Chapter 14, Problem 14.11QAP

Interpretation Introduction

(a)

Interpretation:

A calibration curve from the given data should be plotted.

Concept introduction:

A calibration curve or standard curve is a method used in analytical chemistry to determine the concentration of unknown sample by comparing to a set of samples with known concentrations.

Interpretation Introduction

(b)

Interpretation:

Using the method of least squares, an equation relating absorbance and the concentration of Fe(II) should be developed.

Concept introduction:

For equations,

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

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 the intercept should be calculated.

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, $s_b=s_r\sqrt{\frac{{\displaystyle \sum x_i^2}}{N{\displaystyle \sum x_i^2}-{\left({\displaystyle \sum x_i}\right)}^2}}$