Question #641fa

You start by writing the dissociation eqution for potassium sulfate, `K_2SO_4`, in aqueous solution.

Because potassium sulfate is a soluble compound, it will dissociate completely to form potassium cations, `K^(+)`, and sulfate anions, `SO_4^(2-)`

`K_2SO_(4(aq)) -> color(red)(2)K_((aq))^(+) + SO_(4(aq))^(2-)`

Notice that each mole of potassium sulfate produces `color(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 * 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

`5.0cancel("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.