Question

Thermal decomposition of compound '$X$' is a first order reaction. If 75 % of '$X$' is decomposed in 100 min. How long will it take for 90% of the compound to decompose?

[Given : log 2 = 0.30]

• A. 190 min
• B. 176.66 min
• C. 166.66 min
• D. 156.66 min

Answer 1

The correct option is C 166.66 min

$k=\frac{1}{t}ln\left(\frac{a}{a-x}\right)$

Given, 75% of X decomposes in 100 min.

$k=\frac{1}{100}ln\left(\frac{1}{0.025}\right)⟶\left(1\right)$

$k=\frac{1}{100}ln\left(4\right){min}^{-1}$

For 90% decomposition,

$t=\frac{1}{k}ln\left(\frac{1}{0.1}\right)$

Using value of k from (1)

$t=\frac{100}{ln4}ln10=\frac{100ln10}{2ln2}$

$t=\frac{100\times 2.303}{0.60\times 2.303}=166.66min$

The time taken for 90% decomposition = 166.66 min.