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A solution is made by mixing equal masses of methanol, CH4O, and ethanol, C2H6O. Determine the mole fraction of each component to at least three significant figures. Xmeth=_____? Xeth= ______?
A solution is made by mixing equal masses of methanol, CH4O, and ethanol, C2H6O. Determine the mole fraction of each component to at least three significant figures. Xmeth=_____? Xeth= ______?
Answer:Mole fraction of methanol: 0.5898Mole fraction of ethanol: 0.4102Explanation:Themole fractionof a component is the ratio of thenumber of moles of the component to the total number of moles of the solution.X of component A = number of moles of component A / number of moles of all components.Now, the number of moles of each component is determined from its molar mass as:Number of moles = mass in grams / molar mass.Thus, you can write:Number of molesCH₄O= mass CH₄O / molar mass CH₄OMolar mass CH₄O = 32.04 g/molNumber of moles CH₄O = mass CH₄O / 32.04 g/molNumber of moles ofC₂H₆O= mass of C₂H₆O / molar mass of C₂H₆OMolar mass C₂H₆O = 46.07 g/molNumber moles C₂H₆O = mass of C₂H₆O / 46.07 g/molSince both masses are equal, call them m.Number of moles CH₄O = m / 32.04Number of moles C₂H₆O = m / 46.07Total number of moles = m / 32.04 + m / 46.07Mole fraction of CH₄O= [ m / 32.04 ] / [ m / 32.04 + m / 46.07]m is common factor of the numerator and the denominator, so they cancel out, and you get:[ 1 / 32.04] / [1 / 32.04 + 1 /46.07] = 0.5898Since, the sum of the mole fractions of all the components is 1 and there are only two components:Mole fraction of C₂H₆O= 1 - 0.5898 = 0.4102Those numbers are rounded tofour significant figures....