Is it permissible to pay Zakat with the intention of purifying the heart without possessing funds to calculate its amount, or would it be considered Sadaqah (voluntary charity) in this case?

Charity is of two types: obligatory, such as Zakat (definition), and voluntary. If the questioner does not possess wealth upon which Zakat is due, then Zakat is not obligatory upon her. If she wishes to give charity, she is permitted to do so, and it would be voluntary charity, for which she will be rewarded. It also entails purification and sanctification for herself and her wealth. It has been said in the interpretation of Allah Almighty’s saying: (Take, [O, Muhammad], from their wealth a charity by which you purify them and cause them increase) that it refers to the charity they gave voluntarily or to Zakat. The non-acceptance of charity from unlawful earnings was linked to the non-acceptance of prayer without ablution because giving charity is a purification for the soul and a cleansing for it.