# The density of water is 1.00 g/mL at 4°C. How many water molecules are present in 2.46 mL of water at this temperature?

Nov 7, 2015

$8.23 \cdot {10}^{22}$

#### Explanation:

The idea here is that you need to use the density of water at ${4}^{\circ} \text{C}$ and the volume of the sample to find its mass, then use water's molar mass to find how many moles of water you get in this sample.

So, density is defined as mass per unit of volume. In this case, a density of $\text{`1.00 g/mL}$ tells you that every milliliter of water has a mass of $\text{1.00 g}$.

This means that $\text{2.46 mL}$ will have a mass of

2.46color(red)(cancel(color(black)("mL"))) * "1.00 g"/(1color(red)(cancel(color(black)("mL")))) = "2.46 g"

Now, water has molar mass of $\text{18.015 g/mol}$. This tells you that every mole of water has mass of $\text{18.015 g}$. In your case, the sample will contain

2.46color(red)(cancel(color(black)("g"))) * "1 mole water"/(18.015color(red)(cancel(color(black)("g")))) = "0.1366 moles water"

Finally, the relationship between number of moles and number of molecules is given by Avogadro's number, which tells you that every mole of a substance contains exactly $6.022 \cdot {20}^{23}$ molecules of that substance.

In this case, you will have

0.1366color(red)(cancel(color(black)("moles"))) * (6.022 * 10^(23)"molecules")/(1color(red)(cancel(color(black)("mole")))) = color(green)(8.23 * 10^(22)"molecules")

So, $\text{2.46 mL}$ of water at a temperature of ${4}^{\circ} \text{C}$ wil contain a total of $8.23 \cdot {10}^{22}$ molecules of water.