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Question:

For a first order reaction, A→P, t1/2 (half-life) is 10 days. The time required for 1/4 conversion of A (in days) is: (ln2=0.693, ln3=1.1)

2.5

4.1

3.2

5

Solution:

The half lifet1/2=10days
The decay constant k=0.693/t1/2=0.693/10days=0.0693day-1
The time required for one fourth conversion
t=2.303/k log10(a/(a-x))
t=2.303/0.0693day-1 log10(1/(1-(1/4)))
t=4.11days