Q.21E - Chemistry (OpenStax)

Question

Repeat Exercise 2.20 using an element that has three naturally occurring isotopes.

Step-by-Step Solution

Answer

In this question, we will talk about the isotopes of the Boron elements and their percentage composition and average atomic mass.

Step 1: Describing the isotopes of the Hydrogen element

Hydrogen has the three isotopes such as protium, deuterium, and tritium, denoted as ¹H or H, ²H, or D, and ³H or T, respectively. 

In protium, there is an absence of neutron, whereas one neutron can be found in deuterium and two neutrons in tritium. Protium is the most found isotope in hydrogen, and tritium is found in trace amounts. Deuterium is some about 0.0155 %. 

When an electron is removed from the outermost orbit of the protium atom, which has a proton in its nucleus, the atom is called a proton, and the nucleus of the deuterium is known as the deuteron.

Step 2: Describing the relative amounts of isotopes of hydrogen

The average atomic mass of hydrogen is 1.11 amu.

The atomic mass unit of ¹H is 1.00794 amu and

The atomic mass unit of ²H is 2.014 amu, while the atomic mass of tritium is not considered.

We know that

X = Fraction of Hydrogen - 1

Y = Fraction of Hydrogen - 2

Now,

\(\begin{aligned}{\underline{\phantom{xx}}}X\,\,(1.0079)\,\, + \,\,Y\,(2.014)\,\, &= \,\,1.11\\X\,\,(1.0079)\,\, + \,\,(1 - X)\,(2.014)\,\, &= \,\,1.11\\1.0079X\, + \,\,2.014\,\, - \,\,2.014X\,\, &= \,\,1.11\\ - 1.0061X\,\, &= \,\, - 0.904\\X\,\, &= \,\,0.89851\\and\,\,Y\,\, &= \,\,1\,\, - \,\,X\,\, &= \,\,0.1\,\end{aligned}\)

Therefore, the predicted abundance percentage of hydrogen – 1 is 89.851 %, while for hydrogen – 2 is 10 %.

Step 3: Comparing the prediction of percent composition and average atomic mass of isotopes with the black box mixture

The predicted percentage composition of Hydrogen isotopes is 89.851 and 10 percent, respectively.

The black box mixture has 90.9 and 9.1 percent, respectively.

The difference between the percentage black box mixture and the predicted mixture is

Difference for Hydrogen – 1  = 90.9   -  89.851  =   1.049 %

Difference for Hydrogen – 2  = 10   -  9.1  =  0.9 %

The abundancy for the black box mixture is more than the predicted mixture.

Step 4: Comparing the predicted with nature`s mixture

The predicted percentage composition of Hydrogen isotopes is 89.851 and 10 percent, respectively, while nature’s percentage composition is 99.9885 and 0.0115 %, respectively.

The natural abundance percentages of Hydrogen - 1 and Hydrogen - 2 are 99.9885 and 0.00115 percent, respectively. 

The difference between the predicted and natural is almost 10 % which cannot be ignored.

In the case of atomic mass, the predicted atomic mass is 1.11, and the natural is 1.00794 amu.