Question

Which of the following statements is/are correct with respect to first order kinetics?

• A. The half-life $\left(t_{1/2}\right)$ is directly proportional to the initial concentration raised to the power zero.
• B. If we know the value of rate constant $\left(k\right)$, we can calculate the half-life.
• C. The plot of $\text{log}\left[A\right]$ versus time will give a straight line passing through the origin, where $\left[A\right]$ is the concentration of the reactant $A$ at any time $t$ for following first order reaction.
• D. All natural and artificial radioactive isotopes of unstable nuclei are produced by first order kinetics.

Answer 1

Answer: (A), (B), (D)

The half-life $\left(t_{1/2}\right)$ is directly proportional to the initial concentration raised to the power zero.
All natural and artificial radioactive isotopes of unstable nuclei are produced by first order kinetics.
If we know the value of rate constant $\left(k\right)$, we can calculate the half-life.

The half-life $\left(t_{1/2}\right)$ is directly proportional to the initial concentration raised to the power zero. In other words, for the first-order reaction, the half-life period is independent of the initial concentration as the value of any number raised to the power zero is $1$.

If we know the value of the rate constant $\left(k\right)$, we can calculate the half-life. The relationship between the half-life period and the rate constant is $t_{1/2}=\frac{0.693}{k}$

The plot of $\text{log}\left[A\right]$ versus time will give a straight line with y intercept equal to $\text{log}[A{]}_0$, where $\left[A\right]$ is the concentration of the reactant $A$ at any time $t$ for following first order reaction and $[A{]}_0$ is the initial concentration.Hence, it will not pass through the origin.

All natural and artificial radioactive isotopes of unstable nuclei occur by first order kinetics. They obey the rate equation $k=\frac{2.303}{t}log\frac{[A{]}_0}{\left[A\right]}$

The statements $A,B$ and $D$ are correct with respect to first-order kinetics.