# How do you find the molarity of a salt solution made by dissolving 280 mg of NaCl in 2.00 mL of solution?

##### 1 Answer

#### Explanation:

In order to be able to determine the molarity of a solution, you basically need to know two things

*how many***moles of solute**you have in your sample*the volume of this sample - expressed in***liters**

Molarity is defined as

#color(blue)("molarity" = "moles of solute"/"liters of solution")#

Your solute is *sodium chloride*, *volume of solution*.

Notice that the problem provides you with the volume of the solution, but that it is expressed in *milliliters*. This means that you will have to convert it to **liters** by using the conversion factor

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

The volume of the solution will thus be

#2.00 color(red)(cancel(color(black)("mL"))) * "1 L"/(10^3color(red)(cancel(color(black)("mL")))) = 2.00 * 10^(-3)"L"#

Now, in order to get the number of moles of solute, you need to use sodium chloride's **molar mass**, which tells you the mass of **one mole** of this compound.

Sodium chloride has a molar mass of **one mole** of sodium chloride has a mass of

Notice that the sample you have is expressed in *milligrams*. Once again, a unit conversion is in order.

#280 color(red)(cancel(color(black)("mg"))) * "1 g"/(10^3color(red)(cancel(color(black)("mg")))) = 280 * 10^(-3)"g"#

This means that your sample will contain

#280 * 10^(-3)color(red)(cancel(color(black)("g NaCl"))) * "1 mole NaCl"/(58.44color(red)(cancel(color(black)("g NaCl")))) = 4.79 * 10^(-3)"moles NaCl"#

Therefore, the molarity of this solution will be

#color(blue)(c = n/V)#

#c = (4.79 * color(purple)(cancel(color(black)(10^3)))"moles")/(2.00 * color(purple)(cancel(color(black)(10^3)))"L") = "2.395 M"#

Rounded to two sig figs, the number of sig figs you have for the mass of sodium chloride, the answer will be

#c = color(green)("2.4 M")#

**SIDE NOTE** *Because sodium chloride is soluble in aqueous solution, which means that it exists as sodium cations*, *and chloride anions*, *you wouldn't actually say that you have a* *sodium chloride solution*.

*Instead, you would say that you have a solution that is* *in* *and* *in*