Video Transcript
As a molar percentage, 80.3 percent
of a boron sample is boron 11 and the remainder is boron 10. What is the average molar mass of
the boron sample?
We are told that a sample of boron
consists of 80.3 percent boron 11, while the remainder of the sample consists of
boron 10. Boron 10 and boron 11 are isotopes
of boron. Isotopes are atoms that have the
same number of protons but a different number of neutrons. In other words, isotopes are atoms
of the same element that have a different mass and a different mass number. The mass number is the number
written to the top left of the element symbol. The mass number is the sum of the
number of protons and neutrons in the nucleus. This value is not the exact mass of
an atom of an isotope. However, it is approximately equal
to the isotopic mass and unified atomic mass units.
With this background information in
mind, let’s return to the question. We want to determine the average
molar mass of the boron in the sample. When we think about how to
calculate a standard average, we might think that we could just sum the isotopic
masses, then divide by the total number of isotopes. So, in the case of the sample, we
would sum together the approximate isotopic masses of each isotope, then divide by
two, the total number of isotopes. But this type of average does not
take into account the fact that boron 11 makes up considerably more of the sample
than boron 10. So instead of calculating a
standard average, we need to calculate a weighted average.
More specifically, the weighted
average we need to calculate is the average atomic mass. The average atomic mass is
calculated by multiplying the isotopic abundance of one isotope times its isotopic
mass, then adding this to the isotopic abundance of the second isotope times its
isotopic mass.
Isotopic abundance is a percentage
that represents the relative amount of an isotope. So for boron 11, the isotopic
abundance is 80.3 percent. For this calculation, we’ll use the
approximate isotopic mass, which has the same value as the mass number with units of
unified atomic mass units. The second isotope of boron is
boron 10 with an approximate isotopic mass of 10 unified atomic mass units. The isotopic abundance or molar
percentage of boron 10 was not provided in the question, but it can easily be
determined. 100 percent of the sample contains
80.3 percent boron 11, with the remainder being boron 10. This means that the isotopic
abundance of boron 10 is 19.7 percent.
Before we can continue with the
calculation, we need to rewrite each percentage in decimal notation. We can accomplish this by dividing
each percentage by 100 percent. Now we can perform the calculations
inside of the parentheses, then add together the resulting answers. This gives us an average atomic
mass of 10.803 unified atomic mass units.
But the question asked for the
average molar mass, not the average atomic mass. The average molar mass has the same
numerical value as the average atomic mass but has units of grams per mole instead
of unified atomic mass units. Rounded to one decimal place, we
have determined that the average molar mass of the boron sample is 10.8 grams per
mole.
