University of the West of England
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Method of Standard Additions (Calculation of uncertainty)

The method of ‘standard additions’ is used to measure the amount of silver, Q, in a solution.

In this method, known amounts, x, of silver (measured in μg/ml) are added, and the absorbance, A, of the solution is measured for each value of x using atomic-absorption spectrometry. The results are illustrated in the graph below:

The value of Q is found by extrapolating the best-fit straight line back to the x-axis, and then the intercept on the x-axis (A = 0) is at the point x = – Q.

Enter the following experimental values into an Excel spreadsheet.

 x 0 5 10 15 20 A 0.27 0.36 0.47 0.55 0.65

i)          Draw a suitable graph of A against x, for values of A from 0 to 0.8, and plot the trendline back to the x-axis.

ii)         Enter suitable functions and calculations in your spreadsheet to calculate the best-estimate value for Q (in μg/ml) for the given data.
Assume that the value for A = 0 on the x-axis is an exact value.

iii)         Enter suitable functions and calculations in your spreadsheet to calculate the following values

·         standard deviation uncertainty in Q, u(Q),

·         confidence deviation, Cd(Q),

·         confidence interval, CI(Q).

Note:

You may find the following equation useful for the 95% confidence deviation in an x-y graph for the value, xO, equivalent to the value, yO.

where

 t2,95%,n-2 = appropriate t-value SExy = standard error of regression m = slope of the line of regression  = mean of the calibration data y-values k = number of replicate measurements for yO n = number of calibration data points s2 = sample variance of the calibration data x-values

You may need to use functions SLOPE, INTERCEPT, STEYX, VAR, TINV.

You should perform your calculation in several stages so that it easy to follow and also easy to trace any errors.