Which of the following is not equal 225 g? a. 0.225 kg b. 22,500 cg c. 2.25 dkg d. 2250 dg

C) 2.25 dkg

Explanation: 1 kg = 1000 g

A)  = 225 g

B) cg stands for centigrams. 1 g = 100 cg

So,   = 225 g

C) dkg stands for decagrams. dag is also used in place of dkg which also means decagram.

1 dkg = 10 g

 = 22.5 g

D) dg stands for decigram.

1 g = 10 dg

 = 225 g

On converting all the given mass units to grams, we see that it's choice C which is not equal to 225 g and so it is the right choice.

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

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