In three different experiments, the following results were obtained for the reaction

A - > products:

[A]o = 1.00M, t1/2=50 min;

[A]o = 2.00M, t1/2 = 25 min;

[A]o = 0.50M, t1/2 = 100 min.

Write the rate equation for this reaction, and indicate the value of K?

From the given observations,

You can see that as the concentration is doubled, half-life is halved.

That is, half-life is inversely proportional to concentration

As t (half-life) ~ 1/a^ (n-1)

For this case n = 2, second order reaction.

R = k X a^n

Using the above formula you will get the rate and rate constant.