 # How to Convert Weight Fraction to Mole Fraction?

A mixture consist of n component, e1, e2, e3,…en with molecular weight MW1, MW2, MW3, … MWn. Each component mass are M1, M2, M3, … Mn.

## MASS FRACTION

Mass fraction of component-1, X1 = M1/MT [Eq. 1-1]
Mass fraction of component-2, X2 = M2/MT [Eq. 1-2]
Mass fraction of component-3, X3 = M3/MT [Eq. 1-3]
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Mass fraction of component-i, Xi = Mi/MT [Eq. 1-i]
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Mass fraction of component-n, Xn = Mn/MT [Eq. 1-n]
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Total mass in mixtures, MT = M1 + M2 + M3 +…+ Mn [Eq. 2]

## Number of MOLE

Component-1 number of mole, N1 = M1/MW1 [Eq. 3-1]
Component-2 number of mole, N2 = M2/MW2 [Eq. 3-2]
Component-3 number of mole, N3 = M3/MW3 [Eq. 3-3]
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Component-n number of mole, Nn = Mn/MWn [Eq. 3-n]

Total number of mole,

NT = N1 + N2 + N3 +…+ Nn [Eq. 4]
NT = [M1/MW1 + M2/MW2 + M3/MW3 +…+ Mn/MWn] [Eq. 5]

## MOLE FRACTION

For component-1,

Y1 = N1 / NT
Y1 = (M1/MW1) / NT

From [Eq. 1-1],
X1 = M1/MT
M1 = X1* MT
Y1 = (X1*MT/MW1) / NT

Mole Fraction of component-1,
Y1 = (M1/MW1) / NT [Eq. 6-1a]
Y1 = (X1*MT/MW1) / NT [Eq. 6-1b]

Mole Fraction of component-2,
Y2 = (M2/MW2) / NT [Eq. 6-2a]
Y2 = (X2*MT/MW2) / NT [Eq. 6-2b]

Mole Fraction of component-3,
Y3 = (M3/MW3) / NT [Eq. 6-3b]
Y3 = (X3*MT/MW3) / NT [Eq. 6-3b]
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Mole Fraction of component-n,
Yn = (Mn/MWn) / NT [Eq. 6-na]
Yn = (Xn*MT/MWn) / NT [Eq. 6-nb]

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