When these type of frogs die mysteriously and quickly it is most often from some type of bacterial disease which isn't always noticeable externally. It would be fine to use the same tank for the new frog after cleaning. The best method is to use a bleach solution of 10%. Scrub everything (including all accessory equipment; filters, nets etc.)with the bleach solution and let it sit for a couple minutes. Then rinse everything a couple times with fresh water until all the bleach smell is gone. This should kill any harmful bacteria.

Brian