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We can also do variations of this type of calculation, as shown in the next example.

Calculation of percent abundance

Naturally occurring chlorine consists of 35 Cl (mass 34.96885 amu) and 37 Cl (mass 36.96590 amu), with an average mass of 35.453 amu. What is the percent composition of Cl in terms of these two isotopes?

Solution

The average mass of chlorine is the fraction that is 35 Cl times the mass of 35 Cl plus the fraction that is 37 Cl times the mass of 37 Cl.

average mass = ( fraction of 35 Cl × mass of 35 Cl ) + ( fraction of 37 Cl × mass of 37 Cl )

If we let x represent the fraction that is 35 Cl, then the fraction that is 37 Cl is represented by 1.00 − x .

(The fraction that is 35 Cl + the fraction that is 37 Cl must add up to 1, so the fraction of 37 Cl must equal 1.00 − the fraction of 35 Cl.)

Substituting this into the average mass equation, we have:

35.453 amu = ( x × 34.96885 amu ) + [ ( 1.00 x ) × 36.96590 amu ] 35.453 = 34.96885 x + 36.96590 36.96590 x 1.99705 x = 1.513 x = 1.513 1.99705 = 0.7576

So solving yields: x = 0.7576, which means that 1.00 − 0.7576 = 0.2424. Therefore, chlorine consists of 75.76% 35 Cl and 24.24% 37 Cl.

Check your learning

Naturally occurring copper consists of 63 Cu (mass 62.9296 amu) and 65 Cu (mass 64.9278 amu), with an average mass of 63.546 amu. What is the percent composition of Cu in terms of these two isotopes?

Answer:

69.15% Cu-63 and 30.85% Cu-65

Got questions? Get instant answers now!

The occurrence and natural abundances of isotopes can be experimentally determined using an instrument called a mass spectrometer. Mass spectrometry (MS) is widely used in chemistry, forensics, medicine, environmental science, and many other fields to analyze and help identify the substances in a sample of material. In a typical mass spectrometer ( [link] ), the sample is vaporized and exposed to a high-energy electron beam that causes the sample’s atoms (or molecules) to become electrically charged, typically by losing one or more electrons. These cations then pass through a (variable) electric or magnetic field that deflects each cation’s path to an extent that depends on both its mass and charge (similar to how the path of a large steel ball bearing rolling past a magnet is deflected to a lesser extent that that of a small steel BB). The ions are detected, and a plot of the relative number of ions generated versus their mass-to-charge ratios (a mass spectrum ) is made. The height of each vertical feature or peak in a mass spectrum is proportional to the fraction of cations with the specified mass-to-charge ratio. Since its initial use during the development of modern atomic theory, MS has evolved to become a powerful tool for chemical analysis in a wide range of applications.

The left diagram shows how a mass spectrometer works, which is primarily a large tube that bends downward at its midpoint. The sample enters on the left side of the tube. A heater heats the sample, causing it to vaporize. The sample is also hit with a beam of electrons as it is being vaporized. Charged particles from the sample, called ions, are then accelerated and pass between two magnets. The magnetic field deflects the lightest ions most. The deflection of the ions is measured by a detector located on the right side of the tube. The graph to the right of the spectrometer shows a mass spectrum of zirconium. The relative abundance, as a percentage from 0 to 100, is graphed on the y axis, and the mass to charge ratio is graphed on the x axis. The sample contains five different isomers of zirconium. Z R 90, which has a mass to charge ratio of 90, is the most abundant isotope at about 51 percent relative abundance. Z R 91 has a mass to charge ratio of 91 and a relative abundance of about 11 percent. Z R 92 has a mass to charge ratio of 92 and a relative abundance of about 18 percent. Z R 94 has a mass to charge ratio of 94 and a relative abundance of about 18 percent. Z R 96, which has a mass to charge ratio of 96, is the least abundant zirconium isotope with a relative abundance of about 2 percent.
Analysis of zirconium in a mass spectrometer produces a mass spectrum with peaks showing the different isotopes of Zr.

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Source:  OpenStax, Ut austin - principles of chemistry. OpenStax CNX. Mar 31, 2016 Download for free at http://legacy.cnx.org/content/col11830/1.13
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