Gravimetric dilution factor ($F=(m_s+m_d)/m_s$)

The gravimetric dilution factor is the ratio of final mixture mass to the stock mass used in a gravimetric dilution:Here $m_d$ is added diluent mass and $f$ is the retained stock mass fraction. For a diluent containing none of the component being measured, mass conservation gives final component mass fraction $w_f=w_s/F$. This mass-based relation avoids assuming that liquid volumes are additive. Its uncertainty follows from the same input masses and their covariance as the uncertainty of a gravimetric dilution.^[ref]

For an original two-step example, combine $2.000\mathrm{g}$ of stock with $18.000\mathrm{g}$ of diluent, giving $F_1=10$. After complete mixing, transfer $1.000\mathrm{g}$ of that mixture and add $4.000\mathrm{g}$ of diluent, giving $F_2=5$. The combined gravimetric dilution factor isIf the original stock has component mass fraction $0.2000$, the first mixture has $0.02000$ and the final mixture $0.004000$. The transferred gram contains $0.02000\mathrm{g}$ of the component; dividing by the final $5.000\mathrm{g}$ checks the result. This calculation requires a representative, homogeneous transferred portion and no component loss.

State whether a dilution number denotes $F$ or its reciprocal $f$: here a tenfold dilution means $F=10$ and $f=0.1$, not that ten parts of diluent were added per part of stock. The latter recipe gives $F=11$.