Average Atomic Mass Calculator
Average Atomic Mass Calculator finds weighted isotopic masses using abundances, shows step-by-step calculations, formulas, and clear chemistry examples instantly.
Equation Preview
Helping Notes
- Formula: \( \text{AM} = \sum_i f_i m_i \) where \( f_i = \) fraction of isotope (percent ÷ 100).
- Use **percent abundances** (must sum to 100%) and **isotopic masses** in amu. We display AM in amu (same number as g/mol).
- Typical examples: Chlorine (² isotopes), Boron (²), Magnesium (³). Values from standard references and Omni’s example.
Results
Average Atomic Mass
Breakdown by Isotope
Error
Steps
What Is an Average Atomic Mass Calculator?
An Average Atomic Mass Calculator computes the weighted mean mass of an element’s isotopes using their natural abundances. Real elements exist as mixtures of isotopes, so the periodic table lists a weighted average rather than an integer mass number. The calculator multiplies each isotopic mass by its fractional abundance and sums the results. It automatically converts between percent and fractional inputs.
About the Average Atomic Mass Calculator
The tool accepts multiple isotopes with exact masses and abundances, ensuring all abundances sum to 1 (or 100%). It can solve for an unknown isotope fraction if the average atomic mass is known, a common chemistry lab task. Output is shown in atomic mass units (u) or grams per mole (g·mol−1), which are numerically equivalent. The interface displays each substitution, partial product, and the total sum in an intuitive formula layout to reinforce understanding.
How to Use the Average Atomic Mass Calculator
- Enter each isotope’s mass \(m_i\) in u and abundance (percent or fraction). Add rows as needed.
- Optionally mark one abundance as unknown and provide \(\bar{A}\) to solve for it.
- Click Calculate to see partial products \(a_i m_i\), the total sum, and the final average atomic mass.
- Select rounding precision (e.g., 4 significant figures) and preferred output unit (u or g·mol−1).
- Copy results or embed generated formulas for lab documentation or homework.
Examples of Average Atomic Mass Calculations
Example 1: Chlorine
Isotopes: \(^{35}\mathrm{Cl}\) (34.96885 u, 75.78%), \(^{37}\mathrm{Cl}\) (36.96590 u, 24.22%).
Example 2: Boron
Isotopes: \(^{10}\mathrm{B}\) (10.0129 u, 19.9%), \(^{11}\mathrm{B}\) (11.0093 u, 80.1%).
Example 3: Solving for an Unknown Abundance
Two isotopes: \(m_1=62.9296\,\text{u}\), \(m_2=64.9278\,\text{u}\), observed \(\bar{A}=63.546\,\text{u}\) (like copper).
Example 4: Fractional Abundance Check
Abundances 40%, 35%, 25% correspond to \(a=0.40, 0.35, 0.25\) and must sum to 1.00 before calculating \(\bar{A}\).
Frequently Asked Questions
What is average atomic mass?
The weighted mean of an element’s isotopic masses using natural abundances. Older texts may call this atomic weight.
Why isn’t the average atomic mass an integer?
It reflects a mixture of isotopes and nuclear binding energy differences. Only the mass number (A) is an integer.
Are u and g·mol−1 interchangeable?
Yes, numerically. 1 u per atom equals 1 g·mol−1 for molar quantity.
Do isotope abundances have to sum to 100%?
Yes. The calculator normalizes rounding discrepancies automatically.
Can I use mass numbers instead of isotopic masses?
Mass numbers are approximate. Use precise isotopic masses for accurate results.
How do I solve for an unknown isotope abundance?
Use the two-isotope formula \(f = (\bar{A}-m_2)/(m_1-m_2)\), or \(\sum a_i=1\) for multi-isotope calculations.
Why might my result differ from the periodic table?
Natural isotopic abundances vary slightly between sources and samples. Rounding and significant figures also influence results.
Can this calculator handle three or more isotopes?
Yes. Enter all isotopic masses \(m_i\) and abundances \(a_i\); the weighted mean formula still applies.
How many significant figures should I report?
Use the precision of the least accurate input. Typically, four to five significant figures are sufficient for general chemistry.
Does isotope instability affect results?
Short-lived radioisotopes usually have negligible impact on natural abundance. Include only relevant isotopes.
Is average atomic mass the same as molar mass?
Numerically yes for elements. For compounds, sum constituent atomic masses according to the molecular formula.