Chapter 1, Problem 1.2Q

Rework Example $1-1$ using Equation $(3-1)$, and then compare reaction rates. How do these values compare with those calculated in the example?

Interpretation Introduction

Interpretation:

The given reaction rates for the given reaction are to be determined and compared with the results provided.

Concept Introduction:

For any given reaction, its rate defines the speed at which the moles of a chemical species get consumed to form other chemical species. For a chemical species A , the reaction rate is represented by $-r_A$ and the SI unit of reaction rate is $\text{moles}/\left(\text{s}\cdot {\text{m}}^3\right)$ . The rate of formation is negative of the rate of consumption or disappearance.

Equation 3-1 to be used for the reaction $aA+bB\to cC+dD$

is:

  $\frac{-r_A}{a}=\frac{-r_B}{b}=\frac{r_C}{c}=\frac{-r_D}{d}$ .........(1)

Here, $a,b,c,\text{ and }d$ are the stoichiometric coefficients of species $A,B,C,\text{ and }D$ respectively.

Answer to Problem 1.2Q

Rate of disappearance of A , $-r_A=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of A , $r_A=-10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of disappearance of B , $-r_B=20\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of B , $r_B=-20\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of C , $r_C=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of disappearance of C , $-r_C=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of D , $r_D=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of disappearance of D , $-r_D=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Explanation of Solution

Given information:

The consumption rate of Chloral (A) is given as 10 moles per second per ${\text{m}}^3$

when it reacts with chlorobenzene (B) according to the reaction:

  $A+2B\to C+D$

The results are as follows:

Rate of disappearance of A , $-r_A=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of A , $r_A=-10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of disappearance of B , $-r_B=20\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of B , $r_B=-20\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of C , $r_C=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of disappearance of C , $-r_C=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of D , $r_D=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of disappearance of D , $-r_D=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

The calculated rates of formation and disappearance of $A,B,C,\text{ and }D$ are the same as given.

For the given reaction of chloral and chlorobenzene is:

  $A+2B\to C+D$

Stoichiometric coefficients of $A,B,C,\text{ and }D$

are:

  $\begin{array}{c}a=1\\ b=2\\ c=1\\ d=1\end{array}$

From equation (1),

  $\frac{-r_A}{1}=\frac{-r_B}{2}=\frac{r_C}{1}=\frac{r_D}{1}$ .........(2)

The rate of consumption/disappearance of chloral (A) is given as, $-r_A=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Thus, the rate of formation of A will be,

  $\begin{array}{c}{r}_A=-\left(-r_A\right)\\ =-\left(10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\right)\\ =-10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\end{array}$

From the first two terms of equation (2), the rate of disappearance of B is

  $\begin{array}{c}\frac{-r_A}{1}=\frac{-r_B}{2}\\ -r_B=2\left(-r_A\right)\\ -r_B=2\left(10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\right)\\ -r_B=20\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\end{array}$

The rate of formation of B will be,

  $\begin{array}{c}{r}_B=-\left(-r_B\right)\\ =-\left(20\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\right)\\ =-20\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\end{array}$

From the first and third terms of equation (2), the rate of appearance of C is,

  $\begin{array}{c}\frac{-r_A}{1}=\frac{r_C}{1}\\ r_C=-r_A\\ r_C=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\end{array}$

The rate of disappearance of C will be,

  $\begin{array}{c}-r_C=-\left(r_C\right)\\ =-\left(10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\right)\\ =-10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\end{array}$

From the first and fourth terms of equation (2), the rate of appearance of D is,

  $\begin{array}{c}\frac{-r_A}{1}=\frac{r_D}{1}\\ r_D=-r_A\\ r_D=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\end{array}$

The rate of disappearance of D will be,

  $\begin{array}{c}-r_D=-\left(r_D\right)\\ =-\left(10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\right)\\ =-10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)\end{array}$

All the rates of formation and disappearance of $A,B,C,\text{ and }D$ are calculated to be the same as given reaction rates.

Conclusion

Thus,

Rate of disappearance of A , $-r_A=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of A , $r_A=-10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of disappearance of B , $-r_B=20\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of B , $r_B=-20\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of C , $r_C=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of disappearance of C , $-r_C=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of formation of D , $r_D=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .

Rate of disappearance of D , $-r_D=10\text{mol}/\left({\text{m}}^{\text{3}}\cdot \text{s}\right)$ .