Estradiol is a female sexual hormone that causes maturation and maintenance of the female reproductive system. elemental analysis of estradiol gave the mass percent composition: c, 79.37%; h, 8.88%; o, 11.75%. the molar mass of estradiol is 272.37 g/mol. find the molecular formula of estradiol.

The answer to your question is: Molecular formula =  C₁₈H₂₄O₂

Explanation:

Estradiol

C = 79.37 %

H = 8.88 %

O = 11.75 %

Molar mass = 272.37

Process    

Carbon   =    79.37 g

Hydrogen  =   8.88 g

Oxygen  =      11.75 g

                       12 g of Carbon    1 mol

                       79.37 g                  x

                        x = (79.37 x 1) / 12

                       x = 6.61 mol

                      1 g of Hydrogen  1 mol

                     8.88 g                     x

                      x = (8.88 x 1 ) / 1

                      x = 8.88 mol

                     16 g of Oxygen  1 mol

                     11.75 g                   x

                     x = (11.75 x 1) / 16

                     x = 0.73

Divide by the lowest number of moles

Carbon    = 6.61 / 0.72 = 9.2

Hydrogen =  8.88 / 0.73 = 12.2

Oxygen = 0.73/0.73 = 1

Empirical formula

                                         C₉H₁₂O₁

MW of the empirical formula = (12 x 9) + (12 x 1) + (16 x 1)

                                                = 136 g

Divide molar mass of estradiol by the molar mass of the empirical formula.

                    = 272 / 136

                   = 2

Then the molecular formula is:

                             2(C₉H₁₂O)  =  C₁₈H₂₄O₂

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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explanation: