By Riti Gupta
Updated Mar 24, 2022

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In a laboratory setting, expressing solution concentration can be done in several ways. The most common expressions are:

• Molarity (M): moles of solute per liter of solution (mol/L)
• Weight‑by‑Volume (w/v): grams of solute per milliliter of solution (g/mL)
• Weight‑by‑Weight (w/w): grams of solute per gram of solution (g/g)
• Volume‑by‑Volume (v/v): milliliters of solute per milliliter of solution (mL/mL)

This article focuses on the w/v designation, which is particularly useful when a dry solute is weighed and dissolved in a liquid solvent.

Why Use W/V?

W/v is preferred when you can directly measure the mass of a solid reagent. For example, if you weigh 5 g of KCl and dissolve it in water to a final volume of 100 mL, you have a 5 % w/v KCl solution. The concentration is simply the mass of solute divided by the total volume of the solution, expressed as a percentage.

The calculation is: \( \mathrm{w/v\% = \frac{\text{mass of solute in g}}{\text{volume of solution in mL}} \times 100\%} \)

Preparing Solutions with a Target W/V Concentration

Suppose you need 100 mL of a 17 % w/v sodium azide solution. Using the formula above: \( \mathrm{17\% = \frac{\text{mass of NaN}_3\text{ in g}}{100\text{ mL}} \times 100\%} \)

Solving gives a required mass of 17 g of sodium azide. Weigh this amount and dilute with water to reach 100 mL.

Conversely, if you already have a solution containing 45 g of magnesium acetate in a total volume of 245 mL, the w/v concentration is: \( \mathrm{w/v\% = \frac{45\text{ g}}{245\text{ mL}} \times 100\% = 18.4\%} \)

W/v calculations avoid the need to determine moles, making them straightforward and efficient for routine preparations.

Converting W/V to Molarity

When a w/v concentration is given and molarity is required, follow these steps. Assume a 21 % w/v NaCl solution.

First, determine the mass of NaCl in 100 mL: \( \mathrm{21\% = \frac{\text{mass of NaCl in g}}{100\text{ mL}} \times 100\%} \ \Rightarrow \text{mass of NaCl} = 21\text{ g} \)

Convert grams to moles using the molar mass of NaCl (58.44 g/mol): \( \mathrm{\frac{21\text{ g NaCl}}{58.44\text{ g/mol}} = 0.36\text{ mol NaCl}} \)

Finally, calculate molarity by dividing moles by the solution volume in liters (0.1 L): \( \mathrm{\frac{0.36\text{ mol}}{0.1\text{ L}} = 3.6\text{ M NaCl}} \)

Thus, a 21 % w/v NaCl solution corresponds to a 3.6 M solution.

By mastering w/v calculations and conversions, you can confidently prepare accurate solutions and translate concentrations across different units.