Homework Help: maths PLEASE HELP

Posted by Amelia on Sunday, November 29, 2009 at 6:44am.

Can you give me some help with this question im not sure how to even start

in a reaction A to P
the mass of A at any given time T is Mt and the rate of transformation of A at time T is prportional to Mt given that the original mass of A is 130g and that 50g has been transformed after 120 seconds

form and solve a differential equation relating Mt to t
and find the mass of A transformed over a 300sec period

maths PLEASE HELP - MathMate, Sunday, November 29, 2009 at 10:46am
d(M(t))/dt = -kM(t)
where k is a constant.
The minus sign indicates M(t) diminishes with time.
Rearranging and integrate
d(M(t))/M(t) = -kdt
ln(M(t))= -kt + C
where C is an arbitrary constant
M(t) = e^-kt+C ....(1)
Put e^C=ln(Mo), the initial mass of A.
(1) can be rewritten as
M(t)=Mo e^-kt
At t=0, e^-kt=1, Mo=130.
At t=120, M(120)=130-50=80
Therefore
M(120)=80=130e^-k(120)
from which k=0.004 approx.
Thus
M(t)=Mo e^-0.004t

The amount transformed at t=300 can be calculated from the expression
M(0)-M(300).

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