Answer:
- Mole fraction of methanol: 0.5898
- Mole fraction of ethanol: 0.4102
Step-by-step explanation:
The mole fraction of a component is the ratio of the number 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 moles CH₄O = mass CH₄O / molar mass CH₄O
Molar mass CH₄O = 32.04 g/mol
Number of moles CH₄O = mass CH₄O / 32.04 g/mol
- Number of moles of C₂H₆O = mass of C₂H₆O / molar mass of C₂H₆O
Molar mass C₂H₆O = 46.07 g/mol
Number moles C₂H₆O = mass of C₂H₆O / 46.07 g/mol
Since both masses are equal, call them m.
- Number of moles CH₄O = m / 32.04
- Number of moles C₂H₆O = m / 46.07
- Total number of moles = m / 32.04 + m / 46.07
Mole 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] = 0.5898
Since, 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 = 0.4102
Those numbers are rounded to four significant figures.