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Lesson 40 · Three ways to say how much
Read the denominator
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Read the denominator

Three measures, three denominators, and the denominator is the whole story.

Molarity: C=nVC = \dfrac{n}{V}, C equals n over V. CC is the molar concentration in mol/L, nn is the amount of solute in moles, and VV is the volume of finished solution in litres — not the volume of solvent you started with. It is the working chemist's default because volume is what a pipette measures.

Molality: b=nmsolventb = \dfrac{n}{m_{\text{solvent}}}, b equals n over m-solvent. bb is in mol/kg, nn is again the moles of solute, and msolventm_{\text{solvent}} is the mass of solvent alone, in kilograms, weighed before the solute ever arrived. Masses do not expand when the room warms, so molality holds still where molarity drifts — which is exactly why the colligative laws in the next lesson are written on it.

Mass percent: c=msolutemsolution×100%c = \dfrac{m_{\text{solute}}}{m_{\text{solution}}} \times 100\%. Here msolutem_{\text{solute}} is the solute's mass and msolutionm_{\text{solution}} is the mass of everything in the beaker, solute included. The classic slip is dividing by the solvent instead — the solute is part of what it is a percent OF, so it belongs downstairs too. Notice the family resemblance: molarity's denominator is the solution, molality's is the solvent, and mass percent goes back to the solution. Read the denominator, name the measure.

VCn

C=nVC = \frac{n}{V}

  • CC= Molar concentration (molar concentration)
  • nn= Amount of solute (amount of substance)
  • VV= Volume of solution (volume)
Molarity (C = n/V) solver →
msolventnb

b=nmsolventb = \frac{n}{m_{\text{solvent}}}

  • bb= Molality (molality)
  • nn= Amount of solute (amount of substance)
  • msolventm_{\text{solvent}}= Mass of solvent (mass)
Molality (b = n/m) solver →
msolutemsolutionc

c=msolutemsolution×100%c = \frac{m_{\text{solute}}}{m_{\text{solution}}} \times 100\%

  • cc= Mass percent (concentration)
  • msolutem_{\text{solute}}= Mass of solute (mass)
  • msolutionm_{\text{solution}}= Mass of solution (mass)
Mass Percent of a Solution solver →