Question

For the reaction X → Y + Z, the rate constant is 0.00058 s^-1. What percentage of X will be decomposed in 50 minutes?

(a) 90.02 percent

(b) 82.44 percent

(c) 88.82 percent

(d) 82.67 percent

The question was asked in a national level competition.

My question is taken from Chemical Kinetics in portion Chemical Kinetics of Chemistry – Class 12

Answer 1

The correct choice is (b) 82.44 percent

To elaborate: Given, rate constant k= 0.00058 s^-1

Time t= 50 minutes = 50 × 60 = 3000 seconds

First-order integrated rate equation, k = \(\frac{2.303}{t}\)log\(\frac{100}{100-a}\)

log\(\frac{100}{100-a}\) = \(\frac{kt}{2.303}\)

log\(\frac{100}{100-a}\) = \(\frac{0.00058 \times 3000}{2.303}\) = 0.756

a=82.44 percent.