Standard addition graph. Tooth enamel consists mainly of the mineral calcium hydroxyapatite, Ca10(PO4)6(OH)2. Trace elements in teeth of archeological specimens provide anthropologists with clues about diet and diseases of ancient people. Students at Hamline University measured strontium in enamel from extracted wisdom teeth by atomic absorption spectroscopy. Solutions were prepared with a constant total volume of 10.0 mL containing 0.750 mg of dissolved tooth enamel plus variable concentrations of added Sr. Added Sr Signal (ng/mL ppb) (arbitrary units) 0 28.0 2.50 34.3 5.00 42.8 7.50 51.5 10.00 58.6 SOURCE: V. J. Porter, P. M. Sanft, J. C. Dempich, D. D. Dettmer, A. E. Erickson, N. A. Dubauskie, S. T. Myster, E. H. Matts, and E. T. Smith, Elemental Analysis of Wisdom Teeth by Atomic Spectroscopy Using Standard Addition, J. Chem. Ed. 2002, 79, 1114. (a) Find the concentration of Sr and its uncertainty in the 10-mL sample solution in parts per billion ng/mL. (b) Find the concentration of Sr in tooth enamel in parts per million g/g. (c) If the standard addition intercept is the major source of uncertainty, find the uncertainty in the concentration of Sr in tooth enamel in parts per million. (d) Find the 95% confidence interval for Sr in tooth enamel.

Problem 5-25

Standard addition graph. Tooth enamel consists mainly of the mineral calcium hydroxyapatite, Ca10(PO4)6(OH)2. Trace elements in teeth of archeological specimens provide anthropologists with clues about diet and diseases of ancient people. Students at Hamline University measured strontium in enamel from extracted wisdom teeth by atomic absorption spectroscopy. Solutions were prepared with a constant total volume of 10.0 mL containing 0.750 mg of dissolved tooth enamel plus variable concentrations of added Sr.

(a) Find the concentration of Sr and its uncertainty in the 10-mL sample solution in parts per billion = ng/mL.

(b) Find the concentration of Sr in tooth enamel in parts per million = ?g/g.

(c) If the standard addition intercept is the major source of uncertainty, find the uncertainty in the concentration of Sr in tooth enamel in parts per million.

(d) Find the 95% confidence interval for Sr in tooth enamel.

Step by Step Solution

Step 1 of 4

a)

In the standard addition method, we can draw a graph concentration of added Sr versus signal. And then it gives a straight line and magnitude of x - intercept is the unknown concentration of Sr.

The graph is as follows.

In the above graph , the straight line is the magnitude of x - intercept is 8.70.

Therefore, the concentration of Sr is 8.70 ng/ml.

The uncertainty of x - intercept can be calculated by the following formula.

= Standard deviation of y

m = Slope of the least square line

n = Number of measurements

= mean value of x

= mean value of y

Use the least square analysis to find the uncertainty in x - intercept.

From the table uncertainty in x - intercept is 0.43 (least value).

Therefore, the concentration of Sr in a 10 ml sample is

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