What mass of anhydrous calcium chloride, cacl2, should be dissolved in 590.0 grams of water in order to produce a 0.82 m solution

First convert the 590.0 grams of water to liters of water.

590.0 grams x  (1 L / 1000 grams) = 0.59 L

Since we're dealing with concentration, recall this formula:

Molarity (M)  = (moles of solute) / (liters of solution)

We know the Molarity and the Liters

0.82 M = (moles) / 0.59 L

To find the moles multiply 0.59 on both sides.

The result is 0.4838 moles of CaCl (the solute).

Then change moles into grams because the question wants grams.

In order to convert the moles of a substance to grams, you will need to multiply the mole value of the substance by its molar mass which is 110.986.

(0.4838 moles CaCl2) x (110.986 g CaCl)/ 1 mol CaCl2