Answer :
Answer: mole fraction of methanol = 0.590
mole fraction of ethanol = 0.410
Explanation:
We are given:
Equal masses of methanol [tex]CH_4O[/tex] and ethanol [tex]C_2H_6O[/tex] are mixed.
let the mass be x g.
Calculating the moles of methanol in the solution, by using the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}=\frac{xg}{32.04g/mol}[/tex]
Calculating the moles of ethanol in the solution, by using the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}=\frac{xg}{46.07g/mol}[/tex]
To calculate the mole fraction of methanol, we use the equation:
[tex]\chi_{methanol}=\frac{n_{methanol}}{n_{methaol}+n_{ethanol}}[/tex]
[tex]\chi_{methanol}=\frac{\frac{xg}{32.04g/mol}}{\frac{xg}{32.04g/mol}+\frac{xg}{46.07g/mol}}=0.590[/tex]
To calculate the mole fraction of ethanol, we use the equation:
[tex]\chi_{ethanol}=\frac{n_{ethanol}}{n_{methaol}+n_{ethanol}}[/tex]
[tex]\chi_{ethanol}=\frac{\frac{xg}{46.07g/mol}}{\frac{xg}{32.04g/mol}+\frac{xg}{46.07g/mol}}=0.410[/tex]
Thus mole fraction of methanol is 0.590 and mole fraction of ethanol 0.410 in three significant figures.