Is zakat obligatory on an amount of money designated for purchasing a house, if a full year has passed over it before the completion of the purchase process?

As long as you have not paid the price to the seller, it remains in your possession and is considered a debt upon you. If you possess other funds in excess of your needs, then pay the Zakat on this price if a year has passed over it and it has reached the Nisab. If you do not possess such funds, then deduct the price from the money on which Zakat is due, and pay Zakat on the remainder if it does not fall below the Nisab.