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)(25%)

The question you've asked requires a few steps to solve. Here's how you can do it:

(i) To predict the concentration of selenium in the solution, we need to establish a relationship between the concentration and the signal. This is typically done by creating a calibration curve, which is a graph of concentration vs. signal. In this case, we can see that the relationship is linear, meaning that as the concentration increases, the signal also increases proportionally.

To find the equation of the line, we can use the formula y = mx + b, where m is the slope of the line, b is the y-intercept, x is the concentration, and y is the signal.

First, we need to calculate the slope (m). This can be done by taking two points from the table (for example, (20, 2.25) and (160, 18.9)) and using the formula m = (y2 - y1) / (x2 - x1).

Next, we calculate the y-intercept (b) by rearranging the equation to b = y - mx and substituting one of the points from the table.

Once we have the equation of the line, we can substitute the average signal (8.67) into the equation and solve for x, which will give us the predicted concentration of selenium in the solution.

(ii) The standard uncertainty of the result due to the calibration curve can be calculated using the formula u(c) = sqrt[sigma^2 + (mu(y))^2 + (xu(m))^2], where u(c) is the uncertainty in the concentration, sigma is the standard deviation of the y-intercept, m is the slope, u(y) is the uncertainty in the signal, and x is the concentration.

The standard deviation of the y-intercept can be calculated using the residuals from the calibration curve, and the uncertainties in the signal and slope can be estimated from the data.

Please note that this is a simplified explanation and the actual calculations may require more detailed statistical analysis.