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

Answer 1

Owen Ambrose

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:

Consequently:

#"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")#

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Answer 2

Luna Chen

To convert from %"w/v" to molarity, divide the percent mass/volume by the molecular weight and multiply by 10.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.