When a volume of a gas is changed from __ l to 4.50 l, the temperature will change from 38.1 c to 15.0c

Assuming that the change of volumen was done at constant pressure and the quantity of gas did not change, you use Charles' Law of gases, which is valid for ideal gases:

V / T = constant => V1 / T1 = V2 / T2 => V1 = [V2 / T2] * T1.

Now plug in the numbers ,where T1 and T2 have to be in absolute scale.

T1 = 38.1 + 273.15 K = 311.25K

T2 = 15.0 + 273.15 K = 288.15K

V1 = 4.5L * 311.25K / 288.15 K = 4.86L.

4.86

They are all solids.

Radon-222 or rn-222 has a half-life of 3.82 days. to determine the fraction of an original sample of rn-222 that remains unchanged after 7.646 days, we calculate the amount of rn-222 remaining after 7.646 days and divide it with the original amount. using 1 gram as a basis and using half-life calculation methods, we can determine that  0.249 or 0.25  grams of rn-222 will remain, and thus the fraction remaining is 0.25 or 1/4.