The pure

Blessed are the pure in heart…
I have spent the day wrestling with this.
I prayed over it, I explored a gazillion different translations, and I just haven’t made much progress. The only places that use a different word than “pure” seems to be the paraphrases. And I always fear that I’m just getting the authors preconceptions with those.
As I began to think about this verse, the first sense of the word “pure” that came to me bares sexual connotations. Purity as opposed to lustful. It seems reasonable to think that we might see God when we are pure in this sense.
But then I began to think that there is a wider sense in which we use the word “pure” as in pure motives. We’re not operating with ulterior motives. Sometimes, for example, I enter into prayer looking for that wonderful God-buzz. I am pure of heart when I do this in the sense that I’m not sexual. But I’m not pure of heart in the sense that I am operating from unmixed motives.
Our motives are always so important to God. He knows them. And these are what He truly judges. And I find myself wondering: is there perhaps a connection? Is sexual impurity somehow related to having mixed motives?
As the Holy Spirit works through translators in creating new versions of scripture, is it possible that sometimes He chooses words like “pure” which have those 2 different senses because Jesus meant it in both senses of the word?
Can anybody out there offer some insight into original Greek?