The Table Below Gives The Data Needed To Calculate The Average Atomic Mass Of Element $B$.$\[ \begin{tabular}{|l|l|l|} \hline Isotope & Atomic Mass (amu) & Relative Abundance (\%) \\ \hline B-10 & 10.01 & 19.91 \\ \hline B-11 & 11.01
Introduction
In chemistry, the average atomic mass of an element is a crucial concept that helps us understand the properties and behavior of that element. It is a weighted average of the masses of the naturally occurring isotopes of an element, taking into account their relative abundance. In this article, we will calculate the average atomic mass of element B using the data provided in the table below.
The Data
| Isotope | Atomic Mass (amu) | Relative Abundance (%) |
|---|---|---|
| B-10 | 10.01 | 19.91 |
| B-11 | 11.01 | 80.09 |
Step 1: Understanding the Concept of Average Atomic Mass
The average atomic mass of an element is calculated by multiplying the atomic mass of each isotope by its relative abundance, expressed as a decimal. The relative abundance is converted to a decimal by dividing by 100. The results are then added together to give the average atomic mass.
Step 2: Converting Relative Abundance to Decimal
To convert the relative abundance from percentage to decimal, we divide by 100.
- B-10: 19.91% ÷ 100 = 0.1991
- B-11: 80.09% ÷ 100 = 0.8009
Step 3: Calculating the Weighted Average
Now, we multiply the atomic mass of each isotope by its relative abundance (in decimal form) and add the results together.
- B-10: 10.01 amu × 0.1991 = 1.9961 amu
- B-11: 11.01 amu × 0.8009 = 8.8089 amu
Step 4: Adding the Results Together
Now, we add the results from step 3 together to get the average atomic mass of element B.
1.9961 amu + 8.8089 amu = 10.8050 amu
Conclusion
In conclusion, the average atomic mass of element B is 10.8050 amu. This value is a weighted average of the masses of the naturally occurring isotopes of element B, taking into account their relative abundance. The calculation of average atomic mass is an essential concept in chemistry, and it helps us understand the properties and behavior of elements.
Importance of Average Atomic Mass
The average atomic mass of an element is important because it helps us:
- Understand the properties and behavior of elements
- Predict the behavior of elements in chemical reactions
- Calculate the molar mass of compounds
- Understand the concept of isotopes and their relative abundance
Real-World Applications
The average atomic mass of an element has many real-world applications, including:
- Nuclear power generation: The average atomic mass of uranium-235 is used to calculate the energy released in nuclear reactions.
- Medicine: The average atomic mass of certain isotopes is used in medical treatments, such as cancer therapy.
- Materials science: The average atomic mass of elements is used to calculate the properties of materials, such as strength and conductivity.
Conclusion
Q: What is the average atomic mass of an element?
A: The average atomic mass of an element is a weighted average of the masses of the naturally occurring isotopes of that element, taking into account their relative abundance.
Q: Why is the average atomic mass of an element important?
A: The average atomic mass of an element is important because it helps us understand the properties and behavior of elements, predict the behavior of elements in chemical reactions, calculate the molar mass of compounds, and understand the concept of isotopes and their relative abundance.
Q: How is the average atomic mass of an element calculated?
A: The average atomic mass of an element is calculated by multiplying the atomic mass of each isotope by its relative abundance (expressed as a decimal) and adding the results together.
Q: What is the difference between atomic mass and average atomic mass?
A: Atomic mass refers to the mass of a single atom of an element, while average atomic mass refers to the weighted average of the masses of the naturally occurring isotopes of an element.
Q: Why is the relative abundance of isotopes important in calculating the average atomic mass?
A: The relative abundance of isotopes is important in calculating the average atomic mass because it determines the weight of each isotope in the calculation. Isotopes with higher relative abundance have a greater impact on the average atomic mass.
Q: Can the average atomic mass of an element change over time?
A: Yes, the average atomic mass of an element can change over time due to changes in the relative abundance of its isotopes. For example, the average atomic mass of carbon-12 has changed slightly over time due to changes in the relative abundance of its isotopes.
Q: How is the average atomic mass of an element used in real-world applications?
A: The average atomic mass of an element is used in a variety of real-world applications, including nuclear power generation, medicine, and materials science. For example, the average atomic mass of uranium-235 is used to calculate the energy released in nuclear reactions.
Q: Can the average atomic mass of an element be used to predict the behavior of elements in chemical reactions?
A: Yes, the average atomic mass of an element can be used to predict the behavior of elements in chemical reactions. By understanding the average atomic mass of an element, we can predict how it will react with other elements and compounds.
Q: How is the average atomic mass of an element related to the molar mass of a compound?
A: The average atomic mass of an element is related to the molar mass of a compound because the molar mass of a compound is calculated by summing the average atomic masses of its constituent elements.
Q: Can the average atomic mass of an element be used to understand the concept of isotopes and their relative abundance?
A: Yes, the average atomic mass of an element can be used to understand the concept of isotopes and their relative abundance. By understanding the average atomic mass of an element, we can understand how the relative abundance of its isotopes affects its properties and behavior.
Conclusion
In conclusion, the average atomic mass of an element is a crucial concept in chemistry that helps us understand the properties and behavior of elements, predict the behavior of elements in chemical reactions, calculate the molar mass of compounds, and understand the concept of isotopes and their relative abundance. By understanding the average atomic mass of an element, we can apply this knowledge to a variety of real-world applications.