Question

T1/2 for first order reaction is 25 s,what is time required for 10g of reactant to get reduced to 1.25g

Answer 1

The time required is 75 seconds.

Answer 2

The time required for the first order reaction is 750.3 seconds

Explanation:

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 = 25 s

Putting values in above equation, we get:

$k=\frac{0.693}{25s}=2.772\times 10^{-3}s^{-1}$

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  = $2.772\times 10^{-3}s^{-1}$

t = time taken for decay process = ? s

$[A_o]$ = initial amount of the sample = 10 grams

[A] = amount left after decay process = 1.25 grams

Putting values in above equation, we get:

$2.772\times 10^{-3}=\frac{2.303}{t}\log\frac{10}{1.25}\\\\t=750.3s$

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