What is the molarity of a KCl solution made by dissolving 24.7 g of KCl in a total volume of 500. mL?

Feb 27, 2016

Answer:

${\text{0.663 mol L}}^{- 1}$

Explanation:

In order to calculate the molarity of a solution, you need to know two things

• the number of moles of solute present in solution
• the total volume of the solution

The problem provides you with a $\text{24.7-g}$ sample of potassium chloride, $\text{KCl}$, and a total volume of a solution of $\text{500. mL}$.

In order to find the number of moles of potassium chloride, your solute, use the compound's molar mass, which as you know tells you the mass of one mole of potassium chloride

24.7 color(red)(cancel(color(black)("g"))) * overbrace("1 mole KCl"/(74.55color(red)(cancel(color(black)("g")))))^(color(purple)("molar mass of KCl")) = "0.3313 moles KCl"

Now, molarity is expressed per liter of solution. Since you dissolve $0.3313$ moles of potassium chloride in $\text{500. mL}$ of solution, you can say that $\text{1.0 L}$ will contain

1.0color(red)(cancel(color(black)("L"))) * (10^3color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("L")))) * "0.3313 moles"/(500. color(red)(cancel(color(black)("mL")))) = "0.6626 moles KCl"

This means that the molarity of the solution will be

$c = \textcolor{g r e e n}{{\text{0.663 mol L}}^{- 1}}$

The answer is rounded to three sig figs.