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
Pick a number, any number, for grams methanol and ethanol. I would use a convenient number like 10 g or 20 g.
Then mols methanol = g/molar mass
moles ethanol = g/molar mass
Xmethanol = moles methanol/total mols.
Xethanol = moles ethanol/total mols.
To determine the mole fraction of each component, we need to know the moles of both methanol (CH4O) and ethanol (C2H6O). From there, we can calculate the mole fraction.
First, let's start by calculating the moles of each component. To do this, we need to know the molar masses of methanol and ethanol.
The molar mass of methanol (CH4O) can be calculated by summing the atomic masses of its constituents:
- The atomic mass of carbon (C) is 12.01 grams/mole
- The atomic mass of hydrogen (H) is 1.01 grams/mole
- The atomic mass of oxygen (O) is 16.00 grams/mole
Molar mass of methanol (CH4O) = (1 × 12.01) + (4 × 1.01) + 16.00 = 32.04 grams/mole
Since we have equal masses of methanol and ethanol, we can assume that the mass of ethanol is also 32.04 grams.
Next, we need to convert the masses of both methanol and ethanol to moles. To do this, we use the molar mass.
Number of moles of methanol = mass of methanol / molar mass of methanol = 32.04 g / 32.04 g/mol = 1 mol
Number of moles of ethanol = mass of ethanol / molar mass of ethanol = 32.04 g / 46.07 g/mol = 0.695 mol (rounded to three significant figures)
Now that we have the moles of each component, we can calculate the mole fraction.
Mole fraction of methanol (CH4O) = moles of methanol / total moles
Mole fraction of methanol = 1 mol / (1 mol + 0.695 mol) ≈ 0.572
Mole fraction of ethanol (C2H6O) = moles of ethanol / total moles
Mole fraction of ethanol = 0.695 mol / (1 mol + 0.695 mol) ≈ 0.428
Therefore, the mole fraction of methanol is approximately 0.572, and the mole fraction of ethanol is approximately 0.428.