If the sample is not pure Fe2O3, adjust percentage here.
Purity must be between 0 and 100.
Total Mass of Iron (Fe)
69.94 g
Stoichiometry Used: Molar Mass Fe = 55.845 g/mol | Molar Mass O = 15.999 g/mol.
Formula: (2 × Fe) / (2 × Fe + 3 × O) × 100
Mass of Oxygen (O)30.06 g
Percent Iron by Weight69.94%
Percent Oxygen by Weight30.06%
Total Molar Mass (Fe2O3)159.69 g/mol
Composition Breakdown by Element based on Sample Size
Element
Atomic Mass (g/mol)
Atoms in Formula
Total Mass in Sample
Iron (Fe)
55.845
2
69.94 g
Oxygen (O)
15.999
3
30.06 g
Impurities
N/A
N/A
0.00 g
What is "Calculate the Weight Percent of Iron in Fe2O3"?
When chemists, geologists, and industrial engineers need to calculate the weight percent of iron in Fe2O3, they are performing a fundamental stoichiometric calculation to determine how much pure iron can be extracted from Iron(III) Oxide. Fe2O3, commonly known as hematite or rust, is one of the most significant ores of iron used in steel production.
Understanding how to calculate the weight percent of iron in Fe2O3 is crucial for refining efficiency, cost estimation in mining, and laboratory synthesis. The "weight percent" (also called mass percent) represents the fraction of the total mass of the compound that is contributed specifically by iron atoms.
Common misconceptions include confusing the atomic ratio (2:3 for Fe:O) with the mass ratio. While there are fewer iron atoms than oxygen atoms in the molecule, iron atoms are significantly heavier, meaning iron makes up the majority of the mass.
Fe2O3 Formula and Mathematical Explanation
To calculate the weight percent of iron in Fe2O3, we use the atomic masses of the constituent elements found in the periodic table. The chemical formula Fe2O3 indicates that one mole of the compound contains 2 moles of Iron (Fe) and 3 moles of Oxygen (O).
Step-by-Step Derivation
Find Atomic Masses: Iron (Fe) is approximately 55.845 g/mol, and Oxygen (O) is approximately 15.999 g/mol.
Calculate Total Mass of Iron: Multiply the atomic mass of Fe by 2. 2 × 55.845 = 111.69 g/mol
Calculate Total Mass of Oxygen: Multiply the atomic mass of O by 3. 3 × 15.999 = 47.997 g/mol
Calculate Molar Mass of Fe2O3: Add the mass of Iron and Oxygen. 111.69 + 47.997 = 159.687 g/mol
Calculate Percentage: Divide the mass of Iron by the total molar mass and multiply by 100.
Formula:
% Fe = (Mass of Fe / Molar Mass of Fe2O3) × 100
% Fe = (111.69 / 159.687) × 100 ≈ 69.94%
Variables Used in Calculation
Variable
Meaning
Unit
Standard Value
M(Fe)
Molar Mass of Iron
g/mol
55.845
M(O)
Molar Mass of Oxygen
g/mol
15.999
M(Fe2O3)
Molar Mass of Compound
g/mol
159.687
Practical Examples (Real-World Use Cases)
Example 1: Mining Ore Assessment
A mining company extracts 1,000 kg of pure hematite (Fe2O3) ore. To estimate the yield of metallic iron, they need to calculate the weight percent of iron in Fe2O3.
Input Mass: 1,000 kg
Calculation: 1,000 kg × 0.6994 (69.94%)
Output: 699.4 kg of pure Iron.
Financial Impact: If iron sells for $0.12 per kg, the recoverable value is based on the 699.4 kg of iron, not the full 1,000 kg of ore.
Example 2: Laboratory Synthesis
A chemist needs exactly 50 grams of pure iron for a reaction but only has Iron(III) Oxide powder available.
Target: 50g Iron
Math: Mass of Oxide needed = Target Mass / 0.6994
Calculation: 50 / 0.6994 = 71.49 grams
Result: The chemist must measure out 71.49 grams of Fe2O3 to ensure they have 50 grams of iron atoms present.
How to Use This Fe2O3 Calculator
Our tool simplifies the stoichiometry for you. Follow these steps:
Enter Sample Mass: Input the total weight of your rock, powder, or ore sample.
Select Unit: Choose grams, kilograms, pounds, or tons. The result will match this unit.
Adjust Purity: If your sample is not 100% pure Fe2O3 (e.g., raw ore with silica), lower the purity percentage. The calculator will discount the impurities before determining the iron content.
Read Results: The "Total Mass of Iron" is your primary yield. Use the intermediate values to see the oxygen content and exact percentages.
Key Factors That Affect Fe2O3 Results
While the theoretical percentage of iron in pure Fe2O3 is constant (69.94%), real-world calculations vary due to several factors:
Sample Purity: Natural hematite is rarely 100% pure. It often contains silica, alumina, or moisture, effectively lowering the percentage of iron in the total bulk mass.
Isotopic Variation: The standard atomic mass of iron is 55.845, but this is an average of isotopes. Samples from specific geological origins might vary slightly in isotopic composition, minutely affecting the molar mass.
Hydration (Rust): Fe2O3 is often found as a hydrate (Fe2O3 · nH2O). The presence of water molecules adds mass without adding iron, significantly lowering the weight percent of iron compared to the anhydrous form.
Oxidation State: If the sample is partially Magnetite (Fe3O4) or Wustite (FeO) rather than pure Fe2O3, the iron percentage will differ. Fe3O4, for example, is approximately 72.4% iron.
Measurement Error: In practical settings, the precision of the weighing scale and the calibration of analytical equipment introduce margins of error in the final calculated mass.
Processing Losses: In industrial smelting, not all iron is recovered. Slag formation and mechanical losses mean the recoverable iron is always less than the theoretical iron calculated here.
Frequently Asked Questions (FAQ)
1. What is the constant weight percent of Iron in pure Fe2O3?
In perfectly pure, anhydrous Fe2O3, the weight percent of Iron is approximately 69.94%. This is a physical constant derived from atomic masses.
2. Does the weight percent change if I have more substance?
No. The percent remains 69.94% regardless of sample size. However, the total mass of iron increases linearly with the sample size.
3. How does this compare to Fe3O4 (Magnetite)?
Magnetite (Fe3O4) has a higher iron content, approximately 72.4%. Fe2O3 (Hematite) has slightly less iron per kilogram of ore due to the higher ratio of oxygen atoms.
4. Can I use this calculator for rust?
Yes, rust is primarily Fe2O3. However, rust often contains water (hydrated iron oxide). If your rust is wet or hydrated, the actual iron content will be lower than 69.94%.
5. Why is the atomic mass of Iron 55.845 and not a whole number?
Atomic mass is a weighted average of all naturally occurring isotopes of iron (Fe-54, Fe-56, Fe-57, Fe-58). The value 55.845 reflects their natural abundance.
6. How do I calculate purity?
If you know the total mass and the mass of impurities, purity is (Mass of Fe2O3 / Total Mass) × 100. Input this value into the calculator's "Purity" field for accurate results.
7. Is Fe2O3 hazardous?
Fe2O3 is generally considered non-toxic and is used in cosmetics and food coloring. However, inhaling fine dust (powder form) can be harmful to lungs (siderosis).
8. Why do I need to calculate the weight percent of iron in Fe2O3 for ceramics?
In ceramics, Fe2O3 is a colorant. Calculating the exact weight percent allows artists to control the intensity of the red/brown glaze precisely.
// Global variables for Chemistry Logic
var atomicMassFe = 55.845;
var atomicMassO = 15.999;
var molarMassFe2O3 = (2 * atomicMassFe) + (3 * atomicMassO); // approx 159.687
// Chart variable
var compChartCtx = null;
var chartInstance = null;
// Helper: format numbers with commas and decimals
function formatNumber(num, decimals) {
return num.toLocaleString('en-US', { minimumFractionDigits: decimals, maximumFractionDigits: decimals });
}
// Main Calculation Function
function calculateStoichiometry() {
// 1. Get Inputs
var sampleMassInput = document.getElementById("sampleMass");
var purityInput = document.getElementById("purity");
var massUnitSelect = document.getElementById("massUnit");
var sampleMass = parseFloat(sampleMassInput.value);
var purity = parseFloat(purityInput.value);
var unit = massUnitSelect.value;
// 2. Validate
var massError = document.getElementById("massError");
var purityError = document.getElementById("purityError");
var isValid = true;
if (isNaN(sampleMass) || sampleMass < 0) {
massError.style.display = "block";
isValid = false;
} else {
massError.style.display = "none";
}
if (isNaN(purity) || purity 100) {
purityError.style.display = "block";
isValid = false;
} else {
purityError.style.display = "none";
}
if (!isValid) return;
// 3. Logic: Calculate the Weight Percent of Iron in Fe2O3 (Theoretical Constant)
var massFeTotalTheoretical = 2 * atomicMassFe;
var percentFeTheoretical = (massFeTotalTheoretical / molarMassFe2O3); // ~0.6994
var percentOTheoretical = 1 – percentFeTheoretical; // ~0.3006
// 4. Adjust for Sample Mass and Purity
// Pure Mass of Fe2O3 in the sample
var pureCompoundMass = sampleMass * (purity / 100);
var impurityMass = sampleMass – pureCompoundMass;
// Absolute Mass of Elements in the Sample
var finalFeMass = pureCompoundMass * percentFeTheoretical;
var finalOMass = pureCompoundMass * percentOTheoretical;
// 5. Update DOM
document.getElementById("resultFeMass").innerText = formatNumber(finalFeMass, 2) + " " + unit;
document.getElementById("resultOMass").innerText = formatNumber(finalOMass, 2) + " " + unit;
// Percentages displayed are relative to the PURE compound logic, but we can also show
// percentage relative to total sample if needed.
// Standard practice: Show the theoretical % of the compound, and the absolute mass derived.
document.getElementById("resultFePercent").innerText = (percentFeTheoretical * 100).toFixed(2) + "%";
document.getElementById("resultOPercent").innerText = (percentOTheoretical * 100).toFixed(2) + "%";
// Table Update
document.getElementById("tableFeMass").innerText = formatNumber(finalFeMass, 2) + " " + unit;
document.getElementById("tableOMass").innerText = formatNumber(finalOMass, 2) + " " + unit;
document.getElementById("tableImpurityMass").innerText = formatNumber(impurityMass, 2) + " " + unit;
var impurityRow = document.getElementById("impurityRow");
if (impurityMass > 0) {
impurityRow.style.display = "table-row";
} else {
impurityRow.style.display = "none";
}
// 6. Update Chart
drawChart(finalFeMass, finalOMass, impurityMass);
}
function drawChart(fe, o, imp) {
var canvas = document.getElementById("compositionChart");
if (!canvas) return;
var ctx = canvas.getContext("2d");
// Clear canvas
ctx.clearRect(0, 0, canvas.width, canvas.height);
// Setup data
var data = [
{ label: "Iron (Fe)", value: fe, color: "#004a99" },
{ label: "Oxygen (O)", value: o, color: "#28a745" }
];
if (imp > 0) {
data.push({ label: "Impurities", value: imp, color: "#ffc107" });
}
var total = fe + o + imp;
if (total === 0) return;
// Set dimensions if not set
if (canvas.width !== canvas.offsetWidth) {
canvas.width = canvas.offsetWidth;
canvas.height = canvas.offsetHeight;
}
var centerX = canvas.width / 2;
var centerY = canvas.height / 2;
var radius = Math.min(centerX, centerY) – 20;
var startAngle = 0;
// Draw Pie Slices
for (var i = 0; i < data.length; i++) {
var sliceAngle = 2 * Math.PI * (data[i].value / total);
ctx.beginPath();
ctx.moveTo(centerX, centerY);
ctx.arc(centerX, centerY, radius, startAngle, startAngle + sliceAngle);
ctx.closePath();
ctx.fillStyle = data[i].color;
ctx.fill();
// Simple Legend text placement (approximate) – Professional approach would use a separate legend HTML
// We will draw a simple legend on the right if space permits, or omit for simplicity and rely on colors/tooltips.
// Since this is a "no library" strict JS requirement, we keep it visual.
startAngle += sliceAngle;
}
// Draw Center Hole (Doughnut style for modern look)
ctx.beginPath();
ctx.arc(centerX, centerY, radius * 0.5, 0, 2 * Math.PI);
ctx.fillStyle = "#ffffff";
ctx.fill();
// Draw Text in Center
ctx.fillStyle = "#333";
ctx.font = "bold 16px Arial";
ctx.textAlign = "center";
ctx.textBaseline = "middle";
ctx.fillText("Fe2O3", centerX, centerY – 10);
ctx.font = "12px Arial";
ctx.fillText("Composition", centerX, centerY + 10);
}
function resetCalculator() {
document.getElementById("sampleMass").value = "100";
document.getElementById("massUnit").value = "g";
document.getElementById("purity").value = "100";
calculateStoichiometry();
}
function copyResults() {
var fe = document.getElementById("resultFeMass").innerText;
var ox = document.getElementById("resultOMass").innerText;
var pct = document.getElementById("resultFePercent").innerText;
var text = "Composition of Fe2O3 Sample:\n" +
"Total Mass of Iron: " + fe + "\n" +
"Total Mass of Oxygen: " + ox + "\n" +
"Iron Percentage: " + pct;
var tempInput = document.createElement("textarea");
tempInput.value = text;
document.body.appendChild(tempInput);
tempInput.select();
document.execCommand("copy");
document.body.removeChild(tempInput);
var btn = document.querySelector(".btn-copy");
var originalText = btn.innerText;
btn.innerText = "Copied!";
setTimeout(function(){ btn.innerText = originalText; }, 2000);
}
// Initialize
window.onload = function() {
calculateStoichiometry();
// Resize listener for chart
window.addEventListener('resize', function() {
calculateStoichiometry();
});
};