Question

Calculate the number of molecules in 1 ml of water:
(A) $3.3 \times {10^{22}}$
(B) 1
(C) $6.02 \times {10^{23}}$
(D) 18

Answer 1

Recall the mole concept to answer this question. Find the total number of moles constituting 1 mL of water. Take the density of water to be 1 g/mL. Therefore, using a density formula you will get that 1 mL is equal to 1 g.

Complete step by step solution:
Molecular mass of water (${H_2}O$) = $2 \times {\text{atomic mass of hydrogen + 1}} \times {\text{atomic mass of oxygen}}$
Therefore, molecular mass of water = $2(1) + 16 = 18g$
Since by mole concept mass of one mole of a substance is equal to its molecular mass in grams.
Therefore, 1 mol of water = 18 g.
Also, there is relation for finding the number of molecules and it is:
$number of molecules =$ ${\text{number of moles }} \times {\text{ Avogadro number}}$ _____(1)
and, Avogadro number is equal to $6.022 \times {10^{23}}$.
So, to find the number of molecules in 1 mL of water, we need to find the number of moles in 1 mL of water.
As the number of moles = $\dfrac{{{\text{Given mass}}}}{{{\text{Molecular Mass}}}}$ .
Here, given mass or water (in 1mL) = 1 g (by taking density of water = 1 g/mL, we get 1mL=1g)
Therefore, the number of moles of water in 1 mL= $\dfrac{1}{{18}}$
Hence, using equation (1), no. of molecules in 1 mL of water = $\dfrac{1}{{18}} \times 6.022 \times {10^{23}} = 0.33 \times {10^{23}}$ molecules
Or, the number of molecules in 1 mL of water is $3.3 \times {10^{22}}$ .

Thus, option (A) is correct.

Note: Avogadro number or Avogadro constant is the proportionality factor that relates the number of molecules or particles in a sample with the amount of substance in that sample. It should be noted from the above calculation that the Avogadro number also relates the molar volume of a substance to the average volume occupied by one of its particles when both are expressed in the same units of volume.