# How many molecules of water are in 500 g of water? Show all calculations.

## Question:

How many molecules of water are in 500 g of water? Show all calculations.

## Number of molecules in water.

We know or we can check the molar mass of water molecules in the book, and one mole contains {eq}6.02 \times 10^{23} {/eq} molecules. We can thus find the mass of one water molecule. Or we can compare the ratios of molar mass to number of molecules to find the number of molecules in some mass.

One mole of water is about 18 g, and one mole contains {eq}6.02 \times 10^{23} {/eq} water molecules. Comparing the ratios of mass to number of molecules, we have

{eq}\begin{align*} \frac{18 \;\text{g}}{6.02 \times 10^{23} \;\text{molecules}}&=\frac{500 \;\text{g}}{x}. \end{align*} {/eq}

Solving for {eq}x {/eq}, we have the number of molecules in 500 g of water

{eq}\begin{align*} x&=1.67 \times 10^{25} \;\text{molecules}. \end{align*} {/eq}