 \, \text{g/cm}^3 \times 0.1 \, \text{cm}^3 = 0.1 \, \text{g}
\][/tex]
3. Calculate the number of moles in the water drop:
The number of moles can be found using the formula:
[tex]\[
\text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}}
\][/tex]
Substituting the mass of the drop and the molar mass of water:
[tex]\[
\text{Number of moles} = \frac{0.1 \, \text{g}}{18 \, \text{g/mol}} = 0.005555555555555556 \, \text{mol}
\][/tex]
4. Calculate the number of molecules in the water drop:
To find the number of molecules, we use Avogadro's number:
[tex]\[
\text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number}
\][/tex]
Substituting the number of moles calculated:
[tex]\[
\text{Number of molecules} = 0.005555555555555556 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol}
\][/tex]
[tex]\[
\text{Number of molecules} \approx 3.3455555555555557 \times 10^{21} \, \text{molecules}
\][/tex]
Thus, there are approximately [tex]\(3.35 \times 10^{21}\)[/tex] molecules in a drop of water with a volume of [tex]\(0.1 \, \text{cm}^3\)[/tex] at room temperature.
