## Statistics Problem Set #2e

1. A sample was prepared from 1.3452 g of soil (weighed on an analytical balance). The mercury in this sample was extracted and diluted to 100.0 mL in a class A volumetric flask.
1. Use the data from the standards to construct a calibration curve.
2. Based upon this calibration curve, what is the concentration of mercury in the solution that was analyzed.
3. Based on the concentration of mercury in the solution, what is the concentration of mercury in the original soil sample?
4. What is the uncertainty in the concentration of the mercury in the solution (based upon the uncertainty in the calibration curve)?
5. What is the uncertainty in the concentration of mercury in the original soil sample (by propagating the error from each step)? (Note: the uncertainty in the balance and the volumetric glassware may be treated as population statistics since these are standard deviations for a very large number of measurements.)
6. Based upon the above calculations, how would you report your results?
7. How could you verify the accuracy of your determination?
 Concentration (ppm) Signal LOG(Po/P) 0 0.00236 0.001 -0.00610 0.002 0.00149 0.005 0.00282 0.01 0.00377 0.05 0.02093 0.07 0.02235 0.09 0.03336 0.12 0.04990 0.15 0.05834 0.18 0.06637 Unknown 0.0353

2. A unknown sample was prepared for analysis by inductively coupled plasma emission.
1. Solution A; 0.0153±0.0001 g of unknown was weighed out on an analytical balance, dissolved and diluted to 250.0±0.1 ml in a volumetric flask.
2. Solution B; 100.0±0.2 ml of solution A was transferred to a second flask and diluted to 250.0±0.1 ml.
3. Solution C; 0.0026±0.0001 g of iron was dissolved, 100.0±0.2 ml of solution A was added, and the solution diluted to 250 ml.
4. Giving the following data:

5.

 Trial 1 Trial 2 Trial 3 Blank 0.026 0.037 0.029 Solution B 11.312 11.292 11.299 Solution C 17.399 17.401 17.390
1. What is the concentration of Fe in solution B?
2. What is the weight percent Fe in the unknown sample?
3. Based upon the replicate samples what is the uncertainty in the concentration of Fe in solution B?
4. Use propagation of error to determine the uncertainty in the weight percent of Fe in the unknown sample. Report your results at the 90% confidence level using the t-test.