# Question 49968

Nov 5, 2017

$4$ moles of ions.

#### Explanation:

The trick here is to realize that potassium nitrate, ${\text{KNO}}_{3}$, is soluble in water, which implies that it dissociates completely in aqueous solution to produce potassium cations and nitrate anions.

${\text{KNO"_ (3(aq)) -> "K"_ ((aq))^(+) + "NO}}_{3 \left(a q\right)}^{-}$

As you can see, for every $1$ mole of potassium nitrate that dissociates, you get $1$ mole of potassium cations and $1$ mole of nitrate anions.

This means that when you dissolve $2$ moles of potassium nitrate in enough water, your solution will contain

2 color(red)(cancel(color(black)("moles KNO"_3))) * "2 moles ions"/(1color(red)(cancel(color(black)("mole KNO"_3)))) = "4 moles ions"#

A solute that produces $2$ moles of particles of solute, which in this case are ions, for every $1$ mole of solute dissolved to make the solution is said to havea van't Hoff factor equal to $2$.

If you want the actual number of ions formed in the solution, use the fact that $1$ mole of ions contains $6.022 \cdot {10}^{23}$ ions $\to$ this is known as Avogadro's constant, ${N}_{\text{A}}$.

So in your case, the number of ions produced in the solution would be equal to $4 \cdot {N}_{\text{A}}$.