Chapter 16, Problem 42A

How would you express the rate of the chemical reaction $A\to B$ based on the concentration of Reactant A? Howwould that rate compare with the reaction rate based onthe Product B?

Interpretation Introduction

Interpretation:

How the rate of a chemical reaction is expressed needs to be determined. The rate of the reaction based on A needs to be compared with B.

Concept introduction:

In a chemical reaction, the reactants are written on the left side of the equation and the product is written on the right side.

The average rate of a reaction can be given by the formula,

Average reaction rate $\text{=}-\frac{\text{Δ}\left[\text{reactant}\right]}{\text{Δt}}$

Here, $\text{Δ}\left[\text{reactant}\right]$ = change in the concentration of the reactant

Answer to Problem 42A

The rate of the reaction in terms of A is $-\frac{\text{Δ}\left[\text{A}\right]}{\text{Δt}}$ and rate of the reaction in terms of B is $\frac{\text{Δ}\left[\text{B}\right]}{\text{Δt}}$

Explanation of Solution

The average rate of a reaction can be given by the formula,

Average reaction rate $\text{=}-\frac{\text{Δ}\left[\text{reactant}\right]}{\text{Δt}}$

Where, the change in the concentration of the reactant is given by $\text{Δ}\left[\text{reactant}\right]$ and $\text{Δt}$ is the change in time.

If on the reaction, $\text{A}\to \text{B}$, A is the reactant and B is the product, the rate of the reaction in terms of A would be $-\frac{\text{Δ}\left[\text{A}\right]}{\text{Δt}}$. The negative sign shows the decrease in reactant concentration to generate a positive average reaction rate.

If on the reaction, $\text{A}\to \text{B}$, the rate in terms of B would be given as $\frac{\text{Δ}\left[\text{B}\right]}{\text{Δt}}$. Here, the concentration of product is already a positive value so there is no negative sign in this expression.

Conclusion

The rate of the reaction in terms of A is $-\frac{\text{Δ}\left[\text{A}\right]}{\text{Δt}}$. The negative value depicts the decrease in concentration of reactant and rate of the reaction in terms of B is $\frac{\text{Δ}\left[\text{B}\right]}{\text{Δt}}$.