IIT JEE , AIEEE Forum - Chemistry , Physical Chemistry

miyo

Hello,

I know u wud glance at this if i put subject as that!

Do solve this ..........

A given sample of milk turns sour at room temperature (20⁰C) in 64 hrs .In a refrigerator at 3⁰C milk can be stored 3 times as long before it sours.

Estimate how long it'll take teh milk to sour at 40⁰C ???

kiran

Hi

Is the answer 11 hours ?? if yes , i'l give the solution.

Good question!

Cheers!

umang

Hey kiran !

pls post how you did this !!!

Thanks !!!

miyo

Sorry kiran,

I don't have the ans ....

Will u plz post ur solu?

kiran

Hi

Milk gets sour at room temperature and is more faster at a bit higher temperature ie 30-40 . Till this temperature we can assume that the lifetime of milk L is inversely proportional to temperature. This can be seen from the fact that milk kept at low temperature lasts longer. ( not for many days) .

Now

L

1/T

L₁*T₁ = L₂ * T₂

ie 3L * 3 = 20 * 64 ( given lifetime of milk at 3 degrees is 3 times the total)

L = 1280/9.

Using in second case. 3 * 1280/9 = 40 * L₄₀

L₄₀ = 10.66 ~ 11 hours .

I dont know whether this approach is right. Friends pls check it.

Cheers!

miyo

Hi kiran......

I think u shud take absolute temperatures.

The ans given in the bk (just looked into it) is 20.5 hrs.

KAB

The ans in the book is correct.

miyo

Hey KAB ,

tell me how u did it (elaborate ur explaination plzzzzzz.)?

also, plz look into my other queries.....

KAB

I'm typing.Just wait.It is bit lengthy.

KAB

This is indeed a really good question!!!

Here the eqn you should use is kt=2.303log((a+x)/a)........(1)

[This is a different eqn applied in this case only]

and

log(k₂/k₁)=E_a(T₂-T₁)/(2.303T₁T₂)........(2)

Also see that the milk sours implies that the no. of bacterias should be same.

ie log((a+x)/a) should be same.

At T₁=293K ,

k₂*64=2.303log((a+x)/a)......(3)

At T₂= 276K

k₁*64*3=2.303log((a+x)/a)

So we get k₂/k₁=3

Use (2)

So log(3)=E_a(293-276)/(2.303*293*276)........(4)

At T₃=313K

log(k₃/k₂)=E_a(313-293)/(2.303*293*313).....(5)

(4)/(5) gives

k₃=3.125k₂

Now

k₃*t=2.303log((a+x)/a)

or

3.125k₂*t=2.303log((a+x)/a)

Divide this by (3)

We get t=20.48hrs

I hope you will be clear!!!

KAB

If you have completed the chapter "Chemical Kinetics" then you could understand this easily.

miyo

Ya,i've done the chap. but not completely........

Do u think there is some hint given in the prob that the reac(souring of milk) is following 1st order kinetics?

KAB

Yes.Souring of milk is first order reaction.

miyo

Oh........

So, here i missed the fact that souring of milk is 1st order....

I didn't know that { else i wud 've solved it ! }

I only knew radioactive disintegration follows 1st order...........

Anyways, thanks 4 ur patience .

Do u know any more of such examples??

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