# Question 485e4

Oct 27, 2015

$8.22 \cdot {10}^{22}$

#### Explanation:

The idea here is that you need to use the given density to determine how many grams of water you get in $\text{2.46 mL}$.

Once you know how many grams of water you have, you can use water's molar mass to find how many moles that sample contains, then finally use Avogadro's number to get the number of molecules.

So, a density of $\text{1.00 g/mL}$ means that every mililiter of water at ${4}^{\circ} \text{C}$ has a mass of $\text{1 g}$.

Since your sample has a volume of $\text{2.46 mL}$, it follows that its mass will be

2.46color(red)(cancel(color(black)("mL"))) * "1 g"/(1color(red)(cancel(color(black)("mL")))) = "2.46 g"

Now, a substance's molar mass tells you exactly what the mass of one mole of that substance is.

In water's case, its molar mass of $\text{18.015 g/mol}$ tells you that every mole of water has a mass of $\text{18.015 g}$.

If that's the case, how many moles would you get in $\text{2.46 g}$?

2.46color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "0.13655 moles H"_2"O"

Now it's time to convert the number of moles to number of molecules.

You know that one mole of any substance contains exactly $6.022 \cdot {10}^{23}$ molecules of that substance - this is Avogadro's number I mentioned earlier.

This means that you would get

0.13655color(red)(cancel(color(black)("moles"))) * (6.022 * 10^(23)"molecules")/(1color(red)(cancel(color(black)("mole")))) = color(green)(8.22 * 10^(22)"molecules of H"_2"O"#