Question

How many molecules are in 50mL of water and how do you calculate how many atoms of hydrogen and oxygen are in it?

Answer 1

Here you need to know the relationship between moles, mass and number of atoms/molecules.

First number of moles can be expressed in two ways
1) as a mass
\[n = \frac{ mass }{ molar ~mass } = \frac{ m }{ M }\]
2) as number of atoms/molecules described using Avogadro's number
\[n = \frac{ number~ of~ particles }{ Avogadro's~ number } = \frac{ N }{ N_A } = \frac{ N }{ 6.022 \times 10^{23} }\]

For 50ml of water, you need to convert this first to a mass. We can assume the density of the water is 1 g/cm^3 = 1g/mL, unless otherwise stated.
Thus 50mL can be estimated as 50 g of water.

Now we must convert this mass quantity into moles.
\[n = \frac{ m }{ M } = \frac{ 50g }{ 18.016g/mol } = 2.775 ~moles\]

Now that it is in moles we use the particle mole formula:
\[n = \frac{ N }{ 6.022 \times 10^{23} } = 2.775 ~so~ N = 2.775 \times 6.022 \times 10^{23} = 1.7 \times 10^{24} \]

Answer 2

The answer above tells you how many water molecules are in 50 g of water.
To find the individual atoms, look at the chemical formula of water
\[H_2O ~has~ 2H + O\]
So each molecule of water corresponds to 2 atoms of hydrogen and one atom of oxygen.

Another way to consider this
If you had 5 boxes of fruit and each box had 2 apples and 1 banana, how much of each fruit do you have?
1 molecule = 1 x 2 apples + 1x 1 banana, so
5 molecules = 5 x 2 apples + 5 x 1 banana = 10 apples and 5 bananas.

Answer 3

Remember molar units is the bridge between masses and particles so be able to use both mass and particle formulae by changing to moles.

\[\frac{ m }{ M } = n = \frac{ N }{ N_A }\]