Question

How do you convert from `%"w/v"` to molarity?

Answer 1

We define `%"w/v"` as:

`%"w/v" = "solute mass in g"/"solution volume in mL" xx 100%`

By unit conversion, we have that `"g" xx "mol"/"g" -> "mol"`, and that `"mL" xx "1 L"/"1000 mL" -> "L"`. Define:

• `m_(solute)` for the solute mass in `"g"`
• `V_(soln)` for the solution volume in `"mL"`
• `M_(solute)` for the molar mass of the solute in `"g/mol"`

Therefore:

`"Molarity" = (m_(solute)/V_(soln) xx 100%) xx (1000 "mL/L")/(100% xx M_(solute))`

Or, rewriting in terms of `%"w/v"` and implied unit cancellation, we have:

`bb("Molarity" ("mol"/"L") = 1000/(M_(solute))(%"w/v")/(100%))`

As an example, if we have a `37%` `"w/v"` aqueous `"HCl"` solution, then:

`color(blue)("Molarity" ("mol"/"L")) = 1000/(36.4609) (37cancel(%) "w/v")/(100cancel(%))`

`=` `color(blue)("10.15 mol/L")`