How To Calculate W/v (Weight By Volume)

When making a solution in a lab, there are different ways to express the concentration. Some of the most common ways are listed below:

1. Molarity (M): moles of solute/liters of solution or moles/L (mol/L)
2. w/v (g/mL): weight in grams of solute/milliliters of solute
3. w/w: weight in grams of solute/weight in grams of solution (g/g)
4. v/v: volume of solute/volume of solution (L/L)

Here, the focus will be specifically on how to make solutions with their concentrations expressed as weight by volume or w/v.

Why are there so many different ways to express concentration? Well, it's because not all solutions are made the same way. For example, w/v is often used when a dry solute is weighed out and added to a liquid solvent. You can imagine weighing out KCl and adding it to water. This makes it really easy to express the concentration since you know how much KCl you weighed out.

What does a 5% w/v solution of KCl mean? It means that for every 100 mL of solution you have 5 grams of KCl.

Here is the equation to use when calculating w/v percent for a solution:

\(\mathrm{w/v \% = \dfrac{mass\enspace in\enspace g\enspace of\enspace solute}{volume\enspace in\enspace mL\enspace of\enspace total\enspace solution} \times 100\%}\)

So then, if you were asked to make 100 mL of a 17% w/v solution of sodium azide, how would you do this?

You can make use of the equation above:

\(\mathrm{17 \% = \dfrac{mass\enspace in\enspace g\enspace of\enspace sodium\enspace azide}{100 mL\enspace of\enspace total\enspace solution} \times 100\%}\)

This means that:

\(\mathrm{17 = mass\enspace in\enspace g\enspace of\enspace sodium\enspace azide}\)

In order to make 100 mL of a 17% sodium azide solution, you would need to weigh out 17 grams of sodium azide and then add water until the final volume is 100 mL.

You can make use of this equation in another way. Say you're told that the solution you will be using has 45 grams of magnesium acetate and the total volume is 245 mL. What is the concentration of this solution in w/v percent?

Again, you can make use of the above equation:

\(\mathrm{w/v \% = \dfrac{45\enspace g\enspace magnesium\enspace acetate}{245\enspace mL} \times 100\%}\)

So:

\(\mathrm{w/v \% = 18.4 \%\)

This means that when 45 grams of magnesium acetate are added to a solution that is a total of 245 mL, the w/v percent magnesium acetate is 18.4%.

The great thing about using w/v is that you don't need to worry about calculating moles of the solute which would require an extra step.

Say, however, your teacher gives you 21% (w/v) solution of NaCl and asks you to find the molarity of this solution. How would you do that?

Begin by figuring out how many grams of solute you have in how much solution. Since the amount of solution you have will not change the concentration you can just assume 100 mL of solution.

So then:

\(\mathrm{21 \% = \dfrac{mass\enspace in\enspace g\enspace of\enspace NaCl}{100 mL\enspace of\enspace total\enspace solution} \times 100\%}\)

Solving for the mass of solute you find:

\(\mathrm{21 = mass\enspace in\enspace g\enspace of\enspace NaCl}\)

This means that there are 21 grams of NaCl in every 100 mL of solution. To find molarity you will need to convert this number of grams into moles by using the molar mass of NaCl:

\(\mathrm{21g\enspace NaCl\Biggl(\dfrac{1mol\enspace NaCl}{58.44g\enspace NaCl}\Biggr)=0.36mol\enspace NaCl}\)

To find the molarity, you can divide the number of moles by the volume of the solute (in liters):

\(\mathrm{\dfrac{0.36mol\enspace NaCl}{0.1L}=3.6M\enspace NaCl}\)

This means that a 21% w/v solution of NaCl is the same as a 3.6 solution of NaCl. In this way, you can convert between concentration designations.