6.5 - Concentration of Aqueous Solution

Meaning and Units of Concentration

• Concentration measures the quantity of solute dissolved in a unit volume of solution, normally $1\mathrm{d}{\mathrm{m}}^3$.

$\text{Concentration }(\mathrm{g}\mathrm{d}{\mathrm{m}}^{-3})=\frac{\text{mass of solute }(\mathrm{g})}{\text{volume of solution }(\mathrm{d}{\mathrm{m}}^3)}$

• Molarity is the number of moles of solute in $1\mathrm{d}{\mathrm{m}}^3$ of solution.

$M=\frac{n}{V}$

where $M$ is in $\mathrm{mol}\mathrm{d}{\mathrm{m}}^{-3}$, $n$ in mol and $V$ in $\mathrm{d}{\mathrm{m}}^3$. Also, $1\mathrm{d}{\mathrm{m}}^3=1000\mathrm{c}{\mathrm{m}}^3$.

Converting Concentration and Molarity

$\text{Concentration }(\mathrm{g}\mathrm{d}{\mathrm{m}}^{-3})=M\times \text{molar mass }(\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1})$

$M=\frac{\text{concentration }(\mathrm{g}\mathrm{d}{\mathrm{m}}^{-3})}{\text{molar mass }(\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1})}$

• Example: $0.5\mathrm{mol}\mathrm{d}{\mathrm{m}}^{-3}$ $\mathrm{HN}{\mathrm{O}}_3$ has molar mass $63\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ and concentration $31.5\mathrm{g}\mathrm{d}{\mathrm{m}}^{-3}$.

Number of Moles in a Solution

For volume in $\mathrm{d}{\mathrm{m}}^3$, $n=MV$. For volume in $\mathrm{c}{\mathrm{m}}^3$:

$n=\frac{MV}{1000}$

• Account for ions per formula unit after dissociation: one mole of $\mathrm{Ba}(\mathrm{OH}{)}_2$ supplies two moles of $\mathrm{O}{\mathrm{H}}^{-}$.