Chapter 15, Problem 15.41P

a)

Interpretation Introduction

Interpretation:

The least squares slope and intercept and their standard deviation from the prepared calibration curve has to be calculated.

Concept Introduction:-

LINEST:

The LINEST is a Microsoft excel function which is uses the least squares method to measure the statistics for a straight line and array describing that line it is built-in function that can be categorized.

LINEARITY:

It is measure of how well a calibration curve follows a straight line and displaying that the response is proportional to the quantity of the analyte.

${\text{R}}^{\text{2}}\text{=}\frac{{\left[{\displaystyle \sum \left({\text{x}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{x}}\right)}\left({\text{y}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{y}}\right)\right]}^{\text{2}}}{{\displaystyle \sum {\left({\text{x}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{x}}\right)}^{\text{2}}}{\displaystyle \sum {\left({\text{y}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{y}}\right)}^{\text{2}}}}$

Where R means square of correlation coefficient.

Standard additions to one solution:

The graph can be drawn using the equation

$\text{plot}\underset{\text{Function}\text{to}\text{plot}\text{on}\text{y-axis}}{\underbrace{{\text{I}}_{\text{S+X}}\left(\frac{\text{V}}{{\text{V}}_{\text{0}}}\right)}}\text{versus }{\text{I}}_{\text{X}}\text{+}\frac{{\text{I}}_{\text{X}}}{{\left[\text{X}\right]}_{\text{i}}}\underset{\text{function}\text{to}\text{plot}\text{on}\text{x-axis}}{\underbrace{{\left[\text{S}\right]}_{\text{i}}\left(\frac{{\text{V}}_{\text{S}}}{{\text{V}}_{\text{0}}}\right)}}$

Where X-intercept is ${\left[\text{X}\right]}_{\text{i}}$

b)

Interpretation Introduction

Interpretation:

The value of $\text{β}$ in the below given equation has to be calculated.

$\text{E=}\text{constant+}\text{β}\left(\frac{\text{0}\text{.05916}}{2}\right)\text{log}\left[{\text{A}}_{{\text{Ca}}^{\text{2+}}}\right]$

Concept Introduction:-

Response of ion-selective electrode:

The response of an ion-selective electrode to its primary ion (A) and to interfering ions of the same charge, when the response to every ion is Nernstian.

$\text{E=}\text{constant+}\text{β}\left(\frac{\text{0}\text{.05916}}{2}\right)\text{log}\left[{\text{A}}_{{\text{Ca}}^{\text{2+}}}\right]$

Where,

$\text{E}$ =cell potential.

$\text{β}$ = close to $\text{1}\text{.00}$

c)

Interpretation Introduction

Interpretation:

The concentration of $\left[{\text{Ca}}^{\text{2+}}\right]$ and its associated uncertainty for a sample has to be calculated.

Concept Introduction:-

Propagation of uncertainty with a calibration curve:

The standard uncertainty for $\text{x}$ has to be calculated using the formula,

${\text{u}}_{\text{x}}\text{=}\frac{{\text{s}}_{\text{y}}}{\left|\text{m}\right|}\sqrt{\frac{\text{1}}{\text{k}}\text{+}\frac{\text{1}}{\text{n}}\text{+}\frac{{\left(\text{y-}\stackrel{\text{-}}{\text{y}}\right)}^{\text{2}}}{{\text{m}}^{\text{2}}{\displaystyle \sum {\left({\text{x}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{x}}\right)}^{\text{2}}}}}$

Where,

${\text{u}}_{\text{x}}\text{=}$ Standard uncertainty for x.

$\text{y}$ =corrected absorbance of unknown.

${\text{x}}_{\text{i}}$= $\text{μg}$ of protein in standards.

$\overline{\text{y}}$= average of $\text{14}\text{y}$ values

$\overline{\text{x}}$= average of $\text{14}\text{x}$ values