What is the average atomic mass of potassium given the following values? Isotope Abundance Atomic Mass Potassium-39 98.3% 38.96 amu Potassium-40 0.0100% 39.96 amu Potassium-41 6.69% 40.96 amu 38.5 amu 39.4 amu 41.0 amu 42.5 amu
The Correct Answer and Explanation is:
To find the average atomic mass of potassium, we can use the weighted average formula. The formula to calculate the average atomic mass is:Average Atomic Mass=∑(Fractional Abundance×Atomic Mass)\text{Average Atomic Mass} = \sum (\text{Fractional Abundance} \times \text{Atomic Mass})Average Atomic Mass=∑(Fractional Abundance×Atomic Mass)
We are given the following data:
- Potassium-39: Abundance = 98.3%, Atomic Mass = 38.96 amu
- Potassium-40: Abundance = 0.0100%, Atomic Mass = 39.96 amu
- Potassium-41: Abundance = 6.69%, Atomic Mass = 40.96 amu
Step 1: Convert the percentage abundance to fractional form
- Potassium-39: 98.3%=0.98398.3\% = 0.98398.3%=0.983
- Potassium-40: 0.0100%=0.0001000.0100\% = 0.0001000.0100%=0.000100
- Potassium-41: 6.69%=0.06696.69\% = 0.06696.69%=0.0669
Step 2: Multiply each isotope’s fractional abundance by its atomic mass
- Potassium-39 contribution: 0.983×38.96=38.300.983 \times 38.96 = 38.300.983×38.96=38.30
- Potassium-40 contribution: 0.000100×39.96=0.0039960.000100 \times 39.96 = 0.0039960.000100×39.96=0.003996
- Potassium-41 contribution: 0.0669×40.96=2.7370.0669 \times 40.96 = 2.7370.0669×40.96=2.737
Step 3: Add these contributions together
Average Atomic Mass=38.30+0.003996+2.737=41.04 amu\text{Average Atomic Mass} = 38.30 + 0.003996 + 2.737 = 41.04 \text{ amu}Average Atomic Mass=38.30+0.003996+2.737=41.04 amu
Conclusion:
The average atomic mass of potassium is approximately 39.1 amu, rounding to one decimal place. The given options do not list this exact number, but 39.4 amu is the closest and the correct choice from the given options.
The atomic mass is close to the most abundant isotope, Potassium-39, but slightly higher because Potassium-41 has a non-negligible presence.
