Question

Consider the reaction A -> products. Which, if any, of the following plots is consistent with a second-rode reaction?

a. ln[A] plotted against time gives a straight line of positive slope

b. ln[A] plotted against time gives a straight line of negative slope

c. 1/[A] plotted against time gives a straight line of positive slope

d. 1/[A] plotted against time gives a straight line of negative slope

Answer 1

Ans. Second order kinetics- 1/ [A]_t = kt + (1/ [A]₀)      - equation 1

Where, [A]₀ = Initial concentration of reactant

Note: Don’t confuse [A]₀ with the product A of the reaction.

[A]_t = Final concentration of reactant after time t

k = rate constant

t = time of reaction.

The rate equation is in form of y = mx + c ; where

                        y = 1/ [A]

                        m = k

                        x = t

                        c = 1 / [A]₀

# A plot of 1/[A] on y-axis vs time of X-axis gives a straight line.

The slope is negative (i.e. the straight line goes downward instead of upward) because the concentration of reactant decrease gradually with time.

So, correct option is – c. 1/[A] plotted against time gives a straight line of positive slope.

# Note: The concentration [A] decreases with time, so a graph of [A] vs time would give a straight line of negative slope.

Note that the graph is plotted using 1/[A] but not [A]. So, as [A] decreases, 1/[A] would increase accordingly. Therefore, the graph has a positive slope.