Question

5.85 g NaCl is dissolved in 1 L water. The number of ions of ${ Na }^{ + }$ and ${ Cl }^{ - }$ in 1 mL of this solution will be:
(a) 6.02$\times { 10 }^{ 19 }$
(b) 1.2$\times { 10 }^{ 22 }$
(c) 1.2$\times { 10 }^{ 20 }$
(d) 6.02$\times { 10 }^{ 20 }$

Answer 1

Hint: NaCl is a strong electrolyte and hence it dissociates completely in water. Therefore one formula unit of NaCl will dissociate to give one ${ Na }^{ + }$ ion and one ${ Cl }^{ - }$ ion, a total of two ions.

Complete step by step answer:
We can solve this question in the following way:
The molar mass of NaCl is 58.44 g/mol. The number of moles of a substance is the ratio of is mass to its molar mass:
$\begin{matrix} Number\ of\ moles \\ of\ a\ substance\ (n) \end{matrix} = \cfrac { mass\ in\ g }{ Molar\ mass\ in\ g/mol } $
$\Rightarrow \begin{matrix} Number\ of\ moles \\ of\ a\ NaCl\ (n) \end{matrix} = \cfrac { 5.85\ g }{ 58.44\ g/mol } = 0.10\ mol$.

0.10 mole of NaCl is present in 1 Litre of water, Hence the number of moles of NaCl present in 1 mL of the solution is = $\cfrac { 0.1.\ mol }{ 1000\ mL } \times 1\ mL = 0.0001\ mol$.

NaCl is a strong electrolyte, therefore it will dissociate completely into its constituent ions. Therefore one formula unit of NaCl will dissociate to give one ${ Na }^{ + }$ ion and one ${ Cl }^{ - }$ ion; in total two ions. Therefore 0.0001 moles of NaCl will give 0.0001 moles of ${ Na }^{ + }$ ions and 0.0001 moles of ${ Cl }^{ - }$ ion. Hence the total number of ions in 0.0001 moles of NaCl is 0.0002 moles.

Now, 1 mole of a species contains $6.023\times { 10 }^{ 23 } $ number of atoms/molecules/ions/any other species. Therefore 0.0002 moles will have = $0.0002\times 6.023\times { 10 }^{ 23 }ions = 1.205\times { 10 }^{ 20 }ions $.

Hence the correct answer to the above question is (c) 1.2$\times { 10 }^{ 20 }$.

Note: Always remember that in this case the electrolyte given was a strong electrolyte, therefore it dissociated completely. This is not the case with weak electrolytes which only partially dissociate in a solution because of their low value of the dissociation constant. In such a case if we want to know the number of ions formed by the weak electrolyte, then we would have to calculate its degree of dissociation.