Select the correct answer.
Vitellium (V) has the following composition:
V-188: 187.9122 amu, 10.861%
V-191: 190.9047 amu, 12.428%
V-193: 192.8938 amu; 76.711%
Based on this data, what can you predict about the average atomic mass of vitellium?
A. It will be equal to the arithmetic mean of the masses of the three isotopes.
B. It will be closer to the mass of Vi-188.
C. It will be closer to the mass of V-193.
D. It will be equal to the mass of Vi-193.
Answer (2)
Calculate the weighted average of the isotopes: (187.9122 * 0.10861) + (190.9047 * 0.12428) + (192.8938 * 0.76711).
The result of the calculation is approximately 192.2025 amu.
Because V-193 has the highest relative abundance (76.711%), the average atomic mass will be closest to its mass.
Therefore, the average atomic mass will be closer to the mass of V-193: OC .
Explanation
Understanding the Problem We are given the isotopic composition of Vitellium (V) and asked to predict its average atomic mass. We have the mass and relative abundance of each isotope: V-188 (187.9122 amu, 10.861%), V-191 (190.9047 amu, 12.428%), and V-193 (192.8938 amu, 76.711%).
Calculating Average Atomic Mass The average atomic mass is calculated by summing the product of each isotope's mass and its relative abundance. This is a weighted average, where the weights are the relative abundances. The formula is:
Average atomic mass = (mass of isotope 1 × relative abundance of isotope 1) + (mass of isotope 2 × relative abundance of isotope 2) + (mass of isotope 3 × relative abundance of isotope 3)
Performing the Calculation Now, we plug in the given values:
Average atomic mass = (187.9122 amu × 0.10861) + (190.9047 amu × 0.12428) + (192.8938 amu × 0.76711)
Average atomic mass = 20.4083 + 23.7256 + 148.0686
Average atomic mass = 192.2025 amu (approximately)
Analyzing the Result Since the relative abundance of V-193 (76.711%) is significantly higher than the other isotopes, the average atomic mass will be closest to the mass of V-193. The calculated average atomic mass (192.2025 amu) is indeed very close to the mass of V-193 (192.8938 amu).
Final Answer Based on the data and our calculations, the correct answer is:
OC. It will be closer to the mass of V-193
Examples
Understanding average atomic mass is crucial in various fields. For instance, in chemistry, it helps in calculating the molar mass of compounds, which is essential for stoichiometric calculations in chemical reactions. In material science, knowing the isotopic composition and average atomic mass is important for predicting the properties of materials, especially in nuclear applications. For example, if you're designing a nuclear reactor, you need to know the exact isotopic composition of the fuel to predict its behavior under neutron bombardment.
The average atomic mass of vitellium is calculated using the weighted average based on the isotopes' masses and their relative abundances. The result is approximately 192.2025 amu, which is closer to the mass of the most abundant isotope, V-193. Thus, the correct answer is C: it will be closer to the mass of V-193.
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