Practice Isotope Calculations #1 Answer Key

Average Atomic Mass Calculator

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); if (isNaN(isotope1Mass) || isNaN(isotope1Abundance) || isNaN(isotope2Mass) || isNaN(isotope2Abundance)) { document.getElementById('result').innerHTML = 'Please enter valid numbers for all fields.'; return; } var averageAtomicMass = (isotope1Mass * (isotope1Abundance / 100)) + (isotope2Mass * (isotope2Abundance / 100)); document.getElementById('result').innerHTML = 'The Average Atomic Mass is: ' + averageAtomicMass.toFixed(5) + ' amu'; }

In the world of chemistry, not all atoms of the same element are identical. While they all share the same number of protons (which defines the element), they can differ in the number of neutrons. These variations are known as isotopes.

What are Isotopes?

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This difference in neutron count leads to different mass numbers for each isotope. For example, Carbon-12 has 6 protons and 6 neutrons, while Carbon-14 has 6 protons and 8 neutrons. Both are carbon, but they have different atomic masses.

Why Calculate Average Atomic Mass?

When you look at the periodic table, the atomic mass listed for each element is rarely a whole number. This is because it represents the average atomic mass of all the naturally occurring isotopes of that element, taking into account their relative abundances. Since elements in nature are typically a mixture of their isotopes, this average mass is a more accurate representation for most chemical calculations.

The Formula for Average Atomic Mass

The average atomic mass is calculated by taking a weighted average of the masses of all naturally occurring isotopes of an element. The "weight" in this average is the natural abundance of each isotope. The general formula is:

Average Atomic Mass = (Mass of Isotope 1 × Fractional Abundance of Isotope 1) + (Mass of Isotope 2 × Fractional Abundance of Isotope 2) + …

Where:

• Mass of Isotope is the atomic mass unit (amu) of a specific isotope.
• Fractional Abundance is the percentage abundance of that isotope divided by 100. For example, if an isotope has an abundance of 75%, its fractional abundance is 0.75.

Example Calculation: Chlorine

Let's use the element Chlorine (Cl) as an example. Chlorine has two major naturally occurring isotopes:

• Chlorine-35: Has an atomic mass of approximately 34.96885 amu and a natural abundance of 75.77%.
• Chlorine-37: Has an atomic mass of approximately 36.96590 amu and a natural abundance of 24.23%.

Using the formula:

Average Atomic Mass = (34.96885 amu × 0.7577) + (36.96590 amu × 0.2423)
Average Atomic Mass = 26.4959 amu + 8.9570 amu
Average Atomic Mass = 35.4529 amu

This calculated value closely matches the atomic mass of Chlorine found on the periodic table (typically rounded to 35.453 amu).

Using the Calculator

Our Average Atomic Mass Calculator above simplifies this process. Simply input the atomic mass (in amu) and the percentage abundance for each isotope. The calculator will then apply the weighted average formula to provide you with the average atomic mass for the element. This tool is perfect for practicing isotope calculations and verifying your answers for various elements.

Remember that the sum of the percentage abundances for all isotopes of an element should ideally add up to 100%. If they don't, the calculation will still proceed based on the numbers provided, but the result might not accurately reflect the true average atomic mass of a naturally occurring element.