Chapter 15, Problem 15.8QAP

Interpretation Introduction

(a)

Interpretation:

A working curve from the data should be constructed.

Concept introduction:

Standard addition method is used to analyze complex samples which matrix effect is significant. One common approach is standard addition technique is spiking of sample. In this method, one or more increments of a standard solution is added to the several aliquots of sample containing same volume. Each solution is then diluted to a fixed volume and experiment is proceeded.

Interpretation Introduction

(b)

Interpretation:

A linear least-squares equation for the data should be determined.

Concept introduction:

$\begin{array}{l}{S}_{yy}={\displaystyle \sum {\left(y_i-\overline{y}\right)}^2}\\ S_{xx}={\displaystyle \sum {\left(x_i-\overline{x}\right)}^2}\\ S_{xy}={\displaystyle \sum \left(x_i-\overline{x}\right)}\left(y_i-\overline{y}\right)\end{array}$

The slope of the line, $m=\frac{S_{xy}}{S_{xx}}$

The intercept, $b=\overline{y}-m\overline{x}$

Interpretation Introduction

(c)

Interpretation:

The standard deviation of the slope and intercept and the standard deviation about regression for the curve should be determined.

Concept introduction:

Standard deviation about regression, $s_r=\sqrt{\frac{S_{yy}-m^2{S}_{xx}}{N-2}}$

N − number of points used.

The standard deviation of the slope, $s_m=\sqrt{\frac{s_r^2}{S_{xx}}}$

The standard deviation of the intercept, $s_b=s_r\sqrt{\frac{{\displaystyle \sum x_i^2}}{N{\displaystyle \sum x_i^2}-{\left({\displaystyle \sum x_i}\right)}^2}}$

Interpretation Introduction

(d)

Interpretation:

The concentration of Zn²+ in the sample should be calculated.

Concept introduction:

Standard addition method is used to analyze complex samples which matrix effect is significant. One common approach is standard addition technique is spiking of sample. In this method, one or more increments of a standard solution is added to the several aliquots of sample containing same volume. Each solution is then diluted to a fixed volume and experiment is proceeded.

Interpretation Introduction

(e)

Interpretation:

The standard deviation for the result in part (d) should be calculated.

Concept introduction:

Standard deviation of the results obtained from standard addition method = $s_c=C_x\sqrt{{\left(\frac{s_m}{m}\right)}^2+{\left(\frac{s_b}{b}\right)}^2}$

M − number of replicates

N- number of calibration points.