How do I compute the errors? Th eamount of cadmium in a sample was determined us

Question

How do I compute the errors?

Th eamount of cadmium in a sample was determined using absorption spectroscopy as an analytical tecnique. Signals from a set of standards were measured and the resulting calibration curve was fit by a straight line with equation

signal=y-int + slope [Cd]

y-int=0.0158 +/- 0.0276     slope= 0.1791 +/- 0.0126

where [Cd] is measured in ppm. The unknown sample prodced a signal=1.341 +/- 0.076. Determine the concentration and uncertainty of cadmium in the unknown sample.

MY WORK

I rearranged the equation : [Cd]=signal - y /m

                                       [Cd] = [1.341 +/- 0.076) - (0.0158 +/- 0.0276)] / 0.1791 (+/- 0.0126)

Do I calculate the relative errors first for all and then just subtract and add OR

work out the numerator separately from the denominator?

What is the final result?

Explanation / Answer

I believe you need to find the uncertainty involved. Therefore try to find the max value of Cd and the min value of Cd and you will have your uncertainty. As for the concenteration just take the values given for the without the errors.

Concenteration =1.2528

Maximum value= 1.341+.076- (.0158-.0276)/(.1791+.0126)= 1.4786

Min Value= 1.341-.076-(.0158+.0276)/(.1791-.0126)= 1.0043

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