Let C stand for concentration. One definition of spike recovery is$\mathbf{\%}\mathbf{}\mathbf{recovery}\mathbf{=}\frac{{\mathbf{C}}_{\mathbf{spiked}\mathbf{}\mathbf{sample}}\mathbf{}\mathbf{-}{\mathbf{C}}_{\mathbf{unspiked}\mathbf{}\mathbf{sample}}}{{\mathbf{C}}_{\mathbf{aded}}}\mathbf{\times }\mathbf{100}$

An unknown was found to contain$\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{\mu g}$of analyte per liter. A spike ofrole="math" localid="1654945506958" $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{\mu g}\mathbf{/}\mathbf{L}$was added to a replicate portion of unknown. Analysis of the spiked sample gave a concentration of$\mathbf{15}\mathbf{.}\mathbf{3}\mathbf{\mu g}\mathbf{/}\mathbf{L}$Find the percent recovery of the spike.

A spike, also called a fortification, is a known quantity of analyte added to a sample to test whether the response to the spike is the same as that expected from a calibration curve.

Spiked samples are analysed in the same manner as unknowns.

For example, if drinking water is found to contain $\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{\mu g}$of nitrate, a spike of$\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{\mu g}\mathbf{/}\mathbf{L}$could be added. Ideally, the concentration in the spiked portion found by analysis will be$\mathbf{15}\mathbf{.}\mathbf{0}\mathbf{\mu g}\mathbf{/}\mathbf{L}\mathbf{.}$If a number other than $\mathbf{15}\mathbf{.}\mathbf{0}\mathbf{\mu g}\mathbf{/}\mathbf{L}$is found, then the matrix could be interfering with the analysis.

$\%\mathrm{recovery}=\frac{{\mathrm{C}}_{\mathrm{spiked}\mathrm{sample}}-{\mathrm{C}}_{\mathrm{unspiked}\mathrm{sample}}}{{\mathrm{C}}_{\mathrm{aded}}}\times 100$

The percent of the spike found by analysis is

$$\begin{gathered} \%recovery \\ =\frac{15.3\mu g/L-10.0\mu g/L}{5.0\mu g/L}\times 100 \\ =106\% \end{gathered}$$

If the acceptable recovery is specified to be in the range from$96\%\mathrm{to}115\%\mathrm{then}106\%$ is unacceptable. Something in your method or techniques needs improvement.