# How to find the integrated rate law?

## Homework Statement

Find the integrated rate law for a first order reaction

## The Attempt at a Solution

We have r = -d[A]/dt = k[A]

Integration with respect to [A] gives

[A] = (1/2)k*[A]^2

Is this it?

d[A]/dt = k[A]

1/(k*[A]) . d[A] = dt

1/(k*[A]) . d[A] = t

now integrate left side ..

I am pretty sure that you have got it wrong

ln[A] + [A]0 = kt

Is this the correct form?

Last edited:
ln[A] + C = kt

Can anyone explain why the integration constant is ln[A]0?

that's due to the integration limits
{from 0 to t}
ln(A) is at t and ln[A]0 is 0