# What is the molarity of a solution in which 6.9mol of potassium chloride is dissolved in water to a final volume of 1.8L?

Jul 1, 2016

${\text{3.8 mol L}}^{- 1}$

#### Explanation:

Molarity is a measure of a solution's concentration in terms of how many moles of solute you get per liter of solution.

The unit of volume selected for molarity is one liter, $\text{1 L}$. This means that your ultimate goal when calculating a solution's molarity is to figure out how many moles of solute are present in $\text{1 L}$ of solution.

In your case, the solution is said to contain $6.9$ moles of potassium chloride, $\text{KCl}$, your solute, in $\text{1.8 L}$ of solution.

Now, a solution is characterized by the fact that the solute and the solvent, which in your case is water, are evenly mixed. This implies that any sample of this solution will have the same concentration, since scaling down the volume will also scale down the number of moles of solute it contains.

You can thus use the volume of the solution to figure out how many moles of solute you'd get in $\text{1 L}$ of solution

1.0 color(red)(cancel(color(black)("L solution"))) * "6.9 moles KCl"/(1.8 color(red)(cancel(color(black)("L solution")))) = "3.833 moles KCl"

So, if $\text{1 L}$ of solution contains $3.833$ moles of solute, it follows that the molarity of the solution will be

"molarity" = color(green)(|bar(ul(color(white)(a/a)color(black)("3.8 mol L"^(-1))color(white)(a/a)|))) -> rounded to two sig figs