Chapter 15, Problem 15.7QAP

Interpretation Introduction

(a)

Interpretation:

The calibration curve should be constructed in a spread sheet.

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:

The least square slope and the intercept for the plot in (a) 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 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 unknown NADH sample should be calculated using the spreadsheet.

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

(e)

Interpretation:

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

Concept introduction:

Standard deviation of the results obtained from the calibration curve = $s_c=\frac{s_r}{m}\sqrt{\frac{1}{M}+\frac{1}{N}+\frac{{\left({\overline{y}}_c-\overline{y}\right)}^2}{m^2{S}_{xx}}}$

M − number of replicates

N- number of calibration points.

$RSD=\frac{s}{x}\times 100$

RSD − relative standard deviation

x - mean of x values

s − standard deviation

Interpretation Introduction

(f)

Interpretation:

The relative standard deviation for the result in part (d) should be calculated if a result of 7.95 was the mean of three measurements.

Concept introduction:

Standard deviation of the results obtained from the calibration curve = $s_c=\frac{s_r}{m}\sqrt{\frac{1}{M}+\frac{1}{N}+\frac{{\left({\overline{y}}_c-\overline{y}\right)}^2}{m^2{S}_{xx}}}$

M − number of replicates

N- number of calibration points.

$RSD=\frac{s}{x}\times 100$

RSD − relative standard deviation

x - mean of x values

s − standard deviation