Which phrase describes the mass of an ice cube? a. amount of space that the cube occupies
b. estimation of the weight of the ice cube
c. total amount of water in the ice cube
d. value obtained by multiplying its length times width times height

The right option is; c. total amount of water in the ice cube

Mass is an attribute of a physical body and a measure of the amount of matter present in an object. Mass is mainly  measured in grams or kilograms.

The mass of an ice cube is the total amount of water in the ice cube. Ice is the solid form of water. For example, two pounds of ice cube will make two pounds of water after melting because its mass does not change. When in the ice form, the water molecules will spread apart and occupy more space or volume.  

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

tracks, burrows, eggshells, nests, tooth marks, or gastroliths