Question

What is the weighted average mass of chlorine?

Answer 1

Hint: Chlorine is a toxic gas that has a total of 25 isotopes. Out of these 25 isotopes, only two are stable that exist in nature. These are Chlorine-35 and Chlorine-37. The weighted average mass of chlorine is the sum of masses of these isotopes multiplied by abundance.
\[\text{Weighted average mass of Cl}=\left( {{\text{M}}_{\text{Cl-35}}}\times \%\text{Abundance} \right)+\left( {{\text{M}}_{\text{Cl-37}}}\times \%\text{Abundance} \right)\]
Where M denotes the corresponding atomic mass.

Complete answer:
Most elements occur naturally as a mixture of two or more different forms. These different forms of an element contain the same number of protons but possess a different number of neutrons and are known as isotopes.
In such elements, the mass usually taken is the weighted average mass of all the stable isotopes of that element. On the periodic table also, the average mass of an element is written just below the elemental symbol.
Chlorine is a yellow-green coloured toxic gas having an atomic number 17. It also has more than one isotope. Chlorine has a total of 25 isotopes, but out of these only two are stable in nature and known to us. These two isotopes are chlorine-35 and chlorine-37. Here, the numbers 35 and 37 are the atomic masses.
Since the atomic number of chlorine is 17, so chlorine-35 isotope contains 18 neutrons while the chlorine-37 isotope contains 20 neutrons. The former one has a natural abundance of 75.77% relative to natural chlorine atoms and the latter is having 24.23% abundance.
Thus, the average mass of chlorine can be calculated by taking the sum of the masses of isotopes multiplied by their relative abundance in nature.
\[\begin{align}
  & \text{Average mass of Cl}=\left( 35\text{ amu}\times \dfrac{75.77}{100} \right)+\left( 37\text{ amu}\times \dfrac{24.23}{100} \right) \\
 & \Rightarrow \text{Average mass of Cl}=\left( 26.52\text{ amu} \right)+\left( 8.96\text{ amu} \right) \\
 & \Rightarrow \text{Average mass of Cl}=35.48\text{ amu} \\
\end{align}\]
Hence, the weighted average mass of chlorine is 35.48 amu.

Note:
The atomic mass of an element is usually represented in the units of amu. Here, amu stands for an atomic mass unit. This unit is derived from the standard carbon-12 isotope. 1 amu is the 1/12th of the mass of a carbon-12 isotope. However, another unit is used for atomic mass known as Dalton (Da). 1 Dalton is approximately equal to 1 amu.