Paying rent from zakat without telling the renter

My friend is separated from her husband. She is living in my basement. This month she has refused to pay rent as she has not enough money. Can I adjust her monthly rent from the amount of zakat which I have to pay? As she pays me $500 for monthly rent and I have to pay $2500 zakat if I don't take rent for this month, can I consider that I have paid $500 zakat? I don't want to share with her that I have adjusted her rent from zakat money. Is it acceptable?