Oxygen is composed of three isotopes: one of the isotopes has a mass of 16.999 amu with an abundance of 0.037% . The two other isotopes have masses of 15.995 amu and 17.999 amu respectively. Calculate the abundance in percentage ot the two other isotopes of oxygen, using the average atomic mass of oxygen 15.9994 amu ?
Answers
Answer : The abundance in % for other two isotopes of the oxygen is 99.762% and 0.201%
Explanation :
The average atomic mass of an element is the total of isotopic mass times the percent abundance for all the isotopes.
Oxygen has 3 isotope, ¹⁶O, ¹⁷O and ¹⁸O.
The average atomic mass of oxygen can be calculated as follows.
Average Atomic Mass = (Isotopic mass of ¹⁶O x % abundance of ¹⁶O) + (isotopic mass of ¹⁷O x % abundance of ¹⁷O) + (Isotopic mass of ¹⁸O x % abundance of ¹⁸O)
The mass of ¹⁷O = 16.999 amu and its % abundance is 0.037% which is 0.00037
The mass of ¹⁶O = 15.995 amu. Let us assume its % abundance as a
The mass of ¹⁸O = 17.999 amu
The total % abundance for all the isotopes is 100% or 1 .
Therefore % abundance for ¹⁸O would be 1 - ( a + 0.00037) = 0.99963 - a
Let us plug in the above values in the average atomic mass formula .
Average atomic mass = ( 15.995)(a) + (16.999)(0.00037) + (17.999)(0.99963 - a)
The average atomic mass of element O is 15.9994
Therefore we have,
15.9994 = 15.995a + 0.0062896 + 17.99234 - 17.999a
15.9994 = -2.004a + 17.99863
-1.99923 = -2.004a
a = 0.99762
a = 99.762%
The percent abundance of ¹⁶O is 99.762%
The percent abundance of ¹⁸O is 0.99963 - 0.99762 = 0.00201 or 0.201%