Calculating Average Atomic Mass from Isotopic Abundance: Worked Example

📚 Quick Study Guide

• ⚛️ Average atomic mass is the weighted average of the masses of all isotopes of an element.
• 🔢 The formula to calculate average atomic mass is: $\text{Average Atomic Mass} = (\% \text{ Abundance of Isotope 1} \times \text{Mass of Isotope 1}) + (\% \text{ Abundance of Isotope 2} \times \text{Mass of Isotope 2}) + ...$
• ➗ Remember to express the percent abundance as a decimal by dividing by 100. For example, 75% becomes 0.75.
• 💡 Make sure the units of the masses of the isotopes are consistent (usually atomic mass units, amu).
• 📝 If the abundance is given as a ratio, convert it to percentages before using the formula.

🧪 Practice Quiz

1. What information is needed to calculate the average atomic mass of an element?
   1. The number of neutrons in the most common isotope.
   2. The mass and percent abundance of each isotope.
   3. The element's atomic number.
   4. The element's group number on the periodic table.
2. Gallium has two naturally occurring isotopes: Ga-69 (68.9256 amu, 60.11%) and Ga-71 (70.9247 amu, 39.89%). Calculate the average atomic mass of Gallium.
   1. 69.72 amu
   2. 69.93 amu
   3. 70.13 amu
   4. 70.33 amu
3. Magnesium has three isotopes: $^{24}$Mg (mass = 23.985 amu, abundance = 78.99%), $^{25}$Mg (mass = 24.986 amu, abundance = 10.00%), and $^{26}$Mg (mass = 25.983 amu, abundance = 11.01%). What is the average atomic mass of magnesium?
   1. 24.00 amu
   2. 24.31 amu
   3. 25.00 amu
   4. 25.98 amu
4. An element has two isotopes: Isotope X with a mass of 10.0 amu and Isotope Y with a mass of 11.0 amu. If the average atomic mass of the element is 10.8 amu, what is the percent abundance of Isotope X?
   1. 20%
   2. 80%
   3. 50%
   4. 60%
5. Boron has two isotopes, $^{10}$B and $^{11}$B, with masses of 10.013 amu and 11.009 amu, respectively. The average atomic mass of boron is 10.81 amu. What is the abundance of $^{10}$B?
   1. 10%
   2. 20%
   3. 30%
   4. 80%
6. A newly discovered element, Ee, has two isotopes: $^{200}$Ee and $^{204}$Ee. If the average atomic mass of Ee is 201.6 amu, what is the relative abundance of $^{200}$Ee?
   1. 40%
   2. 60%
   3. 70%
   4. 80%
7. Which of the following statements about isotopes is correct?
   1. Isotopes of an element have the same number of neutrons but different numbers of protons.
   2. Isotopes of an element have the same number of protons but different numbers of neutrons.
   3. Isotopes of an element have the same mass number but different atomic numbers.
   4. Isotopes of an element have the same number of electrons but different numbers of protons.