In chemistry, understanding the composition of compounds is fundamental. Two key terms that describe a compound's formula are the empirical formula and the molecular formula.
Empirical Formula (EF): This is the simplest whole-number ratio of atoms of each element present in a compound. It represents the relative number of atoms, not the actual number of atoms in a molecule. For example, the empirical formula for glucose is CH2O.
Molecular Formula (MF): This formula represents the actual number of atoms of each element in one molecule of a compound. It is a whole-number multiple of the empirical formula. For example, the molecular formula for glucose is C6H12O6.
How to Determine the Molecular Formula from the Empirical Formula
To find the molecular formula, you need both the empirical formula and the molecular weight of the compound. The process involves these steps:
Determine the Empirical Formula: This is usually given or calculated from experimental data (like percent composition).
Calculate the Empirical Formula Weight (EFW): Sum the atomic weights of all atoms in the empirical formula.
Find the Whole-Number Multiple (n): Divide the molecular weight of the compound by the empirical formula weight.
n = Molecular Weight / Empirical Formula Weight
This 'n' value should be a whole number (or very close to one, allowing for rounding in experimental data).
Determine the Molecular Formula: Multiply the subscripts in the empirical formula by the whole-number multiple 'n'.
Molecular Formula = (Empirical Formula)n
Example Calculation
Let's say a compound has an empirical formula of CH2O and its molecular weight is 180.18 g/mol.
C(1×6)H(2×6)O(1×6) = C6H12O6 (This is the molecular formula for glucose)
When to Use This Calculator
This calculator is useful for students and chemists who are:
Practicing stoichiometry and formula determination.
Analyzing experimental data to identify unknown compounds.
Verifying calculations for empirical and molecular formulas.
It simplifies the process of converting an empirical formula, given its elemental composition and the compound's molecular weight, into its true molecular formula.
function calculateMolecularFormula() {
var elementsInput = document.getElementById("elements").value.trim().toLowerCase();
var percentagesInput = document.getElementById("percentages").value.trim();
var molecularWeightInput = document.getElementById("molecularWeight").value;
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
// Input validation
if (!elementsInput || !percentagesInput || !molecularWeightInput) {
resultDiv.innerHTML = "Please fill in all fields.";
return;
}
var elements = elementsInput.split(',').map(function(e) { return e.trim(); });
var percentages = percentagesInput.split(',').map(function(p) { return parseFloat(p.trim()); });
var molecularWeight = parseFloat(molecularWeightInput);
if (isNaN(molecularWeight) || molecularWeight <= 0) {
resultDiv.innerHTML = "Please enter a valid positive Molecular Weight.";
return;
}
if (elements.length !== percentages.length || elements.length === 0) {
resultDiv.innerHTML = "The number of elements must match the number of percentages.";
return;
}
var totalPercentage = 0;
for (var i = 0; i < percentages.length; i++) {
if (isNaN(percentages[i]) || percentages[i] 100) {
resultDiv.innerHTML = "Please enter valid percentages (0-100).";
return;
}
totalPercentage += percentages[i];
}
// Allow for small floating point inaccuracies when checking if percentages sum to 100
if (Math.abs(totalPercentage – 100) > 0.1) {
resultDiv.innerHTML = "Percentages should ideally sum to 100%. Current sum: " + totalPercentage.toFixed(2) + "%.";
// Continue calculation, but warn user
}
// Step 1 & 2: Convert percentages to moles (assuming a 100g sample)
var moles = [];
var atomicWeights = {
'h': 1.008, 'he': 4.003, 'li': 6.94, 'be': 9.012, 'b': 10.81, 'c': 12.01, 'n': 14.01, 'o': 16.00, 'f': 19.00,
'ne': 20.18, 'na': 22.99, 'mg': 24.31, 'al': 26.98, 'si': 28.09, 'p': 30.97, 's': 32.06, 'cl': 35.45,
'ar': 39.95, 'k': 39.10, 'ca': 40.08, 'sc': 44.96, 'ti': 47.87, 'v': 50.94, 'cr': 52.00, 'mn': 54.94,
'fe': 55.85, 'co': 58.93, 'ni': 58.69, 'cu': 63.55, 'zn': 65.38, 'ga': 69.72, 'ge': 72.63, 'as': 74.92,
'se': 78.97, 'br': 79.90, 'kr': 83.80, 'rb': 85.47, 'sr': 87.62, 'y': 88.91, 'zr': 91.22, 'nb': 92.91,
'mo': 95.95, 'tc': 98, 'ru': 101.1, 'rh': 102.9, 'pd': 106.4, 'ag': 107.9, 'cd': 112.4, 'in': 114.8,
'sn': 118.7, 'sb': 121.8, 'te': 127.6, 'i': 126.9, 'xe': 131.3, 'cs': 132.9, 'ba': 137.3, 'la': 138.9,
'ce': 140.1, 'pr': 140.9, 'nd': 144.2, 'pm': 145, 'sm': 150.4, 'eu': 152.0, 'gd': 157.3, 'tb': 158.9,
'dy': 162.5, 'ho': 164.9, 'er': 167.3, 'tm': 168.9, 'yb': 173.1, 'lu': 175.0, 'hf': 178.5, 'ta': 180.9,
'w': 183.8, 're': 186.2, 'os': 190.2, 'ir': 192.2, 'pt': 195.1, 'au': 197.0, 'hg': 200.6, 'tl': 204.4,
'pb': 207.2, 'bi': 209.0, 'po': 209, 'at': 210, 'rn': 222, 'fr': 223, 'ra': 226, 'ac': 227, 'th': 232.0,
'pa': 231.0, 'u': 238.0, 'np': 237, 'pu': 244, 'am': 243, 'cm': 247, 'bk': 247, 'cf': 251, 'es': 252,
'fm': 257, 'md': 258, 'no': 259, 'lr': 266
};
var minMoles = Infinity;
var empiricalFormulaParts = [];
for (var j = 0; j < elements.length; j++) {
var elementSymbol = elements[j];
var atomicWeight = atomicWeights[elementSymbol];
if (!atomicWeight) {
resultDiv.innerHTML = "Unknown element: " + elementSymbol + ". Please ensure correct spelling and use common element symbols.";
return;
}
// Assuming a 100g sample, mass in grams = percentage
var massGrams = percentages[j];
var moleCount = massGrams / atomicWeight;
moles.push(moleCount);
if (moleCount < minMoles) {
minMoles = moleCount;
}
}
// Step 3: Find the simplest whole-number ratio by dividing by the smallest mole count
var empiricalFormulaRatio = [];
for (var k = 0; k 0.1) {
resultDiv.innerHTML = "Could not determine a clear empirical formula ratio. Check input percentages.";
return;
}
empiricalFormulaRatio.push(roundedRatio);
empiricalFormulaParts.push(elements[k] + (roundedRatio > 1 ? roundedRatio : "));
}
var empiricalFormulaString = empiricalFormulaParts.join(");
var empiricalFormulaWeight = 0;
for (var l = 0; l 0.1) {
resultDiv.innerHTML = "The calculated multiplier (n) is not a whole number. Ensure the Molecular Weight is correct and the empirical formula derived is accurate.";
return;
}
// Step 5: Determine the Molecular Formula
var molecularFormulaParts = [];
for (var m = 0; m 1 ? subscript : "));
}
var molecularFormulaString = molecularFormulaParts.join(");
resultDiv.innerHTML = "Empirical Formula Weight (EFW): " + empiricalFormulaWeight.toFixed(3) + " g/mol" +
"Multiplier (n): " + roundedN + "" +
"Molecular Formula: " + molecularFormulaString + "";
}