Si innocentia reae clara erit, iudex eam statim absolvet.

Because innocentia reae means the innocence of the defendant. Latin often uses the genitive to show of-relationships.

So here:

• innocentia = innocence
• reae = of the female defendant

In other words, reae depends on innocentia, not directly on the verb.

The form reae is ambiguous by itself, but the context makes the meaning clear.

Why it is genitive singular here:

• innocentia naturally takes a genitive: someone’s innocence
• the sentence is about one defendant, not several
• later we get eam, which is her, singular feminine, referring back to the same person

So reae here means of the defendant, not to/for the defendant and not female defendants.

That is a very common difference between English and Latin.

Latin often uses the future indicative in both parts of a future condition:

• Si ... clara erit = If ... is/will be clear
• iudex ... absolvet = the judge will acquit

English usually prefers a present tense in the if-clause, but Latin is perfectly happy to use a future there. So si ... erit is normal Latin for a real future possibility.

This is a future more vivid condition, or more simply a real future condition.

It presents something as a genuine future possibility:

• If the defendant’s innocence becomes/is clear, the judge will acquit her immediately.

The pattern is:

• si
  • future indicative
• future indicative in the main clause

So:

• erit = future
• absolvet = future

The subject of erit is innocentia.

So:

• innocentia = nominative singular feminine
• clara = nominative singular feminine
• erit = will be

clara is a predicate adjective, and it agrees with innocentia in:

• gender: feminine
• number: singular
• case: nominative

So literally, the innocence will be clear.

Here clara means clear, evident, or plain.

It does not mean bright in a physical sense here, and it does not mean famous here either, even though clarus, clara, clarum can sometimes mean those things in other contexts.

So innocentia reae clara erit means that the defendant’s innocence will be obvious / evident.

eam is the accusative singular feminine form of is, ea, id and means her in this sentence.

It refers back to rea:

• rea = the female defendant
• eam = her

It is the direct object of absolvet:

• iudex eam absolvet = the judge will acquit her

Latin often uses a pronoun instead of repeating the noun.

Because rea is feminine. It means female defendant or accused woman.

That is why the sentence has:

• reae = of the female defendant
• eam = her

If the defendant were male, Latin would normally use reus and then a masculine pronoun such as eum.

iudex is the subject of absolvet.

So:

• iudex = the judge
• absolvet = will acquit

Even though the ending may not look obvious to an English speaker, iudex here is nominative singular.

absolvet is:

• 3rd person singular
• future indicative active
• from absolvo, absolvere

So it means he/she will acquit, and here the subject is iudex, so:

• iudex eam statim absolvet = the judge will immediately acquit her

statim means immediately, at once, or straightaway.

It modifies the verb absolvet:

• iudex eam statim absolvet = the judge will acquit her immediately

Its position before the verb gives it a natural emphasis, but Latin word order is flexible.

The word order is meaningful, but not rigid in the way English word order usually is.

This order is natural:

• condition first: Si innocentia reae clara erit
• result next: iudex eam statim absolvet

Latin uses endings to show grammatical roles, so the sentence could be rearranged more freely than in English without changing the basic meaning.

Still, this order is stylistically clear:

1. the condition
2. the judge
3. the object
4. the adverb
5. the verb

That is a good question, because Latin often does use the future perfect in if-clauses.

A future perfect would usually stress that one action is completed before the main action. But here the sentence describes a state:

• the innocence will be clear
• then the judge will acquit

So erit works well because it focuses on the future state of being clear.

A future perfect version could shift the nuance slightly toward once it has become clear, but erit is perfectly natural as written.

Yes. Latin could have repeated the noun, but using the pronoun is very natural and avoids repetition.

So instead of:

• iudex ream statim absolvet

the sentence uses:

• iudex eam statim absolvet

Both are understandable, but eam is smoother because the referent is already clear.