To determine the mass of 1 mole of raindrops, follow these steps:
1. Determine the mass of one raindrop in grams:
Given the mass of one raindrop is 50 milligrams (mg), we need to convert this to grams (g). There are 1000 milligrams in a gram.
[tex]\[
\text{mass of one raindrop in grams} = 50 \, \text{mg} \times \left( \frac{1 \, \text{g}}{1000 \, \text{mg}} \right) = 0.050 \, \text{g}
\][/tex]
2. Use Avogadro's number to find the mass of 1 mole of raindrops:
Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex], which is the number of particles (in this case, raindrops) in 1 mole.
[tex]\[
\text{mass of 1 mole of raindrops} = 0.050 \, \text{g} \times 6.022 \times 10^{23}
\][/tex]
3. Calculate the result:
Performing the multiplication,
[tex]\[
\text{mass of 1 mole of raindrops} = 0.050 \, \text{g} \times 6.022 \times 10^{23} = 3.011 \times 10^{22} \, \text{g}
\][/tex]
4. Round the answer to 2 significant digits:
The result in scientific notation is already in the correct form. Rounding the answer to 2 significant digits, we get:
[tex]\[
\text{mass of 1 mole of raindrops} \approx 3.0 \times 10^{22} \, \text{g}
\][/tex]
Thus, the mass of 1 mole of raindrops is approximately [tex]\(3.0 \times 10^{22} \, \text{g}\)[/tex].
