# Question #31da1

##### 2 Answers

27.745 g of calcium chloride

#### Explanation:

Molarity is number of moles of solute per litre of solution. You need to determine the number of grams of solute, so first you need to know the number of moles.

Rearranging Molarity = moles / litres gives Moles = Litres x molarity.

125 g of water is equivalent to 125 ml, which is 0.125 litre. Molarity is 2.0M, so the number of moles is 0.125 x 2 = 0.25 mol.

Now simply multiply this by the molar mass of calcium chloride, which is 110.98 g/mol, giving you the answer 27.745 g.

#### Explanation:

A solution's **molality** will tell you how many *moles of solute*, which in your case is calcium chloride, **per kilogram of solvent**.

Basically, molality uses moles of solute and mass of solvent to express the concentration of a given solution.

#color(blue)(|bar(ul(color(white)(a/a)"molality" = "moles of solute"/"kilogram of solution"color(white)(a/a)|)))#

So, you know that your target solution must have a molaity of **every kilogram** of water, which is the solvent, will contain **moles** of calcium chloride.

Now, you know that you only have *conversion factor* to help you determine how many moles of calcium chloride must be dissolved in

Keep in mind that molality uses **kilograms** of solvent, so use the conversion factor

#"1 kg" =10^3"g"#

to go from *grams* of water to *kilograms* of water. You will thus have

#125 * 10^(-3)color(red)(cancel(color(black)("kg water"))) * overbrace("2.0 moles CaCl"_2/(1color(red)(cancel(color(black)("kg water")))))^(color(purple)("equivalent to 2.0 m")) = "0.250 moles CaCl"_2#

To find how many grams of calcium chloride would contain this many moles, use the compound's **molar mass**

#0.250color(red)(cancel(color(black)("moles CaCl"_2))) * "111 g"/(1color(red)(cancel(color(black)("mole CaCl"_2)))) = "27.75 g"#

Rounded to two **sig figs**, the number of sig figs you have for the molality of the target solution, the answer will be

#"mass of CaCl"_2 = color(green)(|bar(ul(color(white)(a/a)"28 g"color(white)(a/a)|)))#

A cool video on *molality* and *molarity*