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Every substance around us is made up of tiny particles called atoms. Atoms are the fundamental building blocks of matter. But not all atoms of an element are exactly the same. They can vary slightly in their mass due to differences in the number of neutrons they contain. This variation leads us to the concept of atomic mass.
Atomic mass helps us understand the average mass of atoms of an element, taking into account these variations. Since atoms are extremely small, we use a special scale and unit to measure their mass relative to a standard. This section will guide you through the ideas of isotopes, isotopic abundance, and how to calculate the average atomic mass of elements.
An atom consists of a nucleus containing protons and neutrons, surrounded by electrons. The number of protons defines the atomic number of the element and determines its chemical identity. However, atoms of the same element can have different numbers of neutrons. These different forms are called isotopes.
Isotopes of an element have the same atomic number but different mass numbers (sum of protons and neutrons). For example, chlorine has two common isotopes:
Here, Cl-35 and Cl-37 are isotopes of chlorine. Both have 17 protons, but different numbers of neutrons (18 and 20 respectively). The numbers after the element symbol represent the mass number.
The natural abundance of each isotope affects the average atomic mass of the element. For chlorine, about 75% of atoms are Cl-35 and 25% are Cl-37.
Since isotopes have different masses, the atomic mass of an element is not a single fixed number but a weighted average based on the abundance of each isotope. This weighted average is called the relative atomic mass (or average atomic mass).
It is important to note that relative atomic mass is a dimensionless quantity because it is measured relative to a standard (carbon-12 atom).
| Isotope | Isotopic Mass (amu) | Percentage Abundance (%) |
|---|---|---|
| Cl-35 | 34.969 | 75 |
| Cl-37 | 36.966 | 25 |
Using this data, the relative atomic mass of chlorine is calculated by multiplying each isotopic mass by its fractional abundance (percentage divided by 100) and summing the results.
Because atoms are so tiny, their masses are extremely small in grams. To make measurement and comparison easier, scientists use the atomic mass unit (amu). One amu is defined as exactly one twelfth of the mass of a carbon-12 atom.
This means:
Using amu allows us to express atomic masses as convenient numbers close to whole numbers, such as 12 amu for carbon-12, 1 amu for hydrogen, and so on.
To calculate the average atomic mass of an element with multiple isotopes, follow these steps:
graph TD A[Start with isotopic masses and abundances] --> B[Convert percentage abundance to decimal fraction] B --> C[Multiply each isotopic mass by its fractional abundance] C --> D[Sum all the products] D --> E[Result is the average atomic mass]
Mathematically, this is expressed as:
Remember to convert percentage abundance to fractional abundance by dividing by 100:
Step 1: Convert percentage abundances to fractional abundances.
Cl-35: 75% = 0.75, Cl-37: 25% = 0.25
Step 2: Multiply each isotopic mass by its fractional abundance.
Cl-35: 34.969 x 0.75 = 26.22675 amu
Cl-37: 36.966 x 0.25 = 9.2415 amu
Step 3: Add the results to find the average atomic mass.
26.22675 + 9.2415 = 35.46825 amu
Answer: The average atomic mass of chlorine is approximately 35.47 amu.
Step 1: Convert percentages to fractions:
A: 0.20, B: 0.50, C: 0.30
Step 2: Multiply each mass by its fractional abundance:
A: 10.012 x 0.20 = 2.0024 amu
B: 11.009 x 0.50 = 5.5045 amu
C: 12.014 x 0.30 = 3.6042 amu
Step 3: Sum the products:
2.0024 + 5.5045 + 3.6042 = 11.1111 amu
Answer: The average atomic mass is approximately 11.11 amu.
Step 1: Calculate molecular mass of water.
Water has 2 hydrogen atoms and 1 oxygen atom:
Molecular mass = (2 x 1.008) + (1 x 16.00) = 2.016 + 16.00 = 18.016 amu
Step 2: Calculate mass of 2 moles of water.
Mass = number of moles x molar mass = 2 x 18.016 = 36.032 grams
Answer: Mass of 2 moles of water is 36.032 grams.
Step 1: Calculate mass of 0.5 moles of copper.
Mass = moles x atomic mass = 0.5 x 63.55 = 31.775 grams
Step 2: Calculate cost.
Cost = mass x price per gram = 31.775 x Rs.500 = Rs.15,887.50
Answer: The cost of 0.5 moles of copper is Rs.15,887.50.
Step 1: Let the fractional abundance of isotope with mass 50 amu be x.
Then, fractional abundance of isotope with mass 52 amu = 1 - x.
Step 2: Write the average atomic mass equation:
50.8 = (50 x x) + (52 x (1 - x))
50.8 = 50x + 52 - 52x
50.8 = 52 - 2x
Step 3: Solve for x:
2x = 52 - 50.8 = 1.2
x = 0.6
Step 4: Convert to percentage:
Isotope 50 amu: 0.6 x 100 = 60%
Isotope 52 amu: 40%
Answer: Percentage abundances are 60% for 50 amu isotope and 40% for 52 amu isotope.
When to use: When calculating average atomic mass from isotopic data.
When to use: To avoid errors in average atomic mass calculation.
When to use: During time-limited entrance exams for faster calculations.
When to use: To understand and explain the basis of atomic mass.
When to use: When solving complex isotopic abundance problems.
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