In the determination of selenium content in soil samples, the following table shows theinstrument response against the concentration of selenium solution.Concentration (ppm) Signal20 2.2540 4.7880 9.98120 14.2160 18.9(i) A soil sample solution was measured three times and gave an average signal of8.67. Calculate the predicted concentration of selenium in the solution from thecalibration curve above.(ii) Calculate also the standard uncertainty of the result in part (a) due to thecalibration curve.(See example on Appendix 1 of "Principles of Instrumental Analysis" fromHoller, Skoog and Crouch)
Question
In the determination of selenium content in soil samples, the following table shows theinstrument response against the concentration of selenium solution.Concentration (ppm) Signal20 2.2540 4.7880 9.98120 14.2160 18.9(i) A soil sample solution was measured three times and gave an average signal of8.67. Calculate the predicted concentration of selenium in the solution from thecalibration curve above.(ii) Calculate also the standard uncertainty of the result in part (a) due to thecalibration curve.(See example on Appendix 1 of "Principles of Instrumental Analysis" fromHoller, Skoog and Crouch)
Solution
(i) To calculate the predicted concentration of selenium in the solution, we first need to establish the relationship between the concentration and the signal. This can be done by plotting the data and fitting a line to it. The relationship appears to be linear, so we can use the equation of a straight line, y = mx + c, where y is the signal, x is the concentration, m is the slope of the line, and c is the y-intercept.
From the data, we can calculate the slope (m) as the change in signal divided by the change in concentration. For example, between 20 ppm and 40 ppm, the signal changes from 2.25 to 4.78. So, m = (4.78 - 2.25) / (40 - 20) = 0.1265.
The y-intercept (c) can be calculated by rearranging the equation to c = y - mx. Using the data point for 20 ppm, c = 2.25 - 0.1265 * 20 = 0.47.
So, the equation of the line is y = 0.1265x + 0.47.
Now, we can use this equation to calculate the concentration (x) for the average signal of 8.67. Rearranging the equation to x = (y - c) / m, we get x = (8.67 - 0.47) / 0.1265 = 64.8 ppm.
(ii) The standard uncertainty of the result due to the calibration curve can be calculated by taking the standard deviation of the residuals (the differences between the observed and predicted signals for each data point). This requires calculating the predicted signal for each data point, subtracting the observed signal, squaring the result, summing these squared differences, dividing by the number of data points minus 2, and taking the square root.
However, without the actual data points, it's not possible to calculate this value.
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