Calculate the mole fraction of ethyl acetate, in a toluene-ethyl acetate mixture if you mix 1 mL of ethyl acetate and 1 mL of toluene. The density of ethyl acetate (C4H8O2) is 0.898 g/mL; the density of toluene (C7H8) is 0.867 g/mL.

The mole fraction of ethyl acetate in the mixture is 0.515 .

Volume of ethyl acetate = 1 mL

Density of ethyl acetate = 0.898 g/mL

Mass of ethyl acetate = 1 mL × 0.898 g/mL = 0.898 g

Molar mass of ethyl acetate = 88 g/mol

Number of moles of ethyl acetate =  0.898 g/88 g/mol = 0.01 moles

Volume of toluene = 1 mL

Density of toluene = 0.867 g/mL

Mass of toluene =  1 mL × 0.867 g/mL = 0.867 g

Molar mass of toluene = 92 g/mol

Number of moles of toluene = 0.867 g/ 92 g/mol = 0.0094 moles

Total number of moles =  0.01 moles + 0.0094 moles = 0.0194 moles

Mole fraction of ethyl acetate = 0.01 moles/0.0194 moles

= 0.515

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Mole fraction ethyl acetate → 0.52

Explanation:

Determine the solution's compound:

Solute: Ethyl-acetate (C₄H₈O₂), molar mass = 88 g/mol

Solvent: Toluene (C₇H₈), molar mass = 92 g/mol

We have density of each, so let's determine their masses:

Density = Mass / volume → Density . volume = Mass

0.898 g/mL . 1mL = 0.898 g of ethyl acetate

0.867 g/mL . 1mL = 0.867 g of tolue

We convert the mass to moles

0.898 g . 1 mol / 88 g = 0.0102 moles of ethyl acetate

0.867 g . 1mol / 92 g = 9.43×10⁻³ moles of tolulene

Mole fraction = Moles of x / Total moles

Mole fraction ethyl acetate = Moles of etyhyl acetate / Total moles

Total moles = 0.0102 + 9.43×10⁻³ = 0.01963

Mole fraction ethyl acetate = 0.0102  / 0.01963 → 0.52