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Gravimetric dilution determines a dilution from measured masses. A measured amount of a stock solution is combined with material containing none of the quantity being diluted. For a closed transfer and a homogeneous mixture, the conserved amount divided by the final mass determines the new mass-based concentration.

Let $m_s$ be the stock's net mass, $m_d$ the added net mass, and $M=m_s+m_d$. Define the stock fraction $f$ and the gravimetric dilution factor $F$ byIf the stock has solute mass fraction $w_s$, thenFor stipulated $m_s=2.000\mathrm{g}$, $m_d=18.000\mathrm{g}$ and $w_s=0.2000$, the final mass is $20.000\mathrm{g}$, $F=10$, and $\boxed{w_f=0.02000}$: 2% by mass. The solute mass is $0.4000\mathrm{g}$ before and after dilution. The net masses exclude their containers. This mass basis does not require an assumption that liquid volumes add.

The uncertainty of a gravimetric dilution depends on which readings share errors. For independently evaluated inputs $w_s,m_s,m_d$, first-order propagation of uncertainty givesHere $u$ denotes standard uncertainty. The sensitivity factors follow from the partial derivatives $\partial f/\partial m_s=m_d/M^2$ and $\partial f/\partial m_d=-m_s/M^2$. With a chosen independent $u(m_s)=u(m_d)=0.001\mathrm{g}$ at the example's nominal masses, the relative mass-ratio contribution is approximately 0.0453%. Adding an independent 0.5% relative stock-value contribution in quadrature gives approximately 0.502%. These are illustrative inputs, rather than a balance specification.^[ref]

If input errors have covariance, their cross terms must be retained. A useful exact check isA common multiplicative mass-scale factor therefore cancels from $f$. Counting it as two independent contributions would lose that correlation. Container subtraction, transfer losses and changes in composition require their own assessment; this cancellation establishes only the common-scale property.

For massic activity, the same conservation argument applies after expressing all activities at a common reference time. A 2000 NIST study compared massic activity ratios inferred from gravimetric dilution with independent liquid scintillation counting. Their agreement within reported uncertainties provided an experimental check on transferring standards through mass ratios.^[ref]

A stock solution is a chemical solution kept as a source from which other chemical solutions are prepared, commonly by dilution. Its known concentration makes repeated preparations traceable to one starting composition. A stock used for measurement calibration must also satisfy the requirements of a standard solution; the word stock alone does not establish that status. The original EPA Method200.8 defines calibration standards as dilutions of stock standards used to relate instrument response to analyte concentration.^[ref]

Suppose an invented stock solution has molar concentration $c_s=10.0\mathrm{mmol}{\mathrm{L}}^{-1}$. To obtain final volume $V_f=50.0\mathrm{mL}$ at $c_f=0.200\mathrm{mmol}{\mathrm{L}}^{-1}$, conservation of dissolved amount of substance givesTransfer that aliquot and add solvent to the final 50.0-millilitre mark of a volumetric flask, then mix. Adding 50.0 millilitres of solvent would specify a different operation: the equation requires final total volume.

The same inventory reasoning underlies serial dilution. A tenfold dilution followed by a fivefold dilution gives the same final concentration reduction of50, provided each transferred portion is representative and the counted solute is conserved. Reactions, losses or incomplete mixing would change those premises.