Chapter 15, Problem 15.44P

a)

Interpretation Introduction

Interpretation:

The concentration and $\text{95\%}$ confidence interval for ammonia nitrogen (ppm) in $\text{100}\text{.0}\text{mL}$ of sea water has to be calculated and standard addition graph has to be plotted.

Concept Introduction:-

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 ${\left[\text{X}\right]}_{\text{i}}$

Confidence Intervals:

The confidence interval is given by the equation:

$\begin{array}{l}\text{Confidence interval = }\overline{\text{x}}\text{±}\frac{\text{ts}}{\sqrt{\text{n}}}\\ \text{=}\overline{\text{x}}{\text{±tu}}_{\text{x}}{\text{(since standard uncertainty(u}}_{\text{x}}\text{)=s/}\sqrt{\text{n}}\text{) }\end{array}$

Where,

$\overline{x}$ is mean

$s$ is standard deviation

$t$ is Student’s t

n is number of measurements

$u_x$ is standard uncertainty

The concentration of original unknown is

${\text{c}}_{\text{X}}\text{=}\frac{\text{-}\left(\text{x-intercept}\right){\text{c}}_{\text{s}}}{{\text{V}}_{{}_{\text{0}}}}$

b)

Interpretation Introduction

Interpretation:

The criticism of this experiment is that too much added standard creates error because the standards contribute too much to the computed result and reading from the initial solution was not weighted heavily enough has to be explained.

Concept Introduction:-

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 ${\left[\text{X}\right]}_{\text{i}}$

Confidence Intervals:

The confidence interval is given by the equation:

$\begin{array}{l}\text{Confidence interval = }\overline{\text{x}}\text{±}\frac{\text{ts}}{\sqrt{\text{n}}}\\ \text{=}\overline{\text{x}}{\text{±tu}}_{\text{x}}{\text{(since standard uncertainty(u}}_{\text{x}}\text{)=s/}\sqrt{\text{n}}\text{) }\end{array}$

Where,

$\overline{x}$ is mean

$s$ is standard deviation

$t$ is Student’s t

n is number of measurements

$u_x$ is standard uncertainty

The concentration of original unknown is

${\text{c}}_{\text{X}}\text{=}\frac{\text{-}\left(\text{x-intercept}\right){\text{c}}_{\text{s}}}{{\text{V}}_{{}_{\text{0}}}}$