Use this calculator to determine the average atomic mass of an element based on the masses and natural abundances of its isotopes. Enter the mass (in atomic mass units, amu) and the percentage abundance for each isotope.
Isotope 1
Isotope 2
Isotope 3 (Optional)
Result:
function calculateAverageAtomicMass() {
var isotope1Mass = parseFloat(document.getElementById('isotope1Mass').value);
var isotope1Abundance = parseFloat(document.getElementById('isotope1Abundance').value);
var isotope2Mass = parseFloat(document.getElementById('isotope2Mass').value);
var isotope2Abundance = parseFloat(document.getElementById('isotope2Abundance').value);
var isotope3Mass = parseFloat(document.getElementById('isotope3Mass').value);
var isotope3Abundance = parseFloat(document.getElementById('isotope3Abundance').value);
var totalWeightedMass = 0;
var totalAbundance = 0;
var resultDiv = document.getElementById('averageAtomicMassResult');
// Validate inputs
if (isNaN(isotope1Mass) || isNaN(isotope1Abundance) || isNaN(isotope2Mass) || isNaN(isotope2Abundance)) {
resultDiv.innerHTML = "Please enter valid numbers for at least the first two isotopes' mass and abundance.";
return;
}
// Isotope 1
totalWeightedMass += isotope1Mass * (isotope1Abundance / 100);
totalAbundance += isotope1Abundance;
// Isotope 2
totalWeightedMass += isotope2Mass * (isotope2Abundance / 100);
totalAbundance += isotope2Abundance;
// Isotope 3 (Optional)
if (!isNaN(isotope3Mass) && !isNaN(isotope3Abundance)) {
totalWeightedMass += isotope3Mass * (isotope3Abundance / 100);
totalAbundance += isotope3Abundance;
}
// Check if total abundance is close to 100%
if (Math.abs(totalAbundance – 100) > 0.1 && totalAbundance > 0) { // Allow for slight floating point inaccuracies
resultDiv.innerHTML = "Warning: The sum of abundances is " + totalAbundance.toFixed(2) + "%. It should ideally be 100% for natural abundance. Calculated Average Atomic Mass: " + totalWeightedMass.toFixed(5) + " amu";
} else if (totalAbundance === 0) {
resultDiv.innerHTML = "Please enter valid abundances.";
}
else {
resultDiv.innerHTML = "The average atomic mass is: " + totalWeightedMass.toFixed(5) + " amu";
}
}
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Understanding the average atomic mass of an element is fundamental in chemistry. Unlike the mass number, which is a simple count of protons and neutrons in a single isotope, the average atomic mass accounts for the natural abundance of all an element's isotopes.
What is Average Atomic Mass?
Most elements exist in nature as a mixture of two or more isotopes. Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons, leading to different atomic masses. For example, carbon exists primarily as Carbon-12 and Carbon-13. While Carbon-12 has an atomic mass of approximately 12 amu, and Carbon-13 has an atomic mass of approximately 13 amu, the carbon listed on the periodic table has an average atomic mass of 12.011 amu. This value is a weighted average, reflecting how common each isotope is in nature.
Why is it a Weighted Average?
The average atomic mass is a weighted average because not all isotopes of an element are equally abundant. If an element has an isotope that makes up 99% of its natural occurrence, and another that makes up only 1%, the average atomic mass will be much closer to the mass of the more abundant isotope. The "weight" in the average comes from the natural abundance (percentage) of each isotope.
The Formula for Average Atomic Mass
The average atomic mass is calculated using the following formula:
Average Atomic Mass = (Isotope₁ Mass × Isotope₁ Abundance) + (Isotope₂ Mass × Isotope₂ Abundance) + ...
Where:
Isotope Mass is the atomic mass of a specific isotope (usually in atomic mass units, amu).
Isotope Abundance is the natural abundance of that isotope, expressed as a decimal (e.g., 75% becomes 0.75).
How to Use the Calculator
Our Average Atomic Mass Calculator simplifies this process for you:
Enter Isotope Mass (amu): For each isotope, input its exact atomic mass in atomic mass units (amu).
Enter Isotope Abundance (%): For each isotope, input its natural abundance as a percentage. For example, if an isotope makes up 75.77% of the element, enter "75.77".
Add More Isotopes (Optional): The calculator provides fields for up to three isotopes. If your element has more, you can conceptually extend the calculation by adding more terms to the formula. For typical elements, two or three isotopes cover the vast majority of natural abundance.
Click "Calculate": The calculator will then compute the average atomic mass based on your inputs.
Example: Calculating the Average Atomic Mass of Chlorine
Let's use the example of Chlorine (Cl), which has two major isotopes:
Chlorine-35: Mass = 34.96885 amu, Abundance = 75.77%
Chlorine-37: Mass = 36.96590 amu, Abundance = 24.23%
Using the formula:
Average Atomic Mass = (34.96885 amu × 0.7577) + (36.96590 amu × 0.2423)
Average Atomic Mass = 26.4959 amu + 8.9563 amu
Average Atomic Mass = 35.4522 amu
When you input these values into the calculator, you will get a result very close to 35.4522 amu, which is the value found on the periodic table for Chlorine.
This calculator is a useful tool for students, educators, and anyone needing to quickly determine the average atomic mass of an element given its isotopic data.