

1. 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.



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:

\[
\text{Average atomic mass} = (\text{fractional abundance of chlorine-35} \times \text{mass of chlorine-35}) + (\text{fractional abundance of chlorine-37} \times \text{mass of chlorine-37})
\]

Let \( x \) represent the fractional abundance of chlorine-35. Therefore, the fractional abundance of chlorine-37 will be \( 1 - x \).

The average atomic mass is given as 35.45 amu, so:

\[
35.45 = (x \times 34.97) + \left((1 - x) \times 36.97\right)
\]

Now, let's solve for \( x \):

\[
35.45 = 34.97x + 36.97 - 36.97x
\]

\[
35.45 = 34.97x - 36.97x + 36.97
\]

\[
35.45 = -2x + 36.97
\]

Subtract 36.97 from both sides:

\[
35.45 - 36.97 = -2x
\]

\[
-1.52 = -2x
\]

Now, divide by -2:

\[
x = \frac{1.52}{2} = 0.76
\]

So, the fractional abundance of chlorine-35 is 0.76, which means the percentage abundance is:

\[
\text{Percentage abundance of chlorine-35} = 0.76 \times 100 = 76\%
\]

**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:

1. Calculate the percentage abundance of chlorine-37 based on the given data.
2. How would the average atomic mass change if the percentage abundance of chlorine-35 were 50%?
3. What is the significance of the average atomic mass in determining the natural abundance of isotopes?
4. How do you calculate the fractional abundance of an isotope given its percentage abundance?
5. 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.

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.

Discover how to calculate the percentage abundance of chlorine-35 given its isotopic mass and the average atomic mass of chlorine. This problem involves algebraic calculations and understanding isotopic abundances, suitable for students in Grades 9-12.

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