A chemical reaction converts a certain chemical into another chemical, and the rate at which the first chemical is converted is proportional to the amount of this chemical present at any time. At the end of one hour, two-thirds $\mathrm{kg}$ of the first chemical remains, while at the end of four hours, only one-third $\mathrm{kg}$ remains.
(a) What fraction of the first chemical remains at the end of seven hours?
(b) When will only one-tenth of the first chemical remain?