In order to change grams of a substance to moles of the same substance, or vice versa, the following should be used: a) mole ratio b) avogadro's number c) molar mass d) mole fraction

C) molar mass

Explanation:

Hello,

In the calculations in chemistry, one of the major computations involve the conversion from mass to mole considering that there is no equipment that allows us to measure the exact moles of a substance since it depends on the type of atom, in spite of this fact, balances have been widely used to measure a substance's mass. In such a way, it is possible to relate them via the molar mass since it relates how many grams of a substance are contained in one mole of such substance. For instance, one mole of sodium chloride has  58.44 grams of sodium chloride or vice versa, so its molar mass is .

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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