Question

In a first order reaction $A\to B,60\%$ of the given sample of compounds decomposes in $45$ minutes. The half life of the reaction is ______________.

• A. $12min$
• B. $34min$
• C. $40min$
• D. $43min$

Answer 1

The correct option is B $34min$

For the first order reaction,

$k=\frac{2.303}{t}\frac{Loga}{a-x}$

where,

$k=rateconstant$

$t=ageofsample$

$a=letinitialamountofthereactant$

$a-x=amountleftafterdecayprocess$

$k=\frac{2.303}{45}\frac{Log100}{100-60}$

$k=\frac{2.303}{45}log\frac{5}{2}$

$k=0.02mi{n}^{-1}$-------------------------------(1)

$t_{1/2}=\frac{0.693}{k}$------------------------------------(2)

on putting value of $k$ in equation (2) from (1) we will get:

$t_{1/2}=\frac{0.693}{0.02}$

$=34.65$

Option B is correct.