Calculator of Alexandria

Molarity calculator

Find the mass of reagent to weigh out for a solution of a given molarity and volume, or solve for concentration, volume or molar mass.

Solve for

Formula weight from the reagent label. 58.44 g/mol is NaCl.

Formula

m=C⋅V⋅Mwm = C \cdot V \cdot M_w
How it's derived

The formula

m=C⋅V⋅Mwm = C \cdot V \cdot M_w

where mm is the mass of solute, CC is the molar concentration, VV is the volume of solution and MwM_w is the molar mass of the solute.

Where it comes from

Molarity is defined as the amount of solute, in moles, per litre of solution:

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

Rearranging gives the number of moles you need in a given volume:

n=C⋅Vn = C \cdot V

You can’t weigh moles directly, but the molar mass links moles to grams. By definition MwM_w is the mass of one mole, so

Mw=mn⇒n=mMwM_w = \frac{m}{n} \quad\Rightarrow\quad n = \frac{m}{M_w}

Setting the two expressions for nn equal and solving for mm:

mMw=C⋅V⇒m=C⋅V⋅Mw\frac{m}{M_w} = C \cdot V \quad\Rightarrow\quad m = C \cdot V \cdot M_w

The units check out: mol/L×L×g/mol=g\text{mol/L} \times \text{L} \times \text{g/mol} = \text{g}.

Worked example

To make 500 mL of 150 mM NaCl (Mw=58.44M_w = 58.44 g/mol):

m=0.150 molL×0.500 L×58.44 gmol=4.38 gm = 0.150\ \tfrac{\text{mol}}{\text{L}} \times 0.500\ \text{L} \times 58.44\ \tfrac{\text{g}}{\text{mol}} = 4.38\ \text{g}

Watch out for

  • Use the formula weight on your bottle. Hydrates weigh more than the anhydrous salt. CaCl₂·2H₂O is 147.01 g/mol, while anhydrous CaCl₂ is 110.98 g/mol.
  • Volume means final volume. Dissolve the solute in less than the target volume, then bring it up to the mark.

Sources

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