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.
The Correct Answer and Explanation is:
To calculate the average atomic mass of an element based on its isotopes, we use the formula:
[
\text{Average atomic mass} = \sum (\text{fraction of isotope} \times \text{atomic mass of isotope})
]
1. Average Atomic Mass of Chlorine
Chlorine has two isotopes: chlorine-35 and chlorine-37. The atomic masses and their respective abundances are:
- Chlorine-35: Atomic mass = 34.9689 u, Abundance = 75.771%
- Chlorine-37: Atomic mass = 36.9659 u, Abundance = 24.229%
We can calculate the average atomic mass by multiplying the atomic mass of each isotope by its fractional abundance (converted to a decimal), then summing these products:
[
\text{Fraction of chlorine-35} = \frac{75.771}{100} = 0.75771
]
[
\text{Fraction of chlorine-37} = \frac{24.229}{100} = 0.24229
]
Now, calculate the weighted average:
[
\text{Average atomic mass of chlorine} = (0.75771 \times 34.9689) + (0.24229 \times 36.9659)
]
[
= 26.5089 + 8.9633 = 35.4722 \, \text{u}
]
So, the average atomic mass of chlorine is 35.4722 u.
2. Average Atomic Mass of Copper
Copper has two isotopes: copper-63 and copper-65. The atomic masses and their respective abundances are:
- Copper-63: Atomic mass = 62.93 u, Abundance = 69.1%
- Copper-65: Atomic mass = 64.93 u, Abundance = 30.9%
We will follow the same steps as for chlorine:
[
\text{Fraction of copper-63} = \frac{69.1}{100} = 0.691
]
[
\text{Fraction of copper-65} = \frac{30.9}{100} = 0.309
]
Now, calculate the weighted average:
[
\text{Average atomic mass of copper} = (0.691 \times 62.93) + (0.309 \times 64.93)
]
[
= 43.487 + 20.087 = 63.574 \, \text{u}
]
Thus, the average atomic mass of copper is 63.574 u.
Explanation
The concept of average atomic mass accounts for both the mass and relative abundance of each isotope in a sample. Since the isotopes of an element have slightly different masses, the average atomic mass is not simply the mass of one isotope but a weighted average based on the abundance of each isotope. For each element, the mass of the isotopes is multiplied by its fractional abundance, and these products are summed to get the average atomic mass. This value is the one commonly reported on the periodic table. The process ensures that the atomic mass reflects the natural distribution of isotopes in a sample.