Question

Thermal decomposition of a compound is of the first order. If 50% of a sample of the compound is decomposed in 120 minutes, how long will it take for 90% of the compound to decompose

• A. 399 min
• B. 2.99 min
• C. 39.9 min
• D. 3.99 min

Answer 1

Answer: (A)

399 min

Answer 2

Half life of reaction =120 min

$\mathbf{k =}\frac{\mathbf{0.693}}{\mathbf{t}_{\mathbf{1/2}}}\mathbf{=}\frac{\mathbf{0.693}}{\mathbf{120}}\mathbf{= 5.77}\mathbf{\times}\mathbf{1}\mathbf{0}^{\mathbf{-}\mathbf{3}}\mathbf{\min}^{\mathbf{-}\mathbf{1}}{}$

Applying first order reaction equation,

$t = \frac{2.303}{k}\log_{10}\frac{a}{(a - x)}$; If $a = 100,\mspace{6mu} x = 90$ or $(a - x) = 10$

So, $t = \frac{2.303}{5.77 \times 10^{- 3}}.\log_{10}10 = \frac{2.303}{5.77 \times 10^{- 3}} = 399\min$