Question

If 75% of first order reaction is completeu mi se
min, then 50% of the reaction would be
completed in (प्रथम कोटि की कोई अभिक्रिया 32
मिनट में 75 प्रतिशत पूरी हो जाती है। उसके 50 प्रतिशत
परा होने में कितना समय लगेगा ?)
1.10...
11000​

Answer 1

Answer : The time required in 50 % of reaction completion is 16.0 min

Explanation :

Expression for rate law for first order kinetics is given by:

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

where,

k = rate constant  = ?

t = time passed by the sample at 75 % reaction completion = 32 min

a = let initial amount of the reactant  = 100 g

a - x = amount left after decay process = 25 g

Now put all the given values in above equation, we get

$k=\frac{2.303}{32}\log\frac{100}{25}$

$k=0.0433min^{-1}$

Now we have to calculate the time required in 50 % of reaction completion.

The formula used :

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

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

$t_{1/2}=\frac{0.693}{0.0433min^{-1}}$

$t_{1/2}=16.0min$

Therefore, the time required in 50 % of reaction completion is 16.0 min