Question

The density of water at room temperature is 1.0 g/ml. How many molecules are there in a drop of water if its volume is 0.05 ml?

Answer 1

Hint: We know that avagadro’s law explains that equal volumes of all gases contain equal numbers of molecules under similar conditions. Now since one mole molecules of all gases contain the same number of molecules therefore they occupy the same molecules under STP.

Complete step by step answer:
This question evolves understanding the concept of mole and molar volume which is why we know that molar volume of all gases at STP is 22.4 L. Let us now solve the question above. We need to know the chemical formula of water to calculate the number of molecules and atoms in a water drop. There are two hydrogen atoms and one atom of oxygen in each water molecule as depicted by its molecular formula ${H_2}O$ . The density of water varies depending on the condition (cold water is denser; warm water is less dense) but here we are given that the density of water at room temperature is 1.0g/ml.
We know that Density = $\dfrac{Mass}{Volume}$. Since we are given with density and volume we can calculate mass,
Mass = Density x Volume
Let us write down the values from the question Density of water at room temperature = 1.0 g/ml, Volume = 0.05ml applying to the formulae,
Mass= 1.0 x 0.05= 0.05g
Molecular mass of $H_2O$ = (1 x 2) +16 = 18 g
(we know that atomic mass of oxygen is 1 and hydrogen is 1)
Since the mass of one mole atoms of any element is exactly equal to the atomic mass in grams of that element.
1 g will contain $\dfrac{1}{{18}}$ moles of $H_2O$.
0.05 g will contain $0.05 \times \dfrac{1}{{18}}$
1 mole \[ = {\text{ }}6.023 \times {10^{23}}\] molecules ( from avagadros law)
Total number of molecules in a drop of water,
$= 6.022 \times {10^{23}} \times 0.05 \times \dfrac{1}{{18}} \\
= 1.67 \times {10^{21}} \\ $

Therefore the drop of water with a volume of 0.05ml contains the 1.67 $ \times 10^{21}$.

Note: The exact density of water is not 1 g/ml, but a bit less of 0.099983 g/ml at $4^0$Celsius. The rounded value is 1 g/ml. While calculating the molecular mass of water it is the sum of the atomic mass of all the elements present in the molecule.