[kimi85]

If the relative reactivities of 1^o, 2^o, 3^o hydrogen atoms toward Cl^. are 1.0:3.8:5.0, what percentage by weight of the total yield of monochlorinated products of 2,3,4-trimethylpentane will be accounted for the most abundant of these products?

The correct answer is 40%

Does anyone know how to get that answer?

Thanks!

[Nick]

Sure, this is not too difficult of a problem.  Here's how to solve it.
1) Draw the skeletal structure of 2,3,4-trimethylpentane and label the carbons on the longest chain 1-5.
2) Note that there are 18 primary hydrogens and 3 tertiary hydrogens. 
3) Some of these hydrogens are chemically equivalent: (a) the 12 hydrogens belonging to the four methyl groups on the 2 and 4 carbons, (b) the three hydrogens on the methyl group on the 3 carbon, (c) the two hydrogens on the 2 and 5 carbons, and (d) the lone hydrogen on the 3 carbon.  The hydrogens within each of these groups are equivalent due to rotational symmetry and therefore, the reactivity of any hydrogen within a group is the same as the reactivity of any another hydrogen within that group.  Also note that substitution of any single hydrogen within a group with a chlorine atom gives the same product as you would get if you did the same substitution on any other hydrogen in that same group instead.  This is the definition of chemical equivalency.
4) So, what are your possible products?  There are only four possible monochlorinated products: you could have a chlorine on a group (a) hydrogen, a chlorine on a group (b) hydrogen, and chlorine on a group (c) hydrogen, or a chlorine on a group (d) hydrogen.  But which is most likely?
5) Calculate probabilities using this equation:
relative probability = (# hydrogens)*(relative reactivity based on primary or tertiary)

Group A: (12 hydrogens)*(1) = 12
Group B: (3 hydrogens)*(1) = 3
Group C: (2 hydrogens)*(5) = 10
Group D: (1 hydrogen)*(5) = 5

Since group A has the highest relative probability in the reaction with chlorine, the most abundant monochlorinated product is the one in which a hydrogen in group A is substituted with chlorine.
6) But how much of the total mass of products will be the most abundant product?
% mass = (relative probability of group A substitution)/(sum of all relative probabilites)
= 12/(12+3+10+5) = 0.4

Please repost if you have any questions or need further clarification.

[kimi85]

Thank you very much!!

are there really 18 primary hydrogens? I thinks it's only 15..

How do I know of their equivalence? Is it based on their most stable positions?

[Nick]

You are correct...there are only 15 primary hydrogens.  Sorry for the typo.

Here is the best way to think of chemical equivalence.  Think of a fan.  Now imagine painting one of the fan blades white.  It doesn't matter which one you paint because all of the fan blades were identical to start with.  Your friend could do the same thing on his fan, and without you telling him which blade to paint, would end up with exactly the same result.

This is the same concept in chemistry.  Suppose I have ethene H2C=CH2.  If I substitute any single hydrogen with another atom, I end up with a mono-substituted ethylene.  But it doesn't matter which hydrogen atom I substitute because I get the same product in each case...1-substituted ethene.  As a result, all four hydrogen atoms are chemically equivalent. 

Now, back to your problem.  Note that if you put a chlorine on ANY ONE of the atoms in Group C, you end up with 2-chloro-2,3,4-trimethylpentane.  Note that "4-chloro-2,3,4-trimethylpentane" is exactly identical to 2-chloro-2,3,4,-trimethylpentane if you rotate the molecule along the long axis of your paper.  This is why these positions of 2,3,4-trimethylpentane are said to be chemically equivalent.  You can react at either position to give the same product.

[kimi85]

Wow!! Thank you very much! 

[kimi85]

how about for isobutane?

is it 64% or 38.4%..

My answer is 64% but the answer is 38.4% or 38.4% is wrong?

thanks!!