Question

The decomposition of benzene diazonium chloride is a first-order reaction. The time taken for its decomposition to \( \frac{1}{4} \) and \( \frac{1}{10} \) of its initial concentration are \( t_{1/4} \) and \( t_{1/10} \) respectively. The value of \( \frac{t_{1/4}}{t_{1/10}} \times 100 \) is: (Given: log 2 = 0.3)

• A. 60
• B. 30
• C. 90
• D. 45

Hint:

For first-order reactions, the time to reduce concentration to \( \frac{1}{n} \) is proportional to log n.

Answer 1

The Correct Option is A

Step 1: Using First-Order Reaction Formula 
The time required for the concentration to become \( \frac{1}{n} \) of its initial value in a first-order reaction is: \[ t_{1/n} = \frac{2.303}{k} \log n \] For \( t_{1/4} \): \[ t_{1/4} = \frac{2.303}{k} \log 4 = \frac{2.303}{k} (2 \times \log 2) \] Using \( \log 2 = 0.3 \), \[ t_{1/4} = \frac{2.303}{k} (2 \times 0.3) = \frac{2.303 \times 0.6}{k} \] For \( t_{1/10} \): \[ t_{1/10} = \frac{2.303}{k} \log 10 = \frac{2.303}{k} (1) \] Step 2: Calculating Ratio 
\[ \frac{t_{1/4}}{t_{1/10}} = \frac{2.303 \times 0.6}{2.303 \times 1} = 0.6 \] \[ \frac{t_{1/4}}{t_{1/10}} \times 100 = 0.6 \times 100 = 60 \] Thus, the correct answer is 60.