Question

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

Answer 1

`"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 `"1 L"` of solution as the denominator.

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

`"2.0 M" = "2.0 moles KCl"/"1 L solution"`

Now, you should know that

`"1 L" = 10^3` `"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 `"100.0 mL"` of `"2.0 M"` solution.

In other words, you must find the number of moles that when dissolved in `"100.0 mL"` are equivalent to `2.0` moles dissolved in `10^3` `"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 `"100.0 mL"` of solution, you will have a `"2.0-M"` solution.