English translation:
in order to
Structure:
Verb + のに
Confused as to what のに is doing in this sentence
これといった理由もないのに約束を破ってはいけない。
Since you don’t even have so much as a reason you cannot break your promise.
it sounds like "despite not having a reason, you shouldn’t break your promise.
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Hey 
You are right, it works here as “in spite of” etc. 
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Thanks!!!
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Would it be fair to consider this version of のに really just Verb + nominalizing の + に? Interestingly the Dictionary of Basic Japanese Grammar says that the “in spite of” のに is from that, but doesn’t mention anything for this のに.
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Hey 
Yup!
It is good to look at words that are used with のに from a wider perspective (since it is more limited than ために)
It is used with verbs that express doing something like 使う, adjectives expressing the importance of something like 必要 or 便利。It follows the desired outcome, for what something is needed, etc. Simply put aim.
If we look closely for example at 必要:
ボタンがインターフェースに必要だ
Buttons are needed for the interface.
いいカバンが旅行に必要だ。
A good bag is needed for traveling.
We will see that it is simply used in particular case when 必要 (and others) are used with verbs, working as nominalizer.
コップがビールを飲のむ のに 必要です。
Cup is essential to drink.
Do you see the similarity?
Well, that is basically it. 
Also look at verb[stem]+に+行く construction
スーパーへ食べ物を買いに行ってくる。
I am going to the supermarket to buy food.
In this case, it also expresses aim.
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I was wondering about this sentence:
連絡するのに連絡先が分からない。
There are still plenty of constructions I’m not familiar with and perhaps this is one of those, but the way it’s worded strikes me as odd. The English, “I don’t know his contact information in order to get in touch with him,” seems a bit unnatural but mostly okay, but the literal Japanese would be “To contact him in order his contact information I don’t know.” It doesn’t quite follow, to my mind.
On the other hand, most sentences, despite having the opposite order to English, do follow. For example,
コップがビールを飲のむ のに 必要です。
“A cup beer drink in order to is necessary”. This all flows logically, to me.
Is this a sentence someone would be likely to use? If so, are you able to explain why it would sound okay to a native?
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Well, it will very often sound bizarre if you do left-to-right direct translation like you did there. Maybe it’s better if you try and stick to right-to-left translation as much as possible? My Japanese teachers emphasized that a million times when we translated in class. Now, as for your example sentence, I was surprised by the word order. I would’ve written it as ビールを飲むのにコップが必要です。Now I want to know if both word orders are natural, lol. Sorry I couldn’t really be of much help.
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I wouldn’t ordinarily translate a sentence so literally. Ordinarily sentences make sense to me in Japanese, they’re just presented differently than English, whereas this one doesn’t make sense to me. Maybe this will clarify my issue: I’ve understood “in order to” as “for the purpose of”, so “I don’t know his details for the purpose of contacting him,” is the result. That is, it seems to me that the subject is deliberately ignorant of the contact details because they believe that not knowing them will allow them to contact the person. Maybe this is an ambiguity in English that doesn’t translate to Japanese…
Maybe “in order to” is a bit too specific in English. Here it’s just “for” or something like that. “I don’t know the contact details for contacting him”. The cup is not intentionally necessary so that you drink, either. It’s just necessary for drinking. The part before the のに expresses something one aims to do and the part following it is somehow related to achieving that.
I think it’s less ambiguous in Japanese, I don’t think わからない by itself can be intentional. Intentionally not knowing the address would be more like わからないままにしておく.
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Both are grammatically correct, however ビールを飲むのにコップが必要です。sounds more natural. However, if you want to emphasize the コップ more, then コップがビールを飲むのに必要です。will be OK too. For example:
「あ、コップがない。コップがビールを飲むのに必要ですよ！」
Coming back to the:
連絡するのに連絡先が分からない。
It is exactly like @nekoyama says.
Notice that のに is generally used with 必要だ、役に立つ、要る and 使う and indicate what a something (tool) is used for or needed for - the purpose. If we look from wider perspective, those verbs can actually simply work with に in case of nouns and tells us a bit more about のに。
睡眠は健康に必要だ*。
Sleep is necessary for sleep.
この色はハイライトに使う。
This color is used for highlighting.
I hope it helps,
Cheers
PS
I think we will have to change the sentence, because のに should be generally used with the expressions mentioned.
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Thanks, mrnoone, that makes sense. 
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Hello! I am learning this grammar and I am confused with the difference between it and “no tame ni”. Could someone please explain? thank you!
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Am I the only one who thinks the English translations are actually grammatically incorrect? Like it doesn’t just sound unnatural, it sounds wrong for almost all the examples. I was always under the impression that it was (mostly) used as: X happens in order to Y, with Y being the goal/purpose and X being the means to that end. Very few of the examples fill that definition.
E.g.
宿題をするのに、3時間がかかる。
It takes 3 hours in order to do homework.
Wouldn’t it just be “It takes 3 hours to do homework.”?
Similarly:
食べるのに時間がかかりすぎて、昼休みが終わってしまった。
It took too long in order for me to eat lunch, so my lunch break unfortunately came to an end.
–>“It took too long for me to eat lunch…”
お茶を飲むのに必要なコップがありません。
I do not have the necessary cup in order to drink tea.
→ I do not have the necessary cup to drink tea.
本を読むのに眼鏡を買った。
I bought glasses in order to read books.
→ This one sounds fine since there is a purpose and a means to get there.
電車で音楽を聴くのにイヤフォンを忘れてしまいました。
I forgot to bring the earphones I use in order to listen to music on the train.
→ I forgot to bring the earphones I use to listen to music on the train.
You get the idea. A bunch of them switch to just using “to” and thus sound much more natural.
Additionally, the sentences should make sense if you flip the clauses.
E.g. “In order to drink tea, I do not have the necessary cup.” is legitimately an incorrect sentence.
Am I crazy in thinking these all sound weird? Am I just some crazy American who has been using this phrase wrong my entire life? Please let me know.
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All the sentences are correct. (But they might be more common in British English.)
This is a correct sentence.
Would it sound better if it was “for the purpose of drinking tea…”? The speaker is talking about a cup that is specifically used for tea, as opposed to a cup for any other beverage.
I think they chose to translate it this way to keep “to” in front of the verb in translation and keep the verb un-conjugated (without “ing”). Also, using “to” instead of “in order to” doesn’t convey the sense of purpose in the grammar point.
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Hey @chella1788 and welcome on the community forums!
The sentences are natural, maybe a bit formal. The idea is, like @FredKore says:
・to keep verb in infinitive form
・to clearly express the intended meaning, because “to” by itself might be unclear
・to keep translation consistent between sentences
I hope it helps,
Cheers 
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Oh, I missed this. Thank you!
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In this example sentence:
さっき食べたばかりなのに、またお腹が空いた
I just can’t figure out why there is a な after ばかり.
The structure for のに is: Verb + のに
The structure for ばかりis: Verb［た］+ ばかり
Anyone have an idea?