Chapter 2
Q. 2.2
Bromine is a red-orange liquid with an average atomic mass of 79.90 amu. Its name is derived from the Greek word bromos (βρoμos), which means stench. It has two naturally occurring isotopes: Br-79 (78.92 amu) and Br-81 (80.92 amu).
What is the abundance of the heavier isotope?
| ANALAYSIS | |
| Br-81 mass (80.92 amu); Br-79 mass (78.92 amu) average atomic mass (79.90) |
Information given: |
| abundance of Br-81 | Asked for: |
STRATEGY
1. All abundances must add up to 100%
2. Recall the formula relating abundance and atomic mass (Equation 2.1)
(atomic mass Y_{1} ) × \frac{\% Y_{1}}{100\%} + (atomic mass Y_{2} ) × \frac{\% Y_{2}}{100\%} + . . . (2.1)
atomic mass Y = (atomic mass Y_{1} × \frac{\% Y_{1}}{100\%}) + (atomic mass Y_{2} × \frac{\% Y_{2}}{100\%}) + . . .
Step-by-Step
Verified Solution
| Br-81: x; Br-79: 100 – x | 1. % abundances |
| 79.90 amu = 78.92 amu \left(\frac{100 – x}{100}\right) + 80.92 amu \left(\frac{ x}{100}\right) | 2. Substitute into Equation 2.1. |
| 79.90 = 0.7892(100 – x) + 0.8092 x 79.90 = 78.92 – 0.7892 x + 0.8092 x x = 49% |
3. Solve for x. |
END POINT
The atomic mass of Br, 79.90, is just about halfway between the masses of the two isotopes, 78.92 and 80.92. So, it is reasonable that it should contain nearly equal amounts of the two isotopes.