Which of the following represents the expression for 3/4th life of 1st order reaction

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$\frac{2.303}{k} \log 4$

$\frac{K}{2.303} \log 4$

$\frac{2.303}{k} \log 3 / 4$

$\frac{2.303}{k} \log 3$

answer is C.

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Detailed Solution

The general formula for the time taken in a first-order reaction is:

t = (2.303 / k) * log(a / (a - x))

t: Time elapsed.
k: Rate constant.
a: Initial concentration of the reactant.
x: Amount of reactant consumed at time t.

Step-by-Step Solution:

Understand the Situation:
At 3/4th life (t_3/4), 75% of the reactant has reacted, leaving only 1/4th of the initial concentration. Thus:
```
x = (3a / 4)
 
```
Remaining concentration = a - x = a - (3a / 4) = a / 4.
Substitute in the Formula:
Replace x = 3a / 4 and a - x = a / 4 into the first-order reaction formula:
```
t_3/4 = (2.303 / k) * log(a / (a - 3a / 4))
 
```

Simplify the Expression:

t_3/4 = (2.303 / k) * log(a / (a / 4))
t_3/4 = (2.303 / k) * log(4)

Final Answer:

The expression for the 3/4th life of a first-order reaction is:

t_3/4 = (2.303 / k) * log(4)

Key Point:

To find which of the following represents 3:4, always interpret it as a ratio indicating the consumption or remaining fraction of the reactant, which helps in solving questions like this.

Conclusion:

The correct representation of the expression for the 3/4th life of a first-order reaction is:

Option (C): t_3/4 = (2.303 / k) * log(4).

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