A=Pe^(-(ln2)t)

[peyman2002]

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Do we need to know the half life formula for the DAT?

 

[nze82]

Dear lord peyman!!
Stop trying to figure out what you need to and what you dont need to know for the DAT. Do you have the KAPLAN book? I suggest you read it. If there's something written in that book, then YES! you're better off knowing it than leaving it up to chance and ignoring it. I believe the half-life formula is mentioned in that book and there are multiple problems relating to half-life in their online quizes. So, you should probably know it.

 

[Streetwolf]

Easier yet might be:

y = y(orig)*(1/2)^(t/HL)

If they give you a proportionality constant then you can use:

k = ln(2) / HL

This will let you obtain the HL and use the first equation.

 

[UCfan]

Do we need to know the half life formula for the DAT?

This is a reaction kinetics problems. If you take physical chemistry or reaction engineering, remember that for DAT (general chemistry) only batch reactors are considered. In general, reactor balance is
In-Out+Generation=Accumulation
Batch reactors have no input and output so the balance equation becomes
Generation=Accumulation
Then you may think the simplest reaction
A->B
The mass balance can be writen as
raV=dNa/dt (ra=reaction rate,V=volume of the reactor,Na= mole of species A,t=time,d=change)
Na=Ca*V (Ca=concentration of A)
Then for Oth order reaction
-k(Ca^0)V=dNa/dt
-kV=VdCa/dt (assuming reactor volume is constant)
-kdt=dCa (integrate bot sides)
-kt=Ca-Cao
Ca=Cao-kt
First order reaction
-k(Ca)dt= dCa
-kdt=dCa/Ca (integrate both sides)
-kt=In (Ca/Cao)
exp (-kt)= Ca/Cao
Ca=Cao*exp(-kt)
Second order reaction
-k(Ca^2)dt=dCa
-kdt=(dCa/Ca^2) (integrate both sides)
-kt= -(1/Ca)+(1/Cao)
(1/Ca)=kt+(1/Cao)
Once you know rate expressions, everything is easier. You need to know
that at t1/2= Cao/2 (at half life concentration reduces half of the initial concentration).
For first order reaction
-kt1/2=In [(Cao/2)/Cao]
-kt1/2= In (1/2)
kt1/2=In 2
k=(In2)/(t1/2)

You do not need to memorize, if you know how to derive. If you do not want to learn the derivation,at least know first order reaction (because approximately 90 percent of reactions are studied in chemical engineering are first order reactions).If you have more questions in reaction engineering let me know, it is one of my favourite topic !