Question

Ordinary water contains one part of heavy water per 6000 parts of water by weight. The no. of heavy molecules present in a drop of water of volume 0.01ml is

Answer 1

Explain the solution

Answer 2

Given

Water contains one part of heavy water per 6000 parts of water by weight

To find

No. of heavy molecules present in a drop of water of volume 0.01ml

Solution

$N_A$ = Avogadro's number = $6.022\times 10^{23}\ \text{mol}^{-1}$

M = Molar mass of heavy water = 20 g/mol

Density of water = $1\ \text{g/mL}$

Parts of heavy water in 1 part of water is $\dfrac{1}{6000}$

0.01 mL or 0.01 g of water contains $0.01\times \dfrac{1}{6000}\ \text{g}=m$ of heavy water

Number of moles is given by

$n=\dfrac{m}{M}\\\Rightarrow n=\dfrac{0.01\times \dfrac{1}{6000}}{20}$

Number of molecules is given by

$N_A\times n=6.022\times 10^{23}\times \dfrac{0.01\times \dfrac{1}{6000}}{20}\\ =5.0183\times 10^{16}$

The number of molecules of heavy water is $5.0183\times 10^{16}$.