Chapter 4, Problem 4.HE

(a)

Interpretation Introduction

Interpretation:

Using the spreadsheet, the equation of the least-squares straight line passing through the given points has to be found out with a reasonable number of significant figures.

Concept Introduction:

Equation of a line:

The equation of straight line is:

$\begin{array}{l}y=mx+b\\ y=[m(\pm u_m)]x+[b(\pm u_b)]\end{array}$

Standard deviation of y: $s_y$

The standard deviation of y is:

${\sigma }_y\approx s_y=\sqrt{\frac{{\displaystyle \sum (d_i{}^2)}}{n-2}}$

Standard uncertainty of slope and intercept:

The standard uncertainty of slope is:

${\text{u}}_m^2=\frac{s_y^{2}n}{D}$

The standard uncertainty of intercept is:

${\text{u}}_b^2=\frac{s_y^2{\displaystyle \sum (x_i{}^2)}}{D}$

To Give: The equation of the least-squares straight line passing through the given points with a reasonable number of significant figures using the spreadsheet.

(b)

Interpretation Introduction

Interpretation:

A graph showing the experimental data and the calculated straight line should be drawn.

To Draw: A graph showing the experimental data and the calculated straight line

(c)

Interpretation Introduction

Interpretation:

Using the spreadsheet, the number of micrograms of unknown protein sample and its uncertainty has to be calculated.

Concept Introduction:

Uncertainty with a Calibration Curve:

Propagation for the equation $y=mx+b$ (but not $y=mx)$ gives,

The standard uncertainty in x is given as:

$u_x=\frac{s_y}{\left|m\right|}\sqrt{\frac{1}{k}+\frac{1}{n}+\frac{{(y-\overline{y})}^2}{m^2{\displaystyle \sum {(x_i-\overline{x})}^2}}}$

Where,

$u_x$ is standard uncertainty for $x$

$y$ is the corrected absorbance of unknown

$x_i$ is the mass of sample in standards

$\overline{y}$ is the average of $y$ values

$\overline{x}$ is the average of $x$ values

To Calculate: The number of micrograms of unknown protein sample and its uncertainty using the spreadsheet.