Question

If 1 ml of water contains 20 drops, what is the number of water molecules in the one drop of water? (${N_a}$ = Avogadro no.)
1. 0.5${N_a}$/18
2. 0.05${N_a}$
3. 0.05${N_a}$/18
4. 0.5${N_a}$

Answer 1

Hint: 1ml of water weighs 1 gram. Dividing that by 20 you will get 0.05 grams of water molecules. The molecular mass of one water molecule (in terms of moles) is about 18. If we divide the mass of the water by water's molecular mass, we can find the number of moles.

Complete Step by step answer:It is given in the question that,
1ml of water contains= 20 drops of water
Or we can say that volume of 20 drops of water= 1ml
Or volume of 20 drops of water= 0.001 L
Therefore volume of one drop of water= (1/20) ml = 0.05 ml
Therefore mass of one drop of water= 0.05 gram
(If the density of water is 1g$c{m^{ - 3}}$ that is if the volume of 1 gram of water is 1ml)
Moles of water in one drop of water= given mass/ molar mass
And in this case given mass= 0.05 gm
And molar mass= 18 gm
Therefore moles of water in one drop of water= 0.05/18 moles
And no. of molecules= Avogadro no. $ \times $ No. of moles
Therefore no. of molecules in this case= 0.05${N_a}$/18

So according to this the correct option is 3rd.

Note: Molecular mass can be found by adding the atomic masses (found in the periodic table usually in the bottom left of the element although some outliers mean that it is usually worth just using the bigger number written) of all the components. For water or dihydrogen monoxide, there are 2 atoms of hydrogen and 1 atom of oxygen; hydrogen has an atomic mass of 1 while oxygen has an atomic mass of 16.00. So the mass of water becomes 18.