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

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.