Question

Which of the following statement/s is/are correct? i. half-life is 50 % of the total time taken for the completion of a reaction ii. collision frequency (z), which is the number of collisions per second per unit volume, is same as the rate constant of the reaction iii. a change in the activation energy of a reaction at a particular temperature will result in a proportional change in the rate and rate constant of the reaction at the same temperature iv. all first order reactions are not unimolecular v. for a zero order reaction, slope of a plot of t 1/2 vs. initial concentration will be zero

(a) i, iv
(b) ii only
(c) iv only
(d) ii, iii,v

Answer 1

Only statement iv, which states that not all first order reactions are unimolecular, is correct. The other statements are incorrect as the half-life refers to time to halve the reactant concentration, collision frequency is not equal to the rate constant, and the relationship between activation energy and reaction rate is not strictly proportional according to the Arrhenius equation. The correct answer is option: (c) iv only

Step-by-step explanation:

According to the given student question, they wanted to know which of the statements provided is correct.

• Statement i is incorrect because the half-life of a reaction is the time taken for the reactant concentration to reach half of its initial value, not 50% of the total reaction time.
• Statement ii is incorrect. The collision frequency (Z) is the number of collisions per second per unit volume but is not the same as the rate constant (k) of the reaction.
• Statement iii is partially correct. A change in the activation energy of a reaction does result in a change in the rate and rate constant of the reaction at a given temperature, but the relationship is not necessarily proportional since the rate constant is exponentially dependent on the activation energy according to the Arrhenius equation.
• Statement iv is correct; not all first-order reactions are unimolecular, although many are.
• Statement v is incorrect because for a zero-order reaction, the half-life is inversely proportional to the initial concentration, hence the slope of a plot of t1/2 versus initial concentration would not be zero.

With this information, the correct statements are: iv. all first order reactions are not unimolecular.