He has some money for university expenses and one full hijri year has passed – does he have to pay zakaah on it?

Praise be to Allah.

If the money that you have left reaches the nisaab, and one year has passed, then it is subject to zakaah, even if it is being kept for your living expenses or study fees, because of the general meaning of the evidence that indicates that zakaah becomes obligatory when the conditions for it are met. 

The nisaab is the equivalent of 85 grams of gold or 595 grams of silver, and the rate that must be paid is 2.5%, which is a small amount, praise be to Allaah, in addition to the blessing and growth that it brings to the one who pays zakaah. Allaah says (interpretation of the meaning): 

“Take Sadaqah (alms) from their wealth in order to purify them and sanctify them with it, and invoke Allaah for them. Verily, your invocations are a source of security for them; and Allaah is All-Hearer, All-Knower”

[al-Tawbah 9:103]

And the Prophet (peace and blessings of Allaah be upon him) said: “Charity does not decrease wealth.” Narrated by Muslim (2588). 

And Allaah knows best.