92
2 Analytical Properties
The uncertainties can be calculated from the simplified expression ± U = R . S, with
R = 2 atP = 0.05 (i.e. at the 95% confidence level).
± UA = ± 2 x 0.26 = ± 0.52 }lg/l
± UB = ± 2 x 0.08 = ± 0.16 }lgn
The results for the two experiment series can thus be expressed in full form (including
their respective uncertainties) as
A: 1.75 ± 0.52 }lg/L
B: 1.73 ± 0.16 }lg/L
The higher expeditiousness of method A results in decreased precision (a contradictory relationship between a basic and an accessory analytical property) and hence
in increased uncertainty.
The accuracy of the method cannot be assessed because no appropriate reference
is available. However, one can indeed state that the two methods have a similar bias -
the means are quite similar - and that method A will be less accurate than B because
it is subject to greater uncertainty.
(4) In order to evaluate instrumental precislOn and uncertainty in the
gravimetric determination of nickel in a mineral sample, an amount of
0.8320 g of mineral is weighed and dissolved, and interferents removed. The remaining solution is supplied with NH4ClINH3 and
dimethylglyoxime to precipitate nickel selectively as Ni(DMGh. The
precipitate is flltered, dried at an appropriate temperature and, finally, weighed. The weight thus obtained is 0.391 g. (Random error in the
weighing ± 0.2 mg; molecular weight of DMG 288.71 glmol; atomic weight
of nickel 58.71).
The amount of nickel in the unknown sample is calculated from the following expression:
WNi = nickel weight in the sample
Wat • Ni
58.71
F = gravimetric factor =
= - - = 0.2033
WMNi(DMG)z 288.71
Wg = final gravimetric weighing = 0.3391 g
The final gravimetric weighing is subject to the random errors in two weighings, viz.
that used to tare the crucible and the gravimetric weighing proper. These errors materialize in the combined standard deviation from a subtraction:
sW g = ± ~(0.2)2 + (0.2)2 = ± 0.28 mg '" ± 0.28 mg'" ± 0.3 mg = 3 . 10- 4 g
which is the error in WNi since F is assumed to be subject to no random error.
SWNi = 3 . 10- 4 x 0.203 = 0.6 . 10- 4 g
The initial weighing, Wi' is subject to a standard deviation
SWi = ± 0.20 = 2 . 10- 4 g
The proportion of nickel in the sample will be
WN"
%Ni =-' ·100= 8.31%
WN
2 Analytical Properties
The uncertainties can be calculated from the simplified expression ± U = R . S, with
R = 2 atP = 0.05 (i.e. at the 95% confidence level).
± UA = ± 2 x 0.26 = ± 0.52 }lg/l
± UB = ± 2 x 0.08 = ± 0.16 }lgn
The results for the two experiment series can thus be expressed in full form (including
their respective uncertainties) as
A: 1.75 ± 0.52 }lg/L
B: 1.73 ± 0.16 }lg/L
The higher expeditiousness of method A results in decreased precision (a contradictory relationship between a basic and an accessory analytical property) and hence
in increased uncertainty.
The accuracy of the method cannot be assessed because no appropriate reference
is available. However, one can indeed state that the two methods have a similar bias -
the means are quite similar - and that method A will be less accurate than B because
it is subject to greater uncertainty.
(4) In order to evaluate instrumental precislOn and uncertainty in the
gravimetric determination of nickel in a mineral sample, an amount of
0.8320 g of mineral is weighed and dissolved, and interferents removed. The remaining solution is supplied with NH4ClINH3 and
dimethylglyoxime to precipitate nickel selectively as Ni(DMGh. The
precipitate is flltered, dried at an appropriate temperature and, finally, weighed. The weight thus obtained is 0.391 g. (Random error in the
weighing ± 0.2 mg; molecular weight of DMG 288.71 glmol; atomic weight
of nickel 58.71).
The amount of nickel in the unknown sample is calculated from the following expression:
WNi = nickel weight in the sample
Wat • Ni
58.71
F = gravimetric factor =
= - - = 0.2033
WMNi(DMG)z 288.71
Wg = final gravimetric weighing = 0.3391 g
The final gravimetric weighing is subject to the random errors in two weighings, viz.
that used to tare the crucible and the gravimetric weighing proper. These errors materialize in the combined standard deviation from a subtraction:
sW g = ± ~(0.2)2 + (0.2)2 = ± 0.28 mg '" ± 0.28 mg'" ± 0.3 mg = 3 . 10- 4 g
which is the error in WNi since F is assumed to be subject to no random error.
SWNi = 3 . 10- 4 x 0.203 = 0.6 . 10- 4 g
The initial weighing, Wi' is subject to a standard deviation
SWi = ± 0.20 = 2 . 10- 4 g
The proportion of nickel in the sample will be
WN"
%Ni =-' ·100= 8.31%
WN