How do I find the half life if I was given that Solution A1 (0.008 M) took 261.6

Question

How do I find the half life if I was given that Solution A1 (0.008 M) took 261.6 seconds to change color and Solution B1 (0.04 M) took 388.8 seconds to change color and the average temperature was 55.5 C? (1st order reaction)

Then my experiment data shows: Find the half-life Initial T / Final T / Initial time / Final time / Half-Life

Run 1 85C / 84.5 / 0 / 0:54:97 _____ (thats 0 minutes, 54 seconds, 97 milliseconds)

Run 2 75C / 72.0 / 0 / 1:32:78 _____

Run 3 65.2C / 63.5 / 0 / 3:12:22 _____

Run 4 45.2C / 47.0 / 0 / 29:55:97 _____

Run 5 55.0 C and my lab says that the half life for run 5 is the average of the two half lives (A1 and B1) so what would that be? Using the data above what would be: t1/2, k, ln k, 1/T

Run 1 357.9K _____ _____ _____ _____

Run 2 346.65K _____ _____ _____ _____

Run 3 337.4K _____ _____ _____ _____

Run 4 319.15K _____ _____ _____ _____

Run 5 328.15K _____ _____ _____ _____

And after I find that for all 5 runs, how do I find the EA?

Note: This is the 3rd time I'm posting this question. Please. Help me.

Explanation / Answer

Definition and Formula

By definition, half-life is the period of time it takes for a substance undergoing decay to decrease by half. An exponential decay process can be described by any of the following three equivalent formulas:

Nt = N0(1/2)t/t1/2
Nt = N0e-t/
Nt = N0e-t

where
N0 is the initial quantity
Nt is the quantity that still remains after a time t,
t1/2 is the half-life
is the mean lifetime
is the decay constant

t1/2 = ln(2) = ln(2)/

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