# How many moles of potassium chloride, KCl, are needed to make 100.0 mL of a 2.0 M KCl solution?

Jun 10, 2017

$\text{0.20 moles KCl}$

#### Explanation:

The thing to remember about a solution's molarity is that you can express it as a fraction that has $\text{1 L}$ of solution as the denominator.

In your case, a $\text{2.0-M}$ potassium chloride solution contains $2.0$ moles of potassium chloride, the solute, for every $\text{1 L}$ of solution, which means that you can write it as

$\text{2.0 M" = "2.0 moles KCl"/"1 L solution}$

Now, you should know that

$\text{1 L} = {10}^{3}$ $\text{mL}$

This means that you can rewrite the molarity of the solution as

"2.0 M" = "2.0 moles KCl"/(10^3color(white)(.)"mL solution")

So, you need to figure out how many moles of potassium chloride must be dissolved in water to make $\text{100.0 mL}$ of $\text{2.0 M}$ solution.

In other words, you must find the number of moles that when dissolved in $\text{100.0 mL}$ are equivalent to $2.0$ moles dissolved in ${10}^{3}$ $\text{mL}$ of solution.

(color(blue)(?)color(white)(.)"moles KCl")/"100.0 mL solution" = "2.0 moles KCl"/(10^3color(white)(.)"mL solution")

Solve this equation to find

color(blue)(?) = (100.0 color(red)(cancel(color(black)("mL solution"))))/(10^3color(red)(cancel(color(black)("mL solution")))) * "2.0 moles"

color(blue)(?) = "0.20 moles" -> rounded to two sig figs

Therefore, you can say that if you dissolve $0.20$ moles of potassium chloride in enough water to make $\text{100.0 mL}$ of solution, you will have a $\text{2.0-M}$ solution.