Math Problem Statement
- A sample of naturally occurring chlorine contains two isotopes: chlorine-35 and chlorine-37. If the average atomic mass of chlorine is 35.45 amu, and chlorine-35 has a mass of 34.97 amu while chlorine-37 has a mass of 36.97 amu, calculate the percentage abundance of chlorine-35.
Solution
To calculate the percentage abundance of chlorine-35, we can use the average atomic mass formula. The formula for the average atomic mass based on isotopic masses and their respective abundances is:
Let represent the fractional abundance of chlorine-35. Therefore, the fractional abundance of chlorine-37 will be .
The average atomic mass is given as 35.45 amu, so:
Now, let's solve for :
Subtract 36.97 from both sides:
Now, divide by -2:
So, the fractional abundance of chlorine-35 is 0.76, which means the percentage abundance is:
Answer: The percentage abundance of chlorine-35 is 76%.
Would you like more details on this solution, or do you have any other questions?
Here are some related questions for further practice:
- Calculate the percentage abundance of chlorine-37 based on the given data.
- How would the average atomic mass change if the percentage abundance of chlorine-35 were 50%?
- What is the significance of the average atomic mass in determining the natural abundance of isotopes?
- How do you calculate the fractional abundance of an isotope given its percentage abundance?
- How would the presence of a third isotope affect the calculation of the average atomic mass?
Tip: Always ensure that the sum of the fractional abundances of all isotopes equals 1 when calculating average atomic mass.
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Math Problem Analysis
Mathematical Concepts
Algebra
Isotopic Abundance
Weighted Averages
Formulas
Average atomic mass = (fractional abundance of chlorine-35 × mass of chlorine-35) + (fractional abundance of chlorine-37 × mass of chlorine-37)
Fractional abundance of chlorine-37 = 1 - Fractional abundance of chlorine-35
Theorems
Weighted Average Theorem
Suitable Grade Level
Grades 9-12