Hey renocchi.
Hint: Use separation of variables to get all the X_r terms on the LHS and everything else on the right hand side. (Also note that the anti-derivative of -1/(a - y)dy = ln(a-y))
Hi,
Could someone be so kind and show be how equation (3) in integrated step by step to give (4) (please enlarge attached picture). I am stumped. Also equally frustrating is the fact that I cant even follow the step between (4) to give (5). I would love to hear back from someone to enlighten me.
Thanks very much in advance,
Best,
Renaud
PS. important i think: Xr(t) represents the concentration of species (X) on resin (r) (physical adsorption beads) which are thrown into a solution at t=0. therefore I know that Xr(t) should be 0 at time equals 0. Hope this helps too.
Hey renocchi.
Hint: Use separation of variables to get all the X_r terms on the LHS and everything else on the right hand side. (Also note that the anti-derivative of -1/(a - y)dy = ln(a-y))
Xr(t) = e^c*e^(-kt) - D woa...
a^n · a^m = a^n+m?!?
product rule?
but i thought taking the exponent on both sides would give:
ln(Xr(t) + d) = -kt + C
Xr(t) + d = e^-kt + e^C