Question

Your text presents an example of propagation of error through a dilution operation (p.19). Assume that the relative uncertainty of the commercial solution is the same as in the example and that the dilution still yields a final concentration of 1000. ppb.

Recalculate the uncertainty in ppb if the relative uncertainty of the syringe is 0.02302 and the uncertainty of the volumetric flask is 0.1303 mL. The total volume of the flask is still 250.0mL. Report the +/- value in ppb and to 1 decimal place. Don't type in the "=/-" or units, just the number.

Answer 1

Relative uncertanity in volume of the flask = $\frac{0.1303 mL}{250.0 mL}$ = 5.212*10^-4

Relative uncertainty of the syringe = 0.02302 mL

Uncertainty in ppb = $\sqrt{\left ( \textup{uncertainty in syringe }\right )^{2}+\left ( \textup{uncertainty in volume} \right )^{2}}$

= $\sqrt{\left ( 0.02302\right )^{2}+\left ( 5.212\times 10^{-4}\right )^{2}}$

= 0.02 to 1 decimal place