Examkin

Question

Difficulty: Very hardRelative Atomic Mass, Relative Molecular Mass, and Carbon-12 Scale

An element ZZ exists naturally as two isotopes, 24Z^{24}Z and 26Z^{26}Z. On the carbon-12 scale, one atomic mass unit (1 amu1\text{ amu}) is defined as 112\frac{1}{12} of the mass of a single 12C^{12}\text{C} atom, where the mass of one 12C^{12}\text{C} atom is 1.992×10−23 g1.992 \times 10^{-23}\text{ g}. If the average absolute mass of one atom of element ZZ is 4.0504×10−23 g4.0504 \times 10^{-23}\text{ g}, what is the percentage abundance of the heavier isotope, 26Z^{26}Z?

  1. 20%20\%Answer
  2. B
    40%40\%
  3. C
    50%50\%
  4. D
    80%80\%

Answer

The percentage abundance of the heavier isotope 26Z^{26}Z is 20%20\%.
One atomic mass unit (1 amu1\text{ amu}) on the carbon-12 scale equals 1.992×10−23 g12=1.66×10−24 g\frac{1.992 \times 10^{-23}\text{ g}}{12} = 1.66 \times 10^{-24}\text{ g}. Dividing the absolute mass of one atom of ZZ (4.0504×10−23 g4.0504 \times 10^{-23}\text{ g}) by 1.66×10−24 g1.66 \times 10^{-24}\text{ g} yields a relative atomic mass of 24.424.4. Setting up the weighted average formula 24.4=24(1−p)+26p24.4 = 24(1 - p) + 26p, where pp is the fractional abundance of 26Z^{26}Z, gives 2p=0.42p = 0.4, so p=0.20p = 0.20 or 20%20\%.

Step-by-Step Solution

1
Calculate the value of 1 amu1\text{ amu} in grams using the carbon-12 reference standard
1 amu=1.992×10−23 g12=1.66×10−24 g1\text{ amu} = \frac{1.992 \times 10^{-23}\text{ g}}{12} = 1.66 \times 10^{-24}\text{ g}
Relative atomic mass is based on the carbon-12 scale, where 1 amu1\text{ amu} equals one-twelfth the mass of a carbon-12 atom.
2
Determine the relative atomic mass (RAM) of element ZZ
\text{RAM of } Z = \frac{4.0504 \times 10^{-23}\text{ g}}{1.66 \times 10^{-24}\text{ g}} = 24.4
Relative atomic mass is a dimensionless ratio of the average atomic mass of an element to 1 amu1\text{ amu}.
3
Set up and solve the isotopic abundance equation for percentage xx of 26Z^{26}Z
24.4 = \frac{24(100 - x) + 26x}{100} \implies 2440 = 2400 - 24x + 26x \implies 2x = 40 \implies x = 20\%
The relative atomic mass of an element is the weighted average of the mass numbers of its naturally occurring isotopes.

Key Concept

Relative Atomic Mass calculation on the Carbon-12 scale and isotopic abundance determination
Estimated Time:2m 30s
Rate this question

Topics

Relative Atomic Mass, Relative Molecular Mass, and Carbon-12 Scale

More questions from this topic