Mass Spectra of Elements
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AP Chemistry › Mass Spectra of Elements
A mass spectrum for element W shows two peaks at $m/z=20$ (relative abundance 90) and $m/z=22$ (relative abundance 10). Assuming $+1$ ions, what is the average atomic mass of W?
20.0 amu
20.9 amu
20.2 amu
21.0 amu
22.0 amu
Explanation
The skill being tested is calculating the average atomic mass of an element from its mass spectrum by using the weighted average of isotopic masses based on their relative abundances. The average for element W is (20 × 90/100) + (22 × 10/100) = 18 + 2.2 = 20.2 amu. This value is skewed toward 20 amu due to its 90% abundance, with the 22 amu isotope adding a small upward pull. The principle is that average mass calculation weights each isotope by its prevalence, as seen in mass spectra. A tempting distractor is 20.0 amu, from the misconception of disregarding the minor isotope entirely and using only the major one. Always include all isotopes in the weighted average computation to capture the full isotopic influence on atomic mass.
Element R produces a mass spectrum with peaks at $m/z=78$ (relative abundance 50) and $m/z=80$ (relative abundance 50). Assuming $+1$ ions, what is the average atomic mass of R?
79.5 amu
80.0 amu
78.5 amu
79.0 amu
78.0 amu
Explanation
The skill being tested is calculating the average atomic mass of an element from its mass spectrum by using the weighted average of isotopic masses based on their relative abundances. For element R, with equal abundances of 50 for both 78 and 80 amu, the average is (78 × 50/100) + (80 × 50/100) = 39 + 40 = 79.0 amu. This equidistant average between the two masses demonstrates how equal abundances result in a simple midpoint. The principle underscores that average atomic mass is a balanced reflection of all isotopic contributions in proportion to their occurrence. A tempting distractor is 78.5 amu, possibly from incorrectly averaging the masses without considering abundances, but since they are equal, it coincides closely yet is not exact. To compute average atomic mass reliably, use the formula summing mass times fractional abundance for all isotopes.
A mass spectrum of element T shows two peaks: $m/z=107$ with relative abundance 52 and $m/z=109$ with relative abundance 48. Assuming $+1$ ions, which value is closest to the average atomic mass of T?
107.5 amu
109.0 amu
108.0 amu
108.5 amu
107.0 amu
Explanation
The skill being tested is calculating the average atomic mass of an element from its mass spectrum by using the weighted average of isotopic masses based on their relative abundances. The calculation for element T is (107 × 52/100) + (109 × 48/100) = 55.64 + 52.32 = 107.96 amu, which is closest to 108.0 amu. The slightly higher abundance of the 107 amu isotope pulls the average just below the midpoint but rounds closest to 108.0 amu given the options. This illustrates the weighted average principle, where small differences in abundance significantly affect the final mass. A tempting distractor is 108.5 amu, resulting from mistakenly averaging the masses equally without weighting by abundance, leading to the midpoint misconception. For mass spectra analysis, always calculate the precise weighted average and select the closest value when approximations are required.
A mass spectrum of element Y shows three peaks at $m/z=24$ (relative abundance 79), $m/z=25$ (relative abundance 10), and $m/z=26$ (relative abundance 11). What is the average atomic mass of element Y?
$25.32\ \text{amu}$
$24.50\ \text{amu}$
$24.00\ \text{amu}$
$25.00\ \text{amu}$
$24.32\ \text{amu}$
Explanation
This question tests the skill of calculating average atomic mass from a mass spectrum with multiple isotopes. We calculate the weighted average using all three isotopes: (24 × 0.79) + (25 × 0.10) + (26 × 0.11) = 18.96 + 2.50 + 2.86 = 24.32 amu. The relative abundances (79, 10, 11) must be converted to decimals by dividing by 100 since they sum to 100. A tempting incorrect answer is 24.50 amu (choice D), which might result from incorrectly averaging just the first and last masses while ignoring the middle isotope. When calculating average atomic mass, include all isotopes shown in the mass spectrum and weight each by its relative abundance.
Element R has three isotopes. Its mass spectrum shows peaks at $m/z=20$ (90), $m/z=21$ (5), and $m/z=22$ (5). Assuming singly charged ions, what is the average atomic mass of R?
$20.20\ \text{amu}$
$20.50\ \text{amu}$
$20.10\ \text{amu}$
$21.00\ \text{amu}$
$20.15\ \text{amu}$
Explanation
This question tests the skill of calculating the average atomic mass of an element from its mass spectrum by using the weighted average of isotopic masses and their relative abundances. The average is (20 × 90 + 21 × 5 + 22 × 5) / 100 = (1800 + 105 + 110) / 100 = 2015 / 100 = 20.15 amu. With 90% at 20 amu and only 5% each at 21 and 22, the average is slightly above 20, reflecting the dominant isotope. This illustrates how minor isotopes contribute proportionally to the overall mass. A tempting distractor is 21.00 amu, the arithmetic mean, but this is incorrect due to the misconception of equal weighting rather than using the given abundances. Always verify by summing mass × (abundance/100) for all isotopes in such calculations.
A mass spectrum for element M shows two peaks at $m/z=79$ (50) and $m/z=81$ (50). Assuming singly charged ions, what is the average atomic mass of M?
$80.00\ \text{amu}$
$79.00\ \text{amu}$
$80.50\ \text{amu}$
$79.50\ \text{amu}$
$81.00\ \text{amu}$
Explanation
This question tests the skill of calculating the average atomic mass of an element from its mass spectrum by using the weighted average of isotopic masses and their relative abundances. For equal abundances of 50 each, the average is (79 × 50 + 81 × 50) / 100 = (3950 + 4050) / 100 = 80.00 amu. The 50-50 split places the average exactly in the middle of 79 and 81. This shows the principle of balanced weighting when abundances are equal. A tempting distractor is 79.50 amu, perhaps from miscalculating fractions, but this is incorrect because it underweights the heavier isotope, misunderstanding the equal abundances. To tackle these, treat abundances as percentages and compute the weighted sum divided by 100.
An element Z has a mass spectrum with two peaks at $m/z=10$ and $m/z=11$ of approximately equal height (relative abundance 50 and 50). Assuming singly charged ions, what is the average atomic mass of Z?
$10.00\ \text{amu}$
$10.25\ \text{amu}$
$10.75\ \text{amu}$
$11.00\ \text{amu}$
$10.50\ \text{amu}$
Explanation
This question tests the skill of calculating the average atomic mass of an element from its mass spectrum by using the weighted average of isotopic masses and their relative abundances. With equal abundances of 50 each for m/z 10 and 11, the average is (10 × 50 + 11 × 50) / 100 = (500 + 550) / 100 = 10.50 amu. The equal peak heights indicate equal proportions, so the fractions are both 0.50, making this a straightforward weighted average. This demonstrates the principle that even with equal abundances, the average falls midway between the isotopic masses. A tempting distractor is 10.00 amu, assuming only the lighter isotope matters, but this is incorrect due to the misconception of disregarding the contribution of the heavier isotope despite its equal abundance. For similar questions, ensure abundances are normalized to 100 and calculate the weighted sum divided by 100.
The mass spectrum of element B shows peaks at $m/z=90$ (51) and $m/z=92$ (49). Assuming singly charged ions, what is the average atomic mass of B?
$91.49\ \text{amu}$
$90.98\ \text{amu}$
$91.00\ \text{amu}$
$90.49\ \text{amu}$
$92.00\ \text{amu}$
Explanation
This question tests the skill of calculating the average atomic mass of an element from its mass spectrum by using the weighted average of isotopic masses and their relative abundances. The average is (90 × 51 + 92 × 49) / 100 = (4590 + 4508) / 100 = 90.98 amu. Slight edge to 90 affects it. This reflects abundance influence. A tempting distractor is 91.00 amu, equal average, but wrong without weighting. Normalize and weight by abundance in calculations.
A mass spectrum for element Y shows three peaks at $m/z=24$ (79), $m/z=25$ (10), and $m/z=26$ (11), where numbers in parentheses are relative abundances. Assuming singly charged ions, what is the average atomic mass of Y?
$24.00\ \text{amu}$
$25.32\ \text{amu}$
$25.00\ \text{amu}$
$24.32\ \text{amu}$
$24.50\ \text{amu}$
Explanation
This question tests the skill of calculating the average atomic mass of an element from its mass spectrum by using the weighted average of isotopic masses and their relative abundances. The average atomic mass is (24 × 79 + 25 × 10 + 26 × 11) / 100 = (1896 + 250 + 286) / 100 = 2432 / 100 = 24.32 amu. The abundances 79, 10, and 11 sum to 100, so they represent percentages, and the calculation weights each mass accordingly. This reflects the chemical principle that the average mass is influenced more by the most abundant isotope at m/z 24. A tempting distractor is 24.00 amu, which might come from ignoring the minor isotopes, but this is incorrect because it overlooks the contribution of all isotopes based on their abundances, underestimating the weighted average. When approaching similar mass spectrometry problems, sum the products of each isotopic mass and its percentage abundance, then divide by 100 to find the average.
A mass spectrum of element S shows peaks at $m/z=20$ (relative abundance 90) and $m/z=22$ (relative abundance 10). What is the average atomic mass of element S?
$20.90\ \text{amu}$
$22.00\ \text{amu}$
$20.10\ \text{amu}$
$20.20\ \text{amu}$
$21.00\ \text{amu}$
Explanation
This question tests the skill of calculating average atomic mass when one isotope strongly dominates the mass spectrum. The calculation is: (20 × 0.90) + (22 × 0.10) = 18.00 + 2.20 = 20.20 amu. With 90% abundance of the lighter isotope, the average mass is pulled strongly toward 20 amu. A common error is selecting 21.00 amu (choice B), which might result from incorrectly averaging the masses without considering abundances. When one isotope has very high abundance (>80%), the average atomic mass will be close to that isotope's mass value.