Bromine has two isotopes, Br-79 has 78.9183 amu, while Br-81 has 80.9163 amu. Bromine has an atomic mass of 79.904, calculate the isotopic abundance of the two. Saved

To calculate the isotopic abundances of the two isotopes of bromine (Br-79 and Br-81), we can set up a system of equations based on the given information.

Let:
- \( x \) be the fractional abundance of Br-79.
- \( y \) be the fractional abundance of Br-81.

We know that:
1. The sum of the fractional abundances must equal 1:
   \[
   x + y = 1
   \]
2. The atomic mass of bromine is the weighted average of the masses of its isotopes:
   \[
   78.9183x + 80.9163y = 79.904
   \]

### Step 1: Express \( y \) in terms of \( x \)
From the first equation:
\[
y = 1 - x
\]

### Step 2: Substitute \( y = 1 - x \) into the second equation
\[
78.9183x + 80.9163(1 - x) = 79.904
\]

### Step 3: Expand and simplify the equation
\[
78.9183x + 80.9163 - 80.9163x = 79.904
\]
\[
(78.9183 - 80.9163)x + 80.9163 = 79.904
\]
\[
-1.998x + 80.9163 = 79.904
\]

### Step 4: Solve for \( x \)
\[
-1.998x = 79.904 - 80.9163
\]
\[
-1.998x = -1.0123
\]
\[
x = \frac{-1.0123}{-1.998} \approx 0.5065
\]

### Step 5: Calculate \( y \)
\[
y = 1 - x = 1 - 0.5065 = 0.4935
\]

### Conclusion
- The isotopic abundance of Br-79 is approximately **50.65%**.
- The isotopic abundance of Br-81 is approximately **49.35%**.

Would you like more details on the calculations or have any questions?

Here are 5 related questions:
1. How do isotopes affect the atomic mass of an element?
2. What is the significance of the weighted average in calculating atomic mass?
3. How can mass spectrometry be used to determine isotopic abundances?
4. What are the common applications of isotopic abundance calculations in chemistry?
5. How do isotopic abundances influence the chemical properties of an element?

**Tip:** When dealing with isotopic abundances, always double-check that the sum of the fractions equals 1 to ensure accuracy in your calculations.

Learn how to calculate the isotopic abundances of bromine isotopes Br-79 and Br-81. Detailed step-by-step solution provided using fractional abundance and weighted average concepts. Suitable for advanced high school or college-level chemistry students.

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