# How many water molecules are in a block of ice containing 2.50 mol of water?

Aug 10, 2016

$1.51 \cdot {10}^{24}$

#### Explanation:

This is a pretty straightforward example of how to sue Avogadro's number to figure out the number of molecules present in a given sample.

In your case, the sample is said to contain $2.50$ moles of water. Now, a mole is simply a very, very large collection of molecules. In order to have $1$ mole of a molecular compound you need your sample to contain $6.022 \cdot {10}^{23}$ molecules of that compound.

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{1 mole" = 6.022 * 10^(23)"molecules} \textcolor{w h i t e}{\frac{a}{a}} |}}} \to$ Avogadro's number

This is what Avogadro's number is all about -- the number of molecules needed to form $1$ mole of a molecular compound.

So, now that you know how many molecules are needed to have $1$ mole of water, use Avogadro's number as a conversion factor to calculate the number of molecules present in your sample

2.50 color(red)(cancel(color(black)("moles H"_2"O"))) * (6.022 * 10^(23)"molec. H"_2"O")/(1color(red)(cancel(color(black)("mole H"_2"O")))) = color(green)(|bar(ul(color(white)(a/a)color(black)(1.51 * 10^(24)"molec. H"_2"O")color(white)(a/a)|)))

The answer is rounded to three sig figs.