Standard addition ($c_x=-x_0{V}_f/V_x$)

Standard addition is a measurement calibration procedure that measures an unknown sample both before and after adding known amounts of its analyte. The additions probe sensitivity in the sample's own sample matrix. IUPAC identifies a multiplicative analytical matrix effect as a setting in which this procedure gives an unbiased result.^[ref]

For an original equal-final-volume design, place sample volume $V_x$ in each flask, add standard concentration $c_s$ at different volumes $V_s$, and dilute every flask to $V_f$. Suppose the background-corrected signal is linear:The unknown original concentration is $c_x$; the same sensitivity $k$ must apply to native and added analyte. Plotting $y$ against added final concentration $x=c_s{V}_s/V_f$ gives a regression intercept $a=k{c}_x{V}_x/V_f$ and slope $k$. Its extrapolated horizontal intercept is $x_0=-a/k$, soThe negative intercept is an extrapolation to cancellation of the modeled native amount, not a physically prepared negative-concentration solution.

Take $V_x=5.00$ mL, $V_f=25.00$ mL and $c_s=10.0\mathrm{mg}{\mathrm{L}}^{-1}$. Standard volumes 0, 1.00 and 2.00 mL produce final added concentrations 0, 0.400 and $0.800\mathrm{mg}{\mathrm{L}}^{-1}$. Hypothetical corrected signals 0.120, 0.200 and 0.280 give $k=0.200\mathrm{L}\mathrm{m}{\mathrm{g}}^{-1}$, $x_0=-0.600\mathrm{mg}{\mathrm{L}}^{-1}$ and original $c_x=3.00\mathrm{mg}{\mathrm{L}}^{-1}$.

An unremoved constant background of 0.040 would instead shift the intercept and imply $4.00\mathrm{mg}{\mathrm{L}}^{-1}$. Standard addition does not automatically eliminate an additive interference. It also cannot repair nonlinear response, changing sample matrix, or unequal chemical availability of native and added analyte. Matched volumes, suitable blanks and additions spanning a useful signal range test those assumptions. Since the result involves an extrapolated intercept and fitted slope, their covariance matters in uncertainty propagation.