Question

What is the molarity of a salt solution made by dissolving 280.0 mg of `NaCl` in 2.00 mL of water?

Assume the final volume is the same as the volume of the water.

Answer 1

`"2.40 M"`

Explanation:

The molarity of a solution tells you how many moles of solute you get per liter of solution.

Notice that the problem provides you with the volume of the solution expressed in milliliters, `"mL"`. Right from the start, you should remember that you must convert this volume to liters by using the conversion factor

`"1 L" = 10^3"mL"`

Now, in order to get the number of moles of solute, you must use its molar mass. Now, molar masses are listed in grams per mol, `"g mol"^(-1)`, which means that you're going to have to convert the mass of the sample from milligrams to grams

`"1 g" = 10^3"mg"`

Sodium chloride, `"NaCl"`, has a molar mass of `"58.44 g mol"^(-1)`, which means that your sample will contain

`overbrace(280.0 color(red)(cancel(color(black)("mg"))) * (1color(red)(cancel(color(black)("g"))))/(10^3color(red)(cancel(color(black)("mg")))))^(color(purple)("unit conversion")) * overbrace("1 mole NaCl"/(58.44color(red)(cancel(color(black)("g")))))^(color(brown)("molar mass")) = "0.004791 moles NaCl"`

This means that the molarity of the solution will be

`color(blue)(c = n_"solute"/V_"solution")`

`c = "0.004791 moles"/(2.00 * 10^(-3)"L") = color(green)("2.40 M")`

The answer is rounded to three sig figs, the number of sig figs you have for the volume of the solution.