Question

Write the formula of half-life period for first order reaction.

Hint:

Half-life for a first order reaction is independent of initial concentration.

Answer 1

Step 1: General expression for first order kinetics.
For a first order reaction, the integrated rate law is: \[ k = \frac{2.303}{t} \log \frac{[R]_0}{[R]} \] Step 2: Condition for half-life.
At half-life, \([R] = \frac{[R]_0}{2}\).
Step 3: Substitution.
\[ k = \frac{2.303}{t_{1/2}} \log \frac{[R]_0}{[R]_0/2} = \frac{2.303}{t_{1/2}} \log 2 \] \[ k = \frac{0.693}{t_{1/2}} \] Step 4: Rearranging.
\[ t_{1/2} = \frac{0.693}{k} \]