# Question 641fa

May 28, 2015

You start by writing the dissociation eqution for potassium sulfate, ${K}_{2} S {O}_{4}$, in aqueous solution.

Because potassium sulfate is a soluble compound, it will dissociate completely to form potassium cations, ${K}^{+}$, and sulfate anions, $S {O}_{4}^{2 -}$

${K}_{2} S {O}_{4 \left(a q\right)} \to \textcolor{red}{2} {K}_{\left(a q\right)}^{+} + S {O}_{4 \left(a q\right)}^{2 -}$

Notice that each mole of potassium sulfate produces $\textcolor{red}{2}$ moles of potassium cations in solution. So, if you have 2.5 moles of potassium sulfate, you'll get

2.5cancel("moles"K_2SO_4) * (color(red)(2)" moles" K^(+))/(1cancel("mole"K_2SO_4)) = "5.0 moles"# ${K}^{+}$

To determine the exact number of ions you'd get, use the fact that 1 mole of any substance contains exactly $6.022 \cdot {10}^{23}$ atoms or molecules of that substance - this is known as Avogadro's number.

In your case, 5.0 moles of ${K}^{+}$ ions will contain

$5.0 \cancel{\text{moles") * (6.022 * 10^(23)"K"^(+)"ions")/(1cancel("mole")) = color(green)(3.0 * 10^(24)"K"^(+)"ions}}$

SIDE NOTE If you were actually dealing with a 2.5-M solution, and since no volume was given to you, you can assume a 1-L sample to get the exact same values I got.