From an English grammar standpoint I can say there is not a hard and fast rule about not using a possessive with inanimate objects. There is certainly evidence that there is a preference toward avoiding possessives with inanimate objects but reputable grammar books allow for this usage and there are plenty of examples out there where possessives are used with inanimate objects.

I haven't seen this issue come up on the GMAT. If anyone has I would be interested to know about it.

KW

Posted from my mobile device
_________________

1st step: Check if the Subject and the verb agree.
In this case, there is no Subject verb agreement error.
Use the Acronym, VIPMPS to check for the common grammatical errors tested on the GMAT.
V: Verb Tense
I: Idioms
P: Pronouns
M: Misplaced Modifier
P : Parallelism
S : Subject Verb Agreement.
This acronym is not in a hierarchical order; you always check for the Subject Verb agreement first.
We will now use the Process of Elimination to eliminate wrong answers and hold on to the right one.

A. an especially serious pollutant because it diminishes the respiratory system’s ability to deal. (Correct Answer.) The subject and verb agree and it is clear that the Pronoun ‘it’ refers to ‘ sulphur dioxide and not acid rain, as ‘ a major contributor to acid rain’ is a modifying phrase which modifies Sulphur Dioxide. ‘Ability to’ is the correct idiom usage.

B. an especially serious pollutant because of diminishing the respiratory system’s capability of dealing (“ because of diminishing” is not a correct usage as ‘because of” is usually followed by a Noun phrase which gives a reason for something.) “capability of ……...ing is unidiomatic

C. an especially serious pollutant because it diminishes the capability of the respiratory system in dealing-Can be knocked off) “capability in …………………….. Ing is not the correct idiomatic usage

D. a specially serious pollutant because it diminishes the capability of the respiratory system to deal: This option can be knocked off as : “Specially” means in a special way and therefore is incorrect here. In the context of this sentence, “Especially”, which means ‘in particular’ or ‘ than the others’ should be used
E. a specially serious pollutant because of diminishing the respiratory system’s ability to deal: This option can be knocked off for two reasons: “Specially” means in a special way and therefore is incorrect here. In the context of this sentence, “Especially”, which means ‘in particular’ or ‘ than the others’ should be used” AND “ because of diminishing” is not a correct usage as ‘because of” is usually followed by a Noun phrase which gives a reason for something.) “capability of ……...ing is unidiomatic

CORRECT ANSWER: A
_________________

Nice question. Tough.
Specially or Especially?

We have to use especially because it signifies that Sulphur Dioxide is serious pollutant than others.

Specially is used when we have to say that something is special. This is clearly not the case.

A is the answer.
_________________

Here
A is pretty much straightforward.
Especially is an adverb modifying serious. It means exclusively or something that is important. Specially is not correct in this context.
A is clear and concise.