Question

The velocity constant \(K\) for a first order reaction was found to be \(5.5 \times 10^{-14}\,s^{-1}\). Calculate the half life of this reaction.

Hint:

First order half life \(t_{1/2}=0.693/k\); plug in \(k=5.5\times10^{-14}\,s^{-1}\).

Answer 1

Step 1: Formula. For a first order reaction the half life is independent of initial concentration and is given by \[t_{1/2} = \frac{0.693}{k}.\]
Step 2: Substitute. \(k = 5.5 \times 10^{-14}\,s^{-1}\), so \[t_{1/2} = \frac{0.693}{5.5 \times 10^{-14}}\,s.\]
Step 3: Arithmetic. \(\dfrac{0.693}{5.5} = 0.126\). Therefore \[t_{1/2} = 0.126 \times 10^{14} = 1.26 \times 10^{13}\,s.\]
Step 4: State the result. The half life is about \(1.26 \times 10^{13}\) seconds (a very slow reaction, as expected from the tiny rate constant).
\[\boxed{t_{1/2} \approx 1.26 \times 10^{13}\,s}\]