27.745 g of calcium chloride
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.
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
Now, you know that you only have
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