Pseudo-first order, irreversible reaction...

Question

...of A to B is given by:

k = k0 * e^ -αt.

Determine in terms of α and k0, the batch time required to achieve 90 percent conversion of A, assuming there was no B contained in the feed.

[I know that by taking logs of the equation, the exponent is then removed:

ln k = ln k0 - αt.

And that the half life of this reaction is:

t(1/2) = ln 2 / α.

Any help would be greatly appreciated as the end value I calculated seems too small. Thanks.]

Answer 1

From your top equation, letting k = .9 and k0 = 1,

t = -ln(0.9)/α.