Half life

Mr/Ms Levi

Time in this case is a constant identically equal to the timeperiod specified for you to graduate from this vocational hairdressing school where you learn how to bleach hair of clients.

Make sure you know the temperature inside the refrigerator where the hairdressing salon keeps benzoyl peroxide as well as any delta temperatures whenever one of your hairwashing associates opens or closes the door to stick in his or her soda and you're sure to graduate cum laude, specially if you learn to write square roots as raising a number to a fractional power properly, or learn the chemical composition of the various elements before you blind any unfortunate clients by mistake and most of all thank you very much for warning the rest of us not to have our hair bleached by anyone going by your last name.

And oh Mr/Ms Levi if you're trying to put together explosives please stop posting here, it's a respectable site!!!!! thank you......

Half life is the time that a material takes for it to degrade to half its initial amount. If Refrigerated Benzoyl Peroxide has a half life of 9800 days, then in 9800 days you only have half your Benzoyl Peroxide stash left. (50%)

This decay is normally expressed as an exponential function

T=To*exp(-λ*t)--------(1)
Where T is the amount you have left
To is the initial amount
t is time
and λ is a constant of decay
exp is the exponential function

The first problem is to determine λ
Fortunately you've been given the half life and this the time t where T is one half To
So
(1/2)To=To*exp(-λ*9800 day)
divide through by To and you get
(1/2)= exp(-λ*9800 day)
lake the natural logarithm of both sides
Ln(1/2)=Ln(exp(-λ*9800 day))=-λ*9800 day
So λ=-Ln(1/2)/9800 days

Now you can use this λ to determine how long it takes for 3% of your benzoyl peroxide to degrade. Since 3% degradation means 97% is left the T is 0.97*To

Putting this into the decay function----(1)

0.97*To=To*exp[-(-Ln(1/2)/9800)*t]
and divide through by To
0.97= exp(Ln(1/2)/9800*t)
take the logarithm of each side
Ln(0.97)=Ln(1/2)/9800*t
And solve for t
t=Ln(0.97)/[Ln(1/2)/9800]
Since the units of λ are in reciprocal days (day^(-1)) the unit of t is day

Rap

Answer
[size=7]λ=1.64228E-4/day
t@ 97%=185.46 day[/size]
Rap

Re: Half life


Potency? What would that be in molar equivalents?

(Potency is not a chemical term. )

I actually substituted the percentages provided into the equation I was looking for
t=(1/k)*(ln([A]0/[A]t))
where [A]0 is usually initial concentration and [A]t is concentration at time of 3% decomposition.
I got the correct answer of 431 days.

I thank the three of you for your help.

i don't wanna know how smart you lot are

Me neither!