Which of the following statements is FALSE?

Question

BlackTom AI · Accepted Answer

First, let's restate the question and all options to ensure clarity of what we're evaluating. The question asks which statement is FALSE, and the options are:
- The rate of a first-order reaction is dependent on concentration.
- None of the statements is FALSE.
- The rate of second-order reactions is dependent on concentration.
- The half-life of a second-order reaction is not dependent on concentration.
- The half-life of a zero-order reaction is dependent on concentration.

Now, evaluate each option one by one with the goal of identifying any incorrect claim.
Option 1: 'The rate of a first-order reaction is dependent on concentration.' In a first-order reaction, the rate law is rate = k[A]. This shows the rate is proportional to the concentration of A, so the rate indeed depends on concentration. This statement is true.

Option 2: 'None of the statements is FALSE.' This would be correct only if every other statement were true. At the end, we will determine whether this option holds, but we must first check the others.

Option 3: 'The rate of second-order reactions is dependent on concentration.' For a second-order reaction with rate = k[A]^2 or rate = k[A][B], the rate depends on the square (or product) of concentrations. This is true: concentration affects the rate.

Option 4: 'The half-life of a second-order reaction is not dependent on concentration.' Here we recall the formula for a second-order reaction with a single reactant: t1/2 = 1/(k[A]0). This shows t1/2 is inversely proportional to the initial concentration, so it clearly depends on concentration. Therefore, this statement is false.

Option 5: 'The half-life of a zero-order reaction is dependent on concentration.' For a zero-order reaction, t1/2 = [A]0/(2k), which means the half-life is proportional to the initial concentration; thus it depends on concentration. This statement is true.

In summary, most statements about rates and half-lives align with standard kinetics formulas, except for option 4, which asserts that the second-order half-life is independent of concentration. That assertion contradicts the known t1/2 = 1/(k[A]0) relationship, making it the false statement. The remaining options (1, 3, and 5) are consistent with kinetic theory, while option 2 would only be correct if option 4 were true, which it is not. The overall reasoning shows why option 4 is the false statement.

CHM-1020-LD01.2025SU PS 1-Part I (Kinetics)

Which of the following statements is FALSE?

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