Question

A substance 'A' decomposes by a first order reaction starting initially with [A] = 2.00 M and after 200 min, [A] becomes 0.15 M. For this reaction $t_{1/2}$ is
(a) 53.72 min
(b) 50.49 min
(c) 48.45 min
(d) 46.45 min

Answer 1

Hello

Here is your answer

Option C is the correct answer

THANK you so much for your question

Answer 2

The half life of the reaction is 53.72 minutes

Explanation:

Rate law expression for first order kinetics is given by the equation:

$k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}$

where,

k = rate constant  = ?

t = time taken for decay process = 200 min

$[A_o]$ = initial amount of the sample = 2.00 M

[A] = amount left after decay process =  0.15 M

Putting values in above equation, we get:

$k=\frac{2.303}{200}\log\frac{2}{0.15}\\\\k=0.0129min^{-1}$

The equation used to calculate rate constant from given half life for first order kinetics:

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

where,

$t_{1/2}$ = half life of the reaction = ? min

k = rate constant of the reaction = $0.0129min^{-1}$

Putting values in above equation, we get:

$t_{1/2}=\frac{0.693}{0.0129min^{-1}}=53.72min$

Learn more about first order kinetics:

https://brainly.com/question/14739930

https://brainly.com/question/14634617

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