Using "to" versus "for" between two nouns ("key to success")

Another user provided an example and I have added others:

Key to exercise
Key for exercise

Answer to a problem
Answer for a problem

Bullet to a gun
Bullet for a gun

She bought a taser to self-defense.
She bought a taser for self-defense.

We give alms to the poor.
We give alms for the poor.

She gave the order to the cook.
He put in the order for dinner.

Some of these seem pretty clear to me. I would select {to, to, for, for} for the first four, but the last two made me wonder if there is some rule at work, or if I'm basing it off what sounds better from repeated hearing. For instance, I might give "alms to the poor," but if I were poor then I'd bother passerby with "Alms for the poor?"

Is there some "pairing" going on (i.e. an answer is always to a question/problem/etc.)? Perhaps by plugging words into "this goes to that" or "this is for that", one could determine the proper usage. I'm looking for an explicit description or "rule" of what feels like an innate quality of the words. I believe Spanish has a similar dichotomy with para and por, but I'm not sure whether this translates (no pun intended) to English.

Solution 1:

Here's part of an explanation found here:

TO ... is used in cases where a "transfer" happens. E.g.

• I will give this book to you. (from me to you)
• I will go to work. (from home to work)
• I will talk to her. (information goes from me to her)

FOR is used in the following situations:

for the benefit of

e.g. I will do that for you.

purpose

e.g. This brush is for painting.

Not exactly a rule, but in general to applies if the word coming afterwards is specific. For is used if the situation is more abstract.

For this reason, both of your examples for alms make sense depending on the context.

We give alms to the poor.  (Which poor? The beggars downtown. We give alms to those beggars.)  
We give alms for the poor. (Which poor? I'm not sure. Our charity determines who receives the alms.)

Solution 2:

"To" specifies a direction, an intention, it implies some action, while "for" is more associated with someone/something who is intended to own or use the noun preceding "for".

key to exercise - I cannot find a key to this exercise. key for exercise - The keys for the exercises are on the last page.

bullet to a gun - The police could not find any bullet to the gun in the street. bullet for a gun - We took a lot of bullets for a gun when hunting.

Solution 3:

I do not have a clear answer, but the question poses some ambiguity issues.

Part of the problem is the characterization that the prepositions are used between two nouns. In the cases listed, that is physically true. This seems to imply the prepositions define the grammatical relationship between those nouns. That is not necessarily the case.

In the example

She gave the order to the cook.

the phrase to the cook is not a modifier of order, it is the indirect object of the verb gave.

However, in the example

He put in the order for dinner.

the prepositional phrase for dinner is a modifier of the noun order.

Similarly, in

We give alms to the poor.

the phrase to the poor is the indirect object of give.

I believe (but am not certain) that indirect objects are often introduced by to but not usually by for

If that is so, in

We give alms for the poor

the phrase for the poor should be interpreted to be a modifier of alms.

By no means am I suggesting that to cannot introduce a noun modifier, but in some of these cases, it does not.