Question

For the reaction , [C] vs. time is plotted:

How do you determine each of the following?

(a) The average rate over the entire experiment

(b) The reaction rate at time x

(c) The initial reaction rate

(d) Would the values in parts (a), (b) and (c) be different if you plotted [D] vs. time? Explain.

Short answer

The answer is,

(a) 1

(b) $-\frac{\text{d}\left[\text{C}\right]}{\text{dx}}$

(c) 0

(d) (a) and (c) are same, but (b) will belocalid="1663360591475" $+\frac{\text{d}\left[\text{C}\right]}{\text{dx}}$

Step-by-step solution

Rate of a reaction

The rate of a reaction can be defined as the speed with the reaction takes place or the change of concentration of the substance with time. The concentration of reactant decreases with time and the concentration of product increases with time.

Subpart (a)

The average rate of the entire experiment is equal to 1. This is because the concentration changes uniformly with time and hence the change in concentration and time in a uniform manner causes a unit rate.

Subpart (b)

The rate at time x is $-\frac{\text{d}\left[\text{C}\right]}{\text{dx}}$This shows the change in concentration of the reactant with time as rate at instant x. The rate of consumption of reactant is always negative.

Subpart (c)

The initial rate of the reaction is always zero. Because, initially when the concentration of the reactant is introduced at zero time, the rate will be zero.

Subpart (d)

The D is the product and if the graph is plotted [D] vs. time, the curve will show an increasing plot with time. The average rate and initial rate of the reaction is 1 and 0 respectively for the product graph also. But the rate at time x is $+\frac{\text{d}\left[\text{C}\right]}{\text{dx}}$. This is why because, the rate of formation of product is always positive.