Question

How do you calculate the mass of NaCl required to prepare 0.5 liters of a 2.5 molar solution of NaCl?

Answer 1

Here's how you can do that.

Explanation:

Your starting point here will be the definition of molarity.

As you know, molarity is defined as the number of moles of solute present in exactly `"1 L"` of solution. This implies that a `"1-M"` solution will contain `1` mole of solute in `"1 L"` of solution.

In your case, a `"2.5-M"` solution will contain `2.5` moles of sodium chloride, your solute, for every `"1 L"` of solution. It follows that this sample must contain

`0.5 color(red)(cancel(color(black)("L solution"))) * overbrace("2.5 moles NaCl"/(1color(red)(cancel(color(black)("L solution")))))^(color(blue)("required molarity")) = "1.25 moles NaCl"`

Now, to convert this to grams of sodium chloride, you must use the mass of `1` mole of this compound as a conversion factor. The mass of `1` mole of sodium chloride is given by its molar mass

`1.25 color(red)(cancel(color(black)("moles NaCl"))) * "58.44 g"/(1color(red)(cancel(color(black)("mole NaCl")))) = color(darkgreen)(ul(color(black)("73 g")))`

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one significant figure for the volume of the solution.