# Question f2d31

Nov 24, 2017

${\text{0.270 mol L}}^{- 1}$

#### Explanation:

Your starting point here will be to pick a sample of this potassium chloride solution. To make the calculations easier, let's pick a sample that contains exactly $\text{1 kg}$ of water, the solvent.

As you know, the molality of the solution tells you the number of moles of solute present in exactly $\text{1 kg}$ of the solvent.

In your case, a $\text{0.273-m}$ potassium chloride solution contains $0.273$ moles of potassium chloride, the solute, for every $\text{1 kg}$ of water. This implies that our sample, which contains exactly $\text{1 kg}$ of water, will also contain $0.273$ moles of potassium chloride.

Use the molar mass of potassium chloride to convert the number of moles to grams

0.273 color(red)(cancel(color(black)("moles KCl"))) * "74.55 g"/(1color(red)(cancel(color(black)("mole KCl")))) = "20.35 g"

So, this sample contains $\text{1 kg} = {10}^{3}$ $\text{g}$ of water and $\text{20.35 g}$ of potassium chloride, which means that it has a total mass of

${10}^{3} \textcolor{w h i t e}{.} \text{g" + "20.35 g" = "1020.35 g}$

Next, use the density of the solution to find its volume.

1020.35 color(red)(cancel(color(black)("g solution"))) * "1 L solution"/(1.011 * 10^3color(red)(cancel(color(black)("g")))) = "1.00925 L solution"

Now, in order to find the molarity of the solution, you need to figure out how many moles of solute are present in exactly $\text{1 L}$ of the solution.

Use the fact that $\text{1.00925 L}$ of this solution contain $0.273$ moles of potassium chloride to find the number of moles present in exactly "1 L"3 of the solution.

1 color(red)(cancel(color(black)("L solution"))) * "0.273 moles KCl"/(1.00925color(red)(cancel(color(black)("L solution")))) = "0.270 moles KCl"

You can thus say that this solution has a molarity of

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{molarity = 0.270 mol L}}^{- 1}}}}$

The answer is rounded to three sig figs, the number of sifg figs you have for your data.