# How many molecules of water are there in 36 grams of H_2O?

Aug 2, 2016

$1.2 \times {10}^{24} \text{molecules}$

#### Explanation:

To go from the mass of water to molecules of water, we have to do two things:

1. Convert mass of ${H}_{2} O$ to moles of ${H}_{2} O$ using the molar mass of ${H}_{2} O$ as a conversion factor

2. Convert moles of ${H}_{2} O$ to molecules of ${H}_{2} O$ using Avogadro's number ($6.02 \times {10}^{23}$) as a conversion factor

color(brown)("Step 1:"
Before we start, I should note that the molar mass of ${H}_{2} O$ is $18.01 \frac{g}{m o l}$.

We can go from mass to moles using dimensional analysis. The key to dimensional analysis is understanding that the units that you don't need any more cancel out, leaving the units that are desired:

$36 \cancel{g} \times \frac{1 m o l}{18.01 \cancel{g}}$ $= 2.00 m o l$

color(red)("Step 2:"
We'll use the following relationship: Using the moles of ${H}_{2} O$ that were just obtained, we can use Avogrado's number to perform dimensional analysis to cancel out units of $m o l$ to end up with molecules:

2.00cancel"mol"xx(6.02xx10^(23) "molecules")/(1cancel"mol") $= 1.204 \times {10}^{24} \text{molecules}$

color(blue)("Thus, 36g of water is equivalent to" $1.2 \times {10}^{24} \text{molecules}$