Question

Palladium(II) forms an intensely colored complex at pH 3.5 with arsenazo III at 660 nm.³³ A meteorite was pulverized in a ball mill, and the resulting powder was digested with various strong mineral acids. The resulting solution was evaporated to dryness, dissolved in dilute hydrochloric acid, and separated from interferents by ion-exchange chromatography. The resulting solution containing an unknown amount of Pd(II) was then diluted to 50.00 mL with pH 3.5 buffer. Ten-milliliter aliquots of this analyte solution were then transferred to six 50-mL volumetric flasks. A standard solution was then prepared that was 1.00 x 10^-5 M in Pd(II). Volumes of the standard solution shown in the table were then pipetted into the volumetric flasks along with 10.00 mL of 0.01 M arsenazo III. Each solution was then diluted to 50.00 mL, and the absorbance of each solution was measured at 660 nm in 1.00-cm cells.

(a) Enter the data into a spreadsheet, and construct a standard-additions plot of the data.

(b) Determine the slope and intercept of the line.

(c) Determine the standard deviation of the slope and of the intercept.

(d) Calculate the concentration of Pd(II) in the analyte solution.

(e) Find the standard deviation of the measured concentration.

Short answer

a)

b) Slope = 0.026131

Intercept = 0.212524

c) $$\begin{gathered} {\mathrm{S}}_{\mathrm{m}}=0.000831 \\ {\mathrm{S}}_{\mathrm{b}}=0.012593 \end{gathered}$$

d) $8.13\times {10}^{-6}\mathrm{M}$

e) ${\mathrm{s}}_{\mathrm{c}}=5.47\times {10}^{-7}\mathrm{M}$

Step-by-step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Explanation

Dependent variable is the absorbance at 660 nm and independent variable is the volume of standard solution added to the sample. A plot of absorbance versus volume of standard should be plotted.

Part (b) Step 1: Given Information

The slope and the intercept should be determined.

Part (b) Step 2: Explanation

The slope and the intercept of the graph can be obtained form least square analysis done in spread sheet or can be calculated manually.

$$\begin{gathered} \mathrm{m}=\frac{{\mathrm{S}}_{\mathrm{xy}}}{{\mathrm{S}}_{\mathrm{xx}}}=\frac{11.4325}{437.5}=0.026131 \\ \mathrm{b}=\overline{\mathrm{y}}-\mathrm{m}\overline{\mathrm{x}} \\ \mathrm{b}=0.539167-0.026131\times 12.5 \\ \mathrm{b}=0.212524 \end{gathered}$$

Slope = 0.026131

Intercept = 0.212524

Part (c) Step 1: Given Information

The standard deviation of the slope and the intercept should be determined.

Part (c) Step 2: Explanation

From least squares analysis data from spreadsheet or can be calculated manually.

$$\begin{gathered} s_r=\sqrt{\frac{0.299949-{(0.026131)}^2\times 437.5}{6-2}} \\ {s}_r=0.01740 \\ {s}_m=\sqrt{\frac{{(0.01740)}^2}{437.5}}=0.000831 \\ {s}_b=0.01740\sqrt{\frac{1375}{6\times 1375-{\left(75\right)}^2}}=0.012593 \\ {s}_m=0.000831 \\ {s}_b=0.012593 \end{gathered}$$

Part (d) Step 1: Given Information

The concentration of Pd(II) in the analyte solution should be determined.

Part (d) Step 2: Explanation

$$\begin{gathered} C_x=\frac{b{C}_s}{m{V}_x} \\ {C}_x=\frac{0.212524\times 1\times {10}^{-5}}{0.26131\times 10} \\ {C}_x=8.13\times {10}^{-6}\mathrm{M} \end{gathered}$$

Part (e) Step 1: Given Information

The standard deviation of measured concentration should be determined.

Part (e) Step 2: Explanation

$$\begin{gathered} s_c=C_x\sqrt{{\left(\frac{S_m}{m}\right)}^2+{\left(\frac{S_b}{b}\right)}^2} \\ {s}_c=8.13\times {10}^{-6}\sqrt{{\left(\frac{0.000831}{0.026131}\right)}^2+{\left(\frac{0.012593}{0.212524}\right)}^2} \\ {s}_c=8.13\times {10}^{-6}\times 0.067 \\ {s}_c=5.47\times {10}^{-7}\mathrm{M} \end{gathered}$$