Question

average atomic mass
overview
the average atomic mass of an element can be determined from the relative amounts of each isotope. this is the mass used in most chemical calculations.
in a naturally occurring element, the fractional abundance is the percentage of the abundance of a particular isotope in the total sample of atoms, written as a decimal.
to calculate average atomic mass of an element:
average atomic mass = (fractional abundance of isotope 1)(atomic mass of isotope 1) + (fractional abundance of isotope 2)(atomic mass of isotope 2) +...
practice problems

1. chlorine has two isotopes. chlorine - 35 has an actual mass of 34.9689 u and chlorine - 37 has a mass of 36.9659 u. in any sample of chlorine atoms, 75.771% will be chlorine - 35 and 24.229% will be chlorine 37. calculate the average atomic mass of chlorine.
2. copper has two isotopes. copper - 63, which has an atomic mass of 62.93 u and copper - 65, which has an atomic mass of 64.93 u. in any sample of copper atoms, 69.1% will be copper - 63 and 30.9% will be copper - 65. calculate the average atomic mass of naturally occurring copper.
3. one atom has 20 protons and a mass of 44. another atom has 20 protons and a mass number of 40. what is the identity of these atoms? how do you account for the difference in mass numbers?

Explanation:

Step1: Convert percentages to fractional abundances for chlorine

Chlorine - 35 fractional abundance: $75.771\%= 0.75771$; Chlorine - 37 fractional abundance: $24.229\% = 0.24229$.

Step2: Apply average - atomic - mass formula for chlorine

Average atomic mass of chlorine = $(0.75771\times34.9689)+(0.24229\times36.9659)$
$=26.5997 + 8.9445$
$=35.4442$ u

Step3: Convert percentages to fractional abundances for copper

Copper - 63 fractional abundance: $69.1\%=0.691$; Copper - 65 fractional abundance: $30.9\% = 0.309$.

Step4: Apply average - atomic - mass formula for copper

Average atomic mass of copper=$(0.691\times62.93)+(0.309\times64.93)$
$=43.48463+20.06337$
$=63.548$ u

Step5: Identify the atoms with 20 protons

The number of protons determines the atomic number. An element with atomic number 20 is calcium (Ca).

Step6: Account for the mass - number difference

The mass number is the sum of protons and neutrons. For the first Ca atom with mass number 44, number of neutrons = $44 - 20=24$. For the second Ca atom with mass number 40, number of neutrons = $40 - 20 = 20$. The difference in mass numbers is due to the difference in the number of neutrons. These are isotopes of calcium.

Answer:

1. The average atomic mass of chlorine is $35.4442$ u.
2. The average atomic mass of copper is $63.548$ u.
3. The identity of the atoms is calcium (Ca). The difference in mass numbers is due to the difference in the number of neutrons (isotopes).