Appendix

1078 Analytical Chemistry 2.0Table A2.1 Values and Uncertainties for the Standardization of NaOHsource value, x uncertainty, u(x)m KHP mass of KHP 0.3888 g 0.00013 gV NaOH volume of NaOH at end point 18.64 mL 0.013 mLP KHP purity of KHP 1.0 0.00029M KHP molar mass of KHP 204.2212 g/mol 0.0038 g/molR repeatability 1.0 0.00051000× m × PM × VKHP KHPC NaOH=KHPNaOH× RUsing the values from Table A2.1, we find that the concentration of NaOH is1000× 0. 3888×10 .C NaOH=× 10 . = 0. 1021M204. 2212×18.64Because the calculation of C NaOH includes only multiplication and division, the uncertainty in the concentration,u(C NaOH ) is given by the following propagation of uncertainty.uC (NaOH) uC (NaOH)= =C 0.1021 MNaOH( 0. 00013)2( 0.3888)222( 0. 00029)( 0. 0038)( 00 . 13)+ + +22(.) 10 ( 204. 2212)( 18. 64)22( 0. 0005)+2(.) 102Solving for u(C NaOH ) gives its value as ±0.00010 M, which is the final uncertainty for the analysis.Evaluating the Sources of UncertaintyFigure A2.3 shows the relative uncertainty in the concentration of NaOH and the relative uncertaintiesfor each of the five contributions to the total uncertainty. Of the contributions, the most important is thevolume of NaOH, and it is here to which we should focus our attention if we wish to improve the overalluncertainty for the standardization.m KHPP KHPM KHPV NaOHRC NaOHFigure A2.3 Bar graph showing the relative uncertainty inC NaOH , and the relative uncertainty in each of the mainfactors affecting the overall uncertainty.0.0000 0.0002 0.0004 0.0006 0.0008 0.0010relative uncertainty