Question

a first order reaction is 75% complete in 60 minutes 50% of the reaction will be completed in how many minutes​

Answer 1

you are trying to say that :

$75\% \times x = 60 \\ = > \frac{3}{4} x = 60 \\ = > \frac{3}{4 \times 3} x = \frac{60}{3} \\ = > \frac{1}{4} x = 20$

$50\% = \frac{1}{4}$

then,

$50\% = 20$

Answer 2

A first order reaction is 75% complete in 60 minutes 50% of the reaction will be completed in 30 minutes​.

Explanation:

1) The equation used to calculate half life for first order kinetics:

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

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

$k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}$......(2)

where,  

k = rate constant

t = time taken for decay process = 5 sec

$[A_o]$ = initial amount of the reactant = x

[A] = amount left after 60 minutes=  (100%-75%)of x=25% of x=0.25x

t = 60 minutes

Putting values in above equation(2), we get:

$0.25x=x\times e^{-k\times 60 min}$

$k = 0.023105 min^{-1}$

2) So, 50% of the reaction will be completed in t time:

$A_o=x$

$A=(100%-50%)x=50%x=0.5x$

$0.5x=x\times e^{-0.023105 min^{-1}\times t}$

t = 30 minutes

A first order reaction is 75% complete in 60 minutes 50% of the reaction will be completed in 30 minutes​.

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