I have a second wife, she is a teacher and I do not know anything about her salary and she does not spend of her wages. Is it permissible for me to gift money to the first wife [and not to the second wife] when she asks me for some to spend on some of her needs?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

It is an obligation on the husband to be just between his wives with regard to spending on them and clothing them, however, it is permissible for him to prefer one over the other if the other one is solvent.

Ibn Qudaamah, quoting Imaam Ahmad said about a man who has two wives: 'It is permissible for him to prefer one over the other in spending on them and having sexual intercourse with them, if the other one is solvent.'  Therefore, there is no harm on you to provide your first wife with some necessities and not gift the second wife since she is solvent.

Allaah Knows best.