In which sentence is the bracketed group of words a prepositional phrase acting as an adverb? . my sister’s grades gave her a place [in the top rank of her class].. my sister applied [on tuesday] to a graduate school in england.. my sister is going [to write novels].. my sister hopes to be one [of the finest novelists in the world]..

The prepositions are the words which show the relationship between the pronoun and the nouns. On the other hand, the prepositional phrase starts with the prepositions and end with the object of a preposition, having one or more modifiers to describe.

Adverb phrase refers to the group of words which qualifies adjectives, verbs or adverbs.  

While answering the question of where? when? or how? prepositional phrase is identified as an adverb.

Therefore, the sentence in which group of words is a prepositional phrase acting as an adverb is My sister applied [on Tuesday] to a graduate school in England.

As the above bracketed sentence answer the question of when did she apply? - 'on Tuesday', hence it qualifies to be a prepositional phrase acting as an adverb and modified 'applied.'

impartial means: treating all rivals or disputants equally; fair and just.

i would say that impartial is agreeing with something, because impartial means to treat your rivals, arguments, and reasoning equally and fair. so if you rival says something, agreeing on it means you did the impartial.