Is Zakat obligatory on an amount of 200,000 Saudi Riyals remaining from the sale of a house, designated for the purchase of another house, after settling a bank loan? And is the husband obligated to compensate his wife for the earnest money she paid for a house that was not purchased?

Zakat (definition) is obligatory on money that has completed a full year (hawl) and reached the nisab (definition) (minimum threshold), even if it is designated for purchasing a house. Zakat is not obligatory on any portion of it that has been spent. As for the agreement between the spouses to buy a house, it is a promise from the husband to participate. A promise that is legally binding is one that is contingent on a cause, and the promisee incurred a cost because of it. In such a case, the promisor is obligated to fulfill the promise or compensate for the damage incurred. If the questioner paid the down payment based on her husband's promise, and he then failed to fulfill it without a valid excuse, he must compensate her for the actual damage.