Calculating Relative Atomic Mass: Worked Examples

📚 Quick Study Guide

• ⚛️ The relative atomic mass ($A_r$) is the weighted average mass of the atoms of an element, taking into account the relative abundance of its isotopes.
• 🔢 The formula for calculating relative atomic mass is: $A_r = \frac{(\% \text{ abundance of isotope 1} \times \text{mass of isotope 1}) + (\% \text{ abundance of isotope 2} \times \text{mass of isotope 2}) + ...}{100}$
• 🧪 Isotopes are atoms of the same element that have different numbers of neutrons.
• 📊 Relative abundance is usually given as a percentage.
• 💡 Remember to always include the units (amu or simply u) if specified, but $A_r$ is often given without units.

🧪 Practice Quiz

1. Which of the following statements best describes relative atomic mass?
   1. A. The mass of the most abundant isotope of an element.
   2. B. The average mass of an atom of an element.
   3. C. The weighted average mass of the atoms of an element, considering the relative abundance of its isotopes.
   4. D. The mass of one mole of an element.
2. Magnesium has three isotopes: $^{24}$Mg (79.0%), $^{25}$Mg (10.0%), and $^{26}$Mg (11.0%). Calculate the relative atomic mass of magnesium.
   1. A. 24.0 amu
   2. B. 24.3 amu
   3. C. 25.0 amu
   4. D. 26.0 amu
3. What data is necessary to calculate the relative atomic mass of an element?
   1. A. The number of protons and neutrons.
   2. B. The mass number and atomic number.
   3. C. The mass and relative abundance of each isotope.
   4. D. The number of electrons and protons.
4. Boron has two isotopes, $^{10}$B and $^{11}$B, with relative abundances of 20% and 80% respectively. What is the relative atomic mass of boron?
   1. A. 10.2 amu
   2. B. 10.5 amu
   3. C. 10.8 amu
   4. D. 11.0 amu
5. An element has two isotopes: Isotope 1 has a mass of 63 amu and a relative abundance of 69%, and Isotope 2 has a mass of 65 amu and a relative abundance of 31%. Calculate the relative atomic mass of this element.
   1. A. 63.6 amu
   2. B. 63.9 amu
   3. C. 64.0 amu
   4. D. 64.3 amu
6. If an element has two isotopes, one with a mass of 100 amu and the other with a mass of 102 amu, and its relative atomic mass is 101 amu, what are the relative abundances of the two isotopes?
   1. A. 25% and 75%
   2. B. 50% and 50%
   3. C. 75% and 25%
   4. D. 60% and 40%
7. Chlorine has two isotopes, $^{35}$Cl and $^{37}$Cl. The relative atomic mass of chlorine is 35.5 amu. What is the approximate percentage abundance of $^{35}$Cl?
   1. A. 25%
   2. B. 50%
   3. C. 75%
   4. D. 90%