The element silver has an atomic weight of 108 and consists of two stable isotopes, silver-107 and silver-109. The isotope silver-107 has a mass of 107 amu and a percent natural abundance of 51.8%. The isotope silver-109 has a percent natural abundance of 48.2%. What is the mass of silver-109? B- A certain element consists of two stable isotopes. The first has a mass of 121 amu and a percent natural abundance of 57.3%. The second has a mass of 123 amu and a percent natural abundance of 42.8%. What is the atomic weight of the element? amu C- The element antimony has two stable isotopes, antimony-121 with a mass of 120.90 amu and antimony-123 with a mass of 122.90 amu. From the atomic weight of Sb = 121.76, one can conclude that: – Antimony-121 has the highest percent natural abundance. – Antimony-123 has the highest percent natural abundance. – Most antimony atoms have a mass of 121.76 amu. – Both isotopes have the same percent natural abundance.
CHAPTER 2 – SECTION 8 – AVERAGE ATOMIC WEIGHT A- The element silver has an atomic weight of 108 and consists of two stable isotopes, silver-107 and silver-109. The isotope silver-107 has a mass of 107 amu and a percent natural abundance of 51.8%. The isotope silver-109 has a percent natural abundance of 48.2%. What is the mass of silver-109? B- A certain element consists of two stable isotopes. The first has a mass of 121 amu and a percent natural abundance of 57.3%. The second has a mass of 123 amu and a percent natural abundance of 42.8%. What is the atomic weight of the element? amu C- The element antimony has two stable isotopes, antimony-121 with a mass of 120.90 amu and antimony-123 with a mass of 122.90 amu. From the atomic weight of Sb = 121.76, one can conclude that: – Antimony-121 has the highest percent natural abundance. – Antimony-123 has the highest percent natural abundance. – Most antimony atoms have a mass of 121.76 amu. – Both isotopes have the same percent natural abundance.
The Correct Answer and Explanation is:
A. Mass of Silver-109
We use the formula for average atomic weight:
Average Atomic Weight = (fraction₁ × mass₁) + (fraction₂ × mass₂)
Given:
- Atomic weight of silver = 108 amu
- Silver-107 mass = 107 amu, abundance = 51.8% = 0.518
- Silver-109 mass = unknown, abundance = 48.2% = 0.482
108 = (0.518 × 107) + (0.482 × mass of silver-109)
First, calculate:
0.518 × 107 = 55.426
Substitute into the equation:
108 = 55.426 + (0.482 × mass of silver-109)
Rearrange:
108 – 55.426 = 0.482 × mass of silver-109
52.574 = 0.482 × mass of silver-109
Solve for mass of silver-109:
mass of silver-109 = 52.574 ÷ 0.482 ≈ 109.1 amu
Final Answer: The mass of silver-109 is approximately 109.1 amu
B. Atomic Weight of the Element
Given:
- Isotope 1: mass = 121 amu, abundance = 57.3% = 0.573
- Isotope 2: mass = 123 amu, abundance = 42.8% = 0.428
Apply the formula:
Atomic Weight = (0.573 × 121) + (0.428 × 123)
Calculate:
0.573 × 121 = 69.333
0.428 × 123 = 52.644
Add:
69.333 + 52.644 = 121.98 amu
Final Answer: The atomic weight is 121.98 amu
C. Conclusion About Antimony Isotopes
Given:
- Antimony-121 mass = 120.90 amu
- Antimony-123 mass = 122.90 amu
- Average atomic weight = 121.76 amu
The average atomic weight (121.76 amu) is closer to the mass of antimony-123 (122.90 amu) than to antimony-121 (120.90 amu). This suggests that the heavier isotope, antimony-123, contributes more to the average, meaning it is more abundant.
Correct Conclusion:
- Antimony-123 has the highest percent natural abundance
Explanation
Average atomic weight is calculated based on the masses and relative abundances of an element’s isotopes. In part A, using the average atomic weight and abundance of one isotope allows calculation of the other isotope’s mass. In part B, the average atomic weight is directly determined by applying the weighted average formula. In part C, comparing the average atomic weight to the isotopic masses reveals which isotope is more abundant. When the average is closer to one isotope, that isotope contributes more significantly, indicating higher natural abundance. Understanding these calculations is essential in chemistry for determining atomic structure and isotopic composition.
