Calculations in chemistry
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Calculations in Chemistry:. Average Atomic Mass. Isotopes. An element can exist in a number of forms, called isotopes. Isotopes are forms of the same atom that vary in mass as a result of a different number of neutrons.

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Calculations in chemistry

Calculations in Chemistry:

Average Atomic Mass


Isotopes

Isotopes

  • An element can exist in a number of forms, called isotopes. Isotopes are forms of the same atom that vary in mass as a result of a different number of neutrons.


Calculations in chemistry

  • For example, there are two different types (isotopes) of copper atoms. One type of copper atoms weighs in at 62.93 amu, the other has a mass of 64.94 amu. 

  • These two isotopes have different proportions in a natural sample of copper.

  • The lighter isotope is more common with  69.09% of the naturally occurring copper having a mass of 62.93 amu per atom.

  • What is the percent abundance of the other isotope?


Calculations in chemistry

  • The remainder of the atoms, 30.91 %, have a mass of 64.94 amu.


Average atomic mass

Average Atomic Mass

  • To find the AVERAGE ATOMIC MASS of an atom, we take into account all of the isotopes that exist and the percentage of each type.

  •  The calculation of the average atomic mass is a WEIGHTED AVERAGE.


Calculation of average mass

Calculation of Average Mass

Average atomic mass =

 Σ (mass of isotope × relative abundance)

Σ = sum or to add them all together


Calculation of average mass1

Calculation of Average Mass

  • The bottom line is that to find the average atomic mass of copper, we insert the information about copper’s isotopes into the formula and solve. 

  • There are two isotopes, so we will be adding the contributions of 2 isotopes. (That’s where the Σ sign comes in. ) 

  • The relative abundance is simply the percentage of the isotope, but in decimal format.  69.09% corresponds to a relative abundance of 0.6909.


Calculation of average mass2

Calculation of Average Mass

Average atomic mass of copper =

(62.93 amu × 0.6909)

[the mass and abundance of isotope #1]

+

(64.94 amu × 0.3091)

[the mass and abundance of isotope #2]

=

63.55


Calculation of average mass3

Calculation of Average Mass

  • From the calculation, we know that an AVERAGE atom of copper has a mass of 63.55 amu.

  • Notice that in this problem, we would predict that the average is closer to the weight of the lighter isotope.

  • This is because the lighter form of copper is more abundant.


Practice

Practice


Check your answers

Check Your Answers

  • Silver = 107.87 amu

  • Silicon = 28.09 amu

  • Iron = 55.84 amu


Homework

Homework

  • Read section 1.4 in the text to support what we did in class today.

  • pg27 #1

  • Pg 29 #1-5,9


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