Study Guides/Chemistry/First Order Reaction Formula
Study Guide · Chemistry

First Order Reaction Formula and Kinetics

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.

Question (Click to Flip)

What is the unit of the rate constant (k) for a first-order reaction?

Answer

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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Key Facts

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.

1. The Differential Rate Law

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)..

2. The Integrated Rate Law Formula (Master Formula)

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:

$k = \frac{2.303}{t} \log_{10} \left( \frac{[A]_0}{[A]_t} \right)$

  • $k$ = Rate constant (units: $s^{-1}$ or $min^{-1}$)
  • $t$ = Time elapsed
  • $[A]_0$ = Initial concentration of the reactant (at time t=0)
  • $[A]_t$ = Final concentration of the reactant remaining after time 't'

3. The Half-Life Formula ($t_{1/2}$)

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)..

Questions and Answers

What is the unit of the rate constant (k) for a first-order reaction?+

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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