STEM EVIDENCE WORKBENCH
Calculate normalized weighted average atomic mass from isotope masses and percentage abundances and compare a claimed result with every contribution.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
Weighted average mass equals the sum over isotopes of isotopic mass times fractional abundance. Fractional abundance is percentage divided by 100. When entered percentages total 100 only within the accepted rounding tolerance, the contribution sum is divided by abundance total/100 to normalize that small rounding difference. Claim difference equals entered claim minus calculated weighted average, retaining its sign and five decimal places in the report. Agreement within 0.01 u supports the numerical claim at typical classroom precision. It does not mean every digit is experimentally justified. A positive difference means the claim is above the calculated mean, and a negative difference means it is below. Inspect the individual contribution rows to find a percent-as-decimal error, omitted isotope, transposed mass, or incorrect rounding. Sample composition and reference standards can also explain a small real difference.
Confirm the prompt, source values, units, signs, notation, precision, and model required by the current course. Keep an untouched copy of observations or responses before changing a row.
Run the worked example first, inspect every intermediate row, and compare the table with a hand calculation, diagram, number line, periodic table, or approved laboratory method.
Record the method, assumptions, units, rounding, limits, and any row that needs review. Use the exported report as editable evidence and verify it independently before assessment or laboratory use.
How to interpret the result
Use this diagnostic when learners need to connect isotope abundance with the non-integer average mass shown on a periodic table. The contribution table makes multiplication by a fractional abundance visible and shows why a more abundant isotope pulls the mean closer to its mass. It can check a hand calculation or a claim from supplied data. It does not determine isotope abundance from a spectrum, identify peaks, or guarantee agreement with every natural sample.
The chlorine example uses Cl-35 mass 34.96885 u at 75.78% and Cl-37 mass 36.96590 u at 24.22%. Each abundance is divided by 100 and multiplied by its isotopic mass. The contributions sum to about 35.45254 u, so the entered 35.45 u claim agrees within the disclosed 0.01 u comparison tolerance. The report also shows the exact abundance total and signed claim difference for rounding review.
Weighted average mass equals the sum over isotopes of isotopic mass times fractional abundance. Fractional abundance is percentage divided by 100. When entered percentages total 100 only within the accepted rounding tolerance, the contribution sum is divided by abundance total/100 to normalize that small rounding difference. Claim difference equals entered claim minus calculated weighted average, retaining its sign and five decimal places in the report.
Agreement within 0.01 u supports the numerical claim at typical classroom precision. It does not mean every digit is experimentally justified. A positive difference means the claim is above the calculated mean, and a negative difference means it is below. Inspect the individual contribution rows to find a percent-as-decimal error, omitted isotope, transposed mass, or incorrect rounding. Sample composition and reference standards can also explain a small real difference.
Do not average isotope masses without weights, multiply by 75.78 instead of 0.7578, use abundance as a mass, round every contribution too early, assume the most abundant isotope equals the exact average, or use mass number when precise isotopic mass is supplied. Check that percentages are complete, estimate where the mean must lie, keep guard digits, and round only the final value to the precision required by the question.
Learning boundary
This browser-local workbench applies only the disclosed rules to entered values. It cannot diagnose learning, establish a chemical structure, certify a measurement system, validate an experiment, or replace the method and judgment required by a teacher, curriculum, laboratory, or institution.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid names and other personal information, and retain authoritative records only in the system approved by the school.
No. A matched pattern describes one entered response. Ask the learner to explain, use another representation, and review several evidence sources before deciding the next teaching step.
Treat it as an editable calculation aid. Show your own reasoning, use the method requested by the course, cite required sources, and follow the applicable academic-integrity rules.
YOUR NIRMION
