In the Class 12 Chemistry chapter 'Chemical Kinetics', studying how fast a chemical reaction occurs is crucial. A 'First-Order Reaction' is one where the speed (rate) of the reaction depends directly on the concentration of only ONE reactant. Radioactive decay is the most famous example of a first-order process.
All natural and artificial radioactive decay processes (like Uranium decaying into Lead) strictly follow first-order kinetics.
If you plot a graph of $\ln[A]$ versus time ($t$) for a first-order reaction, you will get a perfectly straight downward line.
For a simple reaction where Reactant A turns into Products ($A \rightarrow Products$):
The basic rate law is written as: $Rate = -\frac{d[A]}{dt} = k[A]^1$
(Where [A] is the concentration of the reactant, and k is the rate constant. The power of 1 indicates it is a first-order reaction)..
To find out how much reactant is left after a certain amount of time, we integrate the formula above. This gives us the most important formula you need for numerical problems:
$k = \frac{2.303}{t} \log_{10} \left( \frac{[A]_0}{[A]_t} \right)$
The 'Half-Life' is the time required for exactly 50% of the reactant to be consumed. A unique mathematical property of first-order reactions is that their half-life is completely independent of the initial concentration.
$t_{1/2} = \frac{0.693}{k}$
(This means if it takes 10 minutes for 100g to become 50g, it will take another exact 10 minutes for 50g to become 25g)..
The unit of k is simply inverse time. It is usually written as $s^{-1}$ (per second) or $min^{-1}$ (per minute). It does not contain any moles or liters.
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