Question

Standard addition graph. Tooth enamel consists mainly of the mineral calcium hydroxyapatite,$C_{10}{\left(P{A}_4\right)}_6{\left(OH\right)}_2$. Trace elements in teeth of archeological specimens provide anthropologists with clues about diet and diseases of ancient people. Students at Hamline University used atomic absorption spectroscopy to measure strontium in enamel from extracted wisdom teeth. Solutions were prepared with a constant total volume of $10.0mL$containing role="math" localid="1667792217398" $0.750mg$of dissolved tooth enamel plus variable concentrations of added Sr.

(a) Find the concentration of Sr and its uncertainty in therole="math" localid="1667792593357" $10-mL$sample solution in parts per billion =$ng/mL$.

(b) Find the concentration of Sr in tooth enamel in parts per million =$\mu \frac{g}{g}$.

(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.

Short answer

1. Concentration,$x=-8.72ng/mL$ ; Uncertainty,$u_x=0.43ppb$.
2. Concentration of Sr in tooth enamel =$116.27\mu g/g$.
3. The uncertainty in the concentration of Sr in tooth enamel= $5.72ppm$.
4. confidence interval =$18.2ppm$.

Step-by-step solution

Absorbance definition

Concentration is defined as the abundance of an ingredient divided by the total volume of a mixture in chemistry.

Uncertainty refers to the range of probable values in which the measurement's true value can be found.

Given information:

We are given the following:

Total volume of solution$=10mL$

The mass of dissolved tooth$=0.75mg$

Solving for part (a)

First, we'll plot the extra Sr Vs signal using the table provided:

Using the equation of the straight line, the concentration ofSris found whenyequals0, so:

y=(3.136x)+27.36 0=(3.136x)+27.36 x=-8.72ng/mL

The negative sign indicates that the point is located in the negativex-axis.

The standard uncertainty of the $x$-intercept is expressed in the below equation:

$u_x=\frac{s_y}{\left|m\right|}\times \sqrt{\frac{1}{n}+\frac{y^{-2}}{m^2\times \sum _{}{\left(x_i-x\right)}^2}}$

Where:

syis the standard deviation

|m|is the absolute value of the slope

nis the number of data points

yis the mean value ofy

x_iis the individual values ofX

xis the mean value ofx

After calculating the above values using excel:

$u_x=0.43ppb$

Solving for part (b)

The concentration of Sr found in parta=8.72ng/mL

Since the volume of solution is10mL:

Mass ofSr=8.72ng/mL10mL=87.2ng

The mass of dissolved tooth is given in the question, so to find the concentration(m/m)ing/g

$\frac{87.2ng}{0.75mg}\times \frac{1mg}{1000g}\times \frac{1000\mu g}{1ng}=116.27g/g$

Solving for part (c)

The concentration of Sr found in part a=8.72ng/mL

Since the volume of solution is10mL:

$MassofSr=(8.72ng/mL0.43)10mL=87.2ng4.3$

The mass of dissolved tooth is given in the question, so to find the concentration(m/m)in$\mu$g/g

$\frac{87.2ng\pm 4.3}{0.75mg}\times \frac{1mg}{1000g}\times \frac{1000g}{1ng}=122g/g=116.27g/g5.73ppm$

Solving for part (d)

The95%confidence interval is found through the below equation:

- Using table 4.4,t=3.182

-sis calculated in part (c)

confidence interval$=\pm t\times s=\pm 3.182\times 5.73=18.2ppm$