Two isotopes of rubidium occur naturally, Rb with mass of 85 and atomic number of 37 at 72.17% (84.91 amu) and Rb with mass of 87 and atomic number of 37 at 27.83% (86.91 amu). Calculate the atomic mass for rubidium using the weighted average mass method.
The Correct Answer and Explanation is:
To calculate the atomic mass of rubidium using the weighted average mass method, we need to consider the relative abundances of the two isotopes and their respective atomic masses. The weighted average mass is calculated by multiplying the atomic mass of each isotope by its relative abundance (expressed as a decimal), then adding the results.
Given:
- Isotope 1: Rubidium-85 (Rb-85)
- Atomic mass = 84.91 amu
- Abundance = 72.17% or 0.7217 (as a decimal)
- Isotope 2: Rubidium-87 (Rb-87)
- Atomic mass = 86.91 amu
- Abundance = 27.83% or 0.2783 (as a decimal)
Formula:
Atomic Mass of Rb=(m1×f1)+(m2×f2)\text{Atomic Mass of Rb} = (m_1 \times f_1) + (m_2 \times f_2)Atomic Mass of Rb=(m1×f1)+(m2×f2)
Where:
- m1m_1m1 and m2m_2m2 are the atomic masses of the isotopes.
- f1f_1f1 and f2f_2f2 are the fractional abundances of the isotopes.
Calculation:
Atomic Mass of Rb=(84.91×0.7217)+(86.91×0.2783)\text{Atomic Mass of Rb} = (84.91 \times 0.7217) + (86.91 \times 0.2783)Atomic Mass of Rb=(84.91×0.7217)+(86.91×0.2783)
Now calculate the individual terms:84.91×0.7217=61.23 amu84.91 \times 0.7217 = 61.23 \text{ amu}84.91×0.7217=61.23 amu86.91×0.2783=24.21 amu86.91 \times 0.2783 = 24.21 \text{ amu}86.91×0.2783=24.21 amu
Now add these together:61.23+24.21=85.44 amu61.23 + 24.21 = 85.44 \text{ amu}61.23+24.21=85.44 amu
Final Result:
The atomic mass of rubidium, calculated using the weighted average mass method, is 85.44 amu.
Explanation:
The reason we use the weighted average mass method is that the atomic mass of an element reflects the average mass of all its naturally occurring isotopes, weighted by their relative abundances. By multiplying each isotope’s atomic mass by its abundance and then adding the results, we obtain a value that accurately represents the average atomic mass of the element in nature.
