Question

A mixture of methanol (Mw = 32.04 g/mol) and ethanol (Mw = 46.07 g/mol) has an average molecular weight of 43.01 g/mol. What is the mol fraction of methanol in this mixture?

Answer 1

The mol fraction of methanol is 0.2181

Step-by-step explanation:

Step 1: Data given

Molar mass of methanol = 32.04 g/mol

Molar mass of ethanol = 46.07 g/mol

Average molecular weight = 43.01 g/mol

Step 2: Calculate the mol fraction of methanol

Mol fraction = number of moles / total number of moles

We know that mol fraction of methanol + mol fraction of ethanol = 1

Mol fraction methanol = 1 - mol fraction of ethanol

X = 1-Y

Let's consider methanol = X and ethanol = Y

32.04*X + 46.07*Y = 43.01

32.04*(1-Y) +46.07Y = 43.01

32.04 - 32.04Y + 46.07Y = 43.01

14.03 Y = 10.97

Y = 0.7819

The mol fraction of ethanol is 0.7819

The mol fraction of methanol is 1 - 0.7819 = 0.2181

Answer 2

The mole fraction of methanol in this mixture is 0.745

Step-by-step explanation:

Molecular weight of methanol in the mixture = 32.04g/mol

Molecular weight of ethanol in the mixture = 46.07g/mol

Average molecular weight of mixture = 43.01g/mol

Mole fraction of methanol = molecular weight of methanol ÷ average molecular weight of mixture = 32.04g/mol ÷ 43.01g/mol = 0.745