A substance decomposes by following first order kinetics. If 50% of the compound is decomposed in 120 minutes, how long will it take for 90% of the compound to decompose ?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the concept of half-life in first-order kinetics
In first-order kinetics, the half-life (t₁/₂) is the time required for the concentration of a reactant to decrease to half of its initial concentration. Given that 50% of the compound is decomposed in 120 minutes, this means that the half-life of the reaction is 120 minutes.

### Step 2: Calculate the rate constant (k)
The rate constant (k) for a first-order reaction can be calculated using the formula:
\[ k = \frac{\ln(2)}{t_{1/2}} \]
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