Chapter 3, Problem 3.69P

Interpretation Introduction

(a)

Interpretation:

The units of $k,k_0\text{ and }{E}_{\text{a}}$ are to be determined.

Concept introduction:

Units of any quantity can be determined with the help of dimensional analysis. It is the analysis done for different physical quantities and their relationships with each other by their base quantities such as length, mass, time etc. It uses the rules of algebra for the conversion of units.

Interpretation Introduction

(b)

Interpretation:

The given equation (1) is to be transformed into the form $y=\text{a}t+\text{b}$. Also, the way to determine $C_{\text{A0}}\text{ and }k$ from this equation is to be stated.

Concept introduction:

For the equation of type $y=\text{a}x+\text{b}$ and given points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$, slope $\text{b}$ is calculated as:

$\text{b}=\frac{y_2-y_1}{x_2-x_1}$ .....(3)

And intercept $\text{a}$ is calculated using the slope and one of the given points.

Interpretation Introduction

(c)

Interpretation:

An excel spreadsheet is to be prepared according to the given structure and from it, conclusion about the given equation (1) is to be stated.

Concept introduction:

For a given set of data to fit in a straight-line, ${\text{R}}^2$ is measured which is known as the coefficient of determination. It provides the measure of how well a straight-line may fit in the given set of data. The closer its value to 1, better is the fit.

Interpretation Introduction

(d)

Interpretation:

The values of $C_{\text{A0}}\text{ and }k$ for the four temperatures are to be calculated from the four trendline equations and the values are to be filled in the spreadsheet according to the given structure.

Interpretation Introduction

(e)

Interpretation:

The difference in the calculated values of $C_{\text{A0}}$ in part (d) even after the enough addition of A as $C_{\text{A0}}=0.25\text{ mol/L}$ is to be explained.

Concept introduction:

Rate of a reaction is dependent on the initial concentration of the reaction, temperature, activation energy and nature of the reactant.

For a reaction whose temperature and final concentration is pre-defined, alterations in the initial concentration and activation energy gives the desired results.

Interpretation Introduction

(f)

Interpretation:

The given equation (2) is to be transformed into the form $y=\text{a}t+\text{b}$. An excel spreadsheet is to be prepared according to the given structure and from it, conclusion about the temperature dependence of the reaction rate constant is to be stated.

Concept introduction:

$k$ is the reaction rate constant.

It is a strong function of the absolute temperature in the reactor:

$k\left(T\right)=k_{\text{0}}\exp \left(-\frac{E_{\text{a}}}{RT\left(\text{K}\right)}\right)$

It is known as the Arrhenius equation. Here, $E_{\text{a}}$ is the activation energy of the reaction, $R$ is the universal gas constant with the value $8.314\text{ J/mol}·\text{K}$ and $k_{\text{0}}$ is a constant.

For the equation of type $y=\text{a}x+\text{b}$ and given points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$, slope $\text{b}$ is calculated as:

$\text{b}=\frac{y_2-y_1}{x_2-x_1}$ .....(3)

And intercept $\text{a}$ is calculated using the slope and one of the given points.

Interpretation Introduction

(g)

Interpretation:

The reason for the temperature control and well-mixing of the reactor contents are to be explained.

Concept introduction:

Yield of a reaction is defined as theoretical amount of the desired product formed in a chemical reaction.

Selectivity of a chemical reaction is the ratio of the desired product and the undesired product formed.

Interpretation Introduction

(h)

Interpretation:

The rows 1-3 and 12 of columns J and K of the excel spreadsheet are to be filled according to the structure given. The value of $k$ and $C_{\text{A}}$ ate the specified temperatures are to be calculated and filled in the sheet. Also, the likelihood of the occurrence of the concentration from the two estimated set of data is to be explained.

Concept introduction:

Rate of a reaction is dependent on the initial concentration of the reaction, temperature, activation energy and nature of the reactant.