Hydrogen is found primarily as two isotopes in nature: (1.0078u) and (2.0140u). Calculate the percentage abundance of each isotope based on hydrogen's average atomic mass.
Answer (3)
hydrogens average atomic mass = 1,01u
x = isotope about mass (1.0078u) y = isotope about mass (2.0140u) x + y = 100% so: x = 100% - y
h y d ro g e n s a v er a g e a t o mi c ma ss = 100 ( 1.0078 ⋅ x ) + ( 2.0140 ⋅ y ) 1.01 = 100 ( 1.0078 ⋅ ( 100 − y )) + ( 2.0140 y ) ∣∣ ⋅ 100 101 = 100.78 − 1.0078 y + 2.0140 101 − 100.78 = 1.0062 y 0 , 22 = 1.0062 y ∣∣ : 1.0062 0.219% = y x = 100% − y x = 100% − 0.219% x = 99.781% answer: x = 99.781% y = 0.219%
To calculate the percentage abundance of each isotope of hydrogen based on its average atomic mass, we need to consider the isotopes hydrogen-1 (¹H) with a mass of 1.0078u, and hydrogen-2 (²H or deuterium) with a mass of 2.0140u. The average atomic mass of hydrogen is around 1.008u, and it's known that hydrogen-1 (¹H) makes up more than 99.98% of hydrogen's natural occurrence.
Given this information, if we let x represent the fraction of ¹H and (1-x) the fraction of ²H, we can set up the equation 1.0078x + 2.0140(1-x) = 1.008. Solving for x gives us the percentage of ¹H, and 1-x gives us the percentage of ²H. However, with ¹H already known to make up more than 99.98% of natural hydrogen, the calculation illustrates why the average atomic mass of hydrogen is very close to the mass of ¹H itself.
For a precise calculation, you would solve the equation for x, but based on the information provided, it's clear that the percentage abundance of ¹H is approximately 99.98%, and for ²H, it would be roughly 0.02%.
The percentage abundance of the isotopes of hydrogen is approximately 99.78% for Protium (¹H) and 0.22% for Deuterium (²H). This conclusion is drawn from using hydrogen's average atomic mass along with the known masses of the isotopes. The calculation reveals that Protium is the dominant isotope in nature.
;
