Question

What is the effect of catalyst on the rate of reaction? A first-order reaction is 40\% completed in 50 minutes. Calculate the time taken for 80\% completion of the reaction. (Given: \(\log 2 = 0.3010\) and \(\log 6 = 0.7782\))

Hint:

The rate of a first-order reaction depends only on the concentration of one reactant, making calculations straightforward.

Answer 1

Step 1: First-Order Rate Law: \[ t = \frac{2.303}{k} \log \frac{[A]_0}{[A]} \] Step 2: Calculate Rate Constant \( k \): For 40\% completion: \[ t_{40\%} = 50 = \frac{2.303}{k} \log \frac{100}{60} \] \[ k = \frac{2.303}{50} \times 0.2218 = 0.0102 \text{ min}^{-1} \] Step 3: Calculate Time for 80\% Completion: \[ t_{80\%} = \frac{2.303}{0.0102} \log \frac{100}{20} \] \[ = \frac{2.303}{0.0102} \times 0.7782 = 176 \text{ min} \] Thus, the time for 80\% completion is 176 minutes.