Calculate Molecular Weight from Mass Fraction Calculator
Use this professional tool to calculate molecular weight from mass fraction quickly. Enter component mass fractions and molecular weights to calculate molecular weight from mass fraction and reveal detailed intermediate metrics.
Calculator: Calculate Molecular Weight from Mass Fraction
Typical range 0–100; must be non-negative.
Example: water = 18 g/mol.
Typical range 0–100; mixture total should approach 100%.
Example: CO2 = 44 g/mol.
Optional third species; keep non-negative.
Example: propane = 44 g/mol; adjust as needed.
Used to display component masses; does not change molecular weight formula.
Primary Result
0.000 g/mol
Formula: 1 / Σ(wᵢ / Mᵢ), where wᵢ = mass fraction (decimal), Mᵢ = molecular weight.
Component Detail Table
Component
Mass Fraction (%)
Molecular Weight (g/mol)
Fraction/MW (1/mol)
Component Mass (g)
A
B
C
Total
–
Chart shows mass fraction distribution and fractional contribution to 1/Mmix.
What is calculate molecular weight from mass fraction?
Calculate molecular weight from mass fraction describes the method of determining a mixture's average molecular weight by using each component's molecular weight and its mass fraction. Professionals in chemical engineering, refining, gas processing, and pharmaceutical formulation use calculate molecular weight from mass fraction to verify blend quality and predict transport properties. A common misconception is that calculate molecular weight from mass fraction can be replaced by mole fractions; the two give different averages, and calculate molecular weight from mass fraction is the correct choice when composition data are given in weight percentages.
Calculate molecular weight from mass fraction Formula and Mathematical Explanation
The core relationship to calculate molecular weight from mass fraction is M_mix = 1 / Σ(wᵢ / Mᵢ). Each wᵢ is the mass fraction expressed as a decimal, and each Mᵢ is the molecular weight of component i. To calculate molecular weight from mass fraction, convert percentages to decimals, divide each by its molecular weight, sum those ratios, then take the reciprocal. This derivation comes from the definition of average molecular weight based on mass composition.
Variable Reference for calculate molecular weight from mass fraction
Variable
Meaning
Unit
Typical range
wᵢ
Mass fraction of component i
dimensionless
0 to 1
Mᵢ
Molecular weight of component i
g/mol
2 to 300
M_mix
Mixture molecular weight
g/mol
2 to 300
Σ(wᵢ / Mᵢ)
Sum of fraction-weighted reciprocals
1/mol
0.001 to 1
Practical Examples (Real-World Use Cases)
Natural Gas Blend
Inputs: methane 75% at 16 g/mol, ethane 15% at 30 g/mol, nitrogen 10% at 28 g/mol. Calculate molecular weight from mass fraction: convert to decimals (0.75/16 + 0.15/30 + 0.10/28) = 0.046875 + 0.005 + 0.003571 = 0.055446; invert to get 18.04 g/mol. The result helps pipeline engineers size compressors.
Solvent Mixture
Inputs: acetone 40% at 58 g/mol, ethanol 35% at 46 g/mol, water 25% at 18 g/mol. Calculate molecular weight from mass fraction: (0.40/58 + 0.35/46 + 0.25/18) = 0.006897 + 0.007609 + 0.013889 = 0.028395; inverse gives 35.22 g/mol. The calculated molecular weight informs evaporation and vapor pressure predictions.
How to Use This calculate molecular weight from mass fraction Calculator
Enter mass fraction percentages for each component and ensure they approximate 100% to calculate molecular weight from mass fraction accurately.
Input each component's molecular weight in g/mol.
Optionally set the total mixture mass to see component masses while you calculate molecular weight from mass fraction.
Review the highlighted mixture molecular weight result and intermediate reciprocal sums.
Use the table and chart to confirm contributions when you calculate molecular weight from mass fraction.
Copy results for reports or simulations.
Key Factors That Affect calculate molecular weight from mass fraction Results
Measurement accuracy of component molecular weights determines fidelity when you calculate molecular weight from mass fraction.
Mass fraction sampling errors propagate directly into the sum, shifting the calculated molecular weight.
Presence of heavy tail components raises the reciprocal-weighted sum, lowering the mixture molecular weight when you calculate molecular weight from mass fraction.
Temperature-dependent composition changes alter mass fractions, influencing the calculate molecular weight from mass fraction output.
Impurities introduce additional terms, modifying the sum used to calculate molecular weight from mass fraction.
Rounding percentages so they no longer sum to 100% distorts the reciprocal sum and the final calculate molecular weight from mass fraction value.
Frequently Asked Questions (FAQ)
What if mass fractions do not sum to 100%? Normalize or rescale before you calculate molecular weight from mass fraction to avoid bias.
Can I use mole fractions? No, calculate molecular weight from mass fraction requires weight-based inputs; mole fractions use a different formula.
How many components can I include? Any number, but this calculator shows three to keep calculate molecular weight from mass fraction fast and clear.
Does unit choice matter? Use consistent g/mol for molecular weights when you calculate molecular weight from mass fraction.
How sensitive is the result? Small errors in heavy components have larger impact on calculate molecular weight from mass fraction.
Can I use ppm values? Convert to mass fraction first, then calculate molecular weight from mass fraction.
What if a component has zero mass fraction? It contributes nothing to the sum when you calculate molecular weight from mass fraction.
Is this valid for liquids and gases? Yes, any mixture defined by weight allows you to calculate molecular weight from mass fraction.
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{related_keywords} – Validate experimental data prior to calculate molecular weight from mass fraction.
var ctx = document.getElementById("mixChart").getContext("2d");
var chartData = {fractions:[0,0,0], contributions:[0,0,0]};
function drawChart(){
var canvas = document.getElementById("mixChart");
var w = canvas.width = canvas.offsetWidth;
var h = canvas.height = canvas.offsetHeight;
var maxVal = 1;
var i;
for(i=0;imaxVal){maxVal=chartData.fractions[i];}}
for(i=0;imaxVal){maxVal=chartData.contributions[i];}}
var padding = 40;
var barWidth = (w – 2*padding)/chartData.fractions.length/2;
var xStart = padding;
ctx.clearRect(0,0,w,h);
ctx.fillStyle = "#eef4fb";
ctx.fillRect(0,0,w,h);
ctx.strokeStyle = "#b8d0f0";
ctx.beginPath();
ctx.moveTo(padding,h-padding);
ctx.lineTo(w-padding,h-padding);
ctx.stroke();
for(i=0;i<chartData.fractions.length;i++){
var fracHeight = (h-2*padding)*(chartData.fractions[i]/maxVal);
var contHeight = (h-2*padding)*(chartData.contributions[i]/maxVal);
ctx.fillStyle = "#004a99";
ctx.fillRect(xStart + i*2*barWidth, h-padding-fracHeight, barWidth, fracHeight);
ctx.fillStyle = "#28a745";
ctx.fillRect(xStart + i*2*barWidth + barWidth, h-padding-contHeight, barWidth, contHeight);
ctx.fillStyle = "#203049";
ctx.font = "12px Arial";
ctx.fillText("Comp "+String.fromCharCode(65+i), xStart + i*2*barWidth, h-padding+14);
}
ctx.fillStyle = "#004a99";
ctx.fillRect(w-160,20,12,12);
ctx.fillStyle = "#203049";
ctx.fillText("Mass Fraction", w-140,30);
ctx.fillStyle = "#28a745";
ctx.fillRect(w-160,40,12,12);
ctx.fillStyle = "#203049";
ctx.fillText("wᵢ/Mᵢ Term", w-140,50);
}
function resetErrors(){
document.getElementById("errFractionA").innerText="";
document.getElementById("errMwA").innerText="";
document.getElementById("errFractionB").innerText="";
document.getElementById("errMwB").innerText="";
document.getElementById("errFractionC").innerText="";
document.getElementById("errMwC").innerText="";
document.getElementById("errTotalMass").innerText="";
}
function validate(value,min,max,id){
if(value==="" || isNaN(value)){ document.getElementById(id).innerText="Enter a valid number."; return false; }
if(valuemax){ document.getElementById(id).innerText="Value must not exceed "+max+"."; return false; }
document.getElementById(id).innerText="";
return true;
}
function recalculate(){
resetErrors();
var fA = parseFloat(document.getElementById("fractionA").value);
var fB = parseFloat(document.getElementById("fractionB").value);
var fC = parseFloat(document.getElementById("fractionC").value);
var mA = parseFloat(document.getElementById("mwA").value);
var mB = parseFloat(document.getElementById("mwB").value);
var mC = parseFloat(document.getElementById("mwC").value);
var totalMass = parseFloat(document.getElementById("totalMass").value);
var valid = true;
if(!validate(fA,0,100,"errFractionA")) valid=false;
if(!validate(fB,0,100,"errFractionB")) valid=false;
if(!validate(fC,0,100,"errFractionC")) valid=false;
if(!validate(mA,0.0001,null,"errMwA")) valid=false;
if(!validate(mB,0.0001,null,"errMwB")) valid=false;
if(!validate(mC,0.0001,null,"errMwC")) valid=false;
if(!validate(totalMass,0,null,"errTotalMass")) valid=false;
if(!valid){ return; }
var sumPercent = fA + fB + fC;
var sumFrac = sumPercent/100;
var termA = (fA/100)/mA;
var termB = (fB/100)/mB;
var termC = (fC/100)/mC;
var sumTerms = termA + termB + termC;
var mixMw = 0;
if(sumTerms>0){ mixMw = 1/sumTerms; }
var massA = totalMass*(fA/100);
var massB = totalMass*(fB/100);
var massC = totalMass*(fC/100);
document.getElementById("mainResult").innerText = mixMw.toFixed(3)+" g/mol";
document.getElementById("intermediate1").innerText = "Sum of mass fractions: "+sumPercent.toFixed(2)+"%";
document.getElementById("intermediate2").innerText = "Sum of reciprocal terms Σ(wᵢ/Mᵢ): "+sumTerms.toFixed(6)+" 1/mol";
document.getElementById("intermediate3").innerText = "Normalized sum of fractions (decimal): "+sumFrac.toFixed(4);
document.getElementById("intermediate4").innerText = "Component masses (g): A "+massA.toFixed(1)+", B "+massB.toFixed(1)+", C "+massC.toFixed(1);
document.getElementById("rowFracA").innerText = fA.toFixed(2);
document.getElementById("rowMwA").innerText = mA.toFixed(3);
document.getElementById("rowTermA").innerText = termA.toFixed(6);
document.getElementById("rowMassA").innerText = massA.toFixed(3);
document.getElementById("rowFracB").innerText = fB.toFixed(2);
document.getElementById("rowMwB").innerText = mB.toFixed(3);
document.getElementById("rowTermB").innerText = termB.toFixed(6);
document.getElementById("rowMassB").innerText = massB.toFixed(3);
document.getElementById("rowFracC").innerText = fC.toFixed(2);
document.getElementById("rowMwC").innerText = mC.toFixed(3);
document.getElementById("rowTermC").innerText = termC.toFixed(6);
document.getElementById("rowMassC").innerText = massC.toFixed(3);
document.getElementById("rowFracTotal").innerText = sumPercent.toFixed(2);
document.getElementById("rowTermTotal").innerText = sumTerms.toFixed(6);
document.getElementById("rowMassTotal").innerText = totalMass.toFixed(3);
chartData.fractions=[fA,fB,fC];
chartData.contributions=[termA,termB,termC];
drawChart();
}
function resetDefaults(){
document.getElementById("fractionA").value = 60;
document.getElementById("mwA").value = 18;
document.getElementById("fractionB").value = 30;
document.getElementById("mwB").value = 44;
document.getElementById("fractionC").value = 10;
document.getElementById("mwC").value = 58;
document.getElementById("totalMass").value = 1000;
recalculate();
}
function copyResults(){
var text = "Mixture molecular weight: "+document.getElementById("mainResult").innerText+"\n"+
document.getElementById("intermediate1").innerText+"\n"+
document.getElementById("intermediate2").innerText+"\n"+
document.getElementById("intermediate3").innerText+"\n"+
document.getElementById("intermediate4″).innerText+"\nKey assumption: average molecular weight calculated by mass fractions (1/sum(wi/Mi)).";
if(navigator.clipboard && navigator.clipboard.writeText){
navigator.clipboard.writeText(text);
} else {
var temp = document.createElement("textarea");
temp.value = text;
document.body.appendChild(temp);
temp.select();
document.execCommand("copy");
document.body.removeChild(temp);
}
}
recalculate();