Question

Calculate the average atomic mass of hydrogen using the following data:

Isotope	Per natural abundance	Molar mass
\[{}^1H\]	$99.985$	$1$
\[{}^2H\]	$0.015$	$2$

Answer 1

Hint: The average atomic mass of an element is the total of masses of isotopes. We can say the average atomic mass of an element by totaling the masses of its isotopes. We can calculate the total masses of its isotopes by multiplying the natural abundance of the isotope and molar mass of the isotope. We can write the formula to calculate average atomic mass of element is,
${\text{Average atomic mass}} = {f_1}{M_1} + {f_2}{M_2} + .....{f_n}{M_n}$
Here, f represents natural abundance of the isotope
M represents the molar mass of the isotope.

Complete step by step answer:
In the question, we are given two isotopes of hydrogen. They are ${}^1H$ and ${}^2H$.
We are given per natural abundance of ${}^1H$ as $99.985$.
We are given per natural abundance of ${}^2H$ as $0.015$.
We are given molar mass of ${}^1H$ as $1$.
We are given molar mass of ${}^2H$ as $2$.
We have to convert the percent natural abundance of ${}^1H$ into decimal. We can get natural abundance in decimal as,
Percent abundance=$\dfrac{{99.985}}{{100}} = 0.99985$
We have calculated the natural abundance of ${}^2H$ as $0.99985$.
We have to convert the percent natural abundance of ${}^2H$ into decimal. We can get natural abundance in decimal as,
Percent abundance=$\dfrac{{0.015}}{{100}} = 0.00015$
We have calculated the natural abundance of ${}^2H$ as $0.00015$.
Let us now calculate the average atomic mass of hydrogen by substituting the values of natural abundance and molar mass in the expression given below.
\[{\text{Average atomic mass}} = {f_1}{M_1} + {f_2}{M_2} + .....{f_n}{M_n}\]
Now we can substitute the known values we get,
\[{\text{Average atomic mass}} = \left( {0.99985} \right)\left( 1 \right) + \left( {0.00015} \right)\left( 2 \right)\]
On simplification we get,
${\text{Average atomic mass}} = 1.00015\mu $
We have calculated the average atomic mass of hydrogen as $1.00\,\mu $.

Note: When we are determining the average atomic mass of an element, it is mandatory to convert the natural abundance in percentage to decimals. We can do this by dividing natural abundance by hundred. If we don’t convert the natural abundance in decimals, we will have error while determining the total masses of isotopes that give average atomic mass.