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Question: What is the mole fraction of methanol in a solution that contains \(6.0\) mol of methanol and \(3.0\...

What is the mole fraction of methanol in a solution that contains 6.06.0 mol of methanol and 3.03.0 mol of water? The formula for methanol is CH3OHC{{H}_{3}}OH.

Explanation

Solution

The calculation of mole fractions can be done using its definition as it says that the mole fraction of a product is the number of moles of that product divided by the total number of moles of that solution (solute+solventsolute+solvent).
Formula to be used:
Mole fraction can be calculated using the formula:
Mole  fraction  of  solute=moles of solutemoles of solute + moles of solventMole\; fraction\; of\; solute = \dfrac{moles~of\text{ }solute}{moles~of\text{ }solute\text{ }+~moles~of\text{ }solvent}

Complete answer: There are many ways for the indication of concentration of the solution and mole fraction is one of them. Basically, mole fraction is a kind of unit of concentration. The relative amount of solute and solvents in a solution are being measured by the mole fraction.
The general definition for mole fraction is, the number of moles of a specific component in the solution when divided by the total number of moles in the given solution gives the mole fraction.
Some advantages of mole fraction are:
Mole fraction is independent of the temperature. So basically it will not be affected by the temperature changes.
We do not require any information about the density of the phase to calculate the mole fraction.
In case if we have an ideal gas mixture then the mole fraction is given by the ratio of partial pressure to the total pressure of the given mixture.
According to the formula:
Moles  of  methanol  (solute)=6.0  molMoles\; of\; methanol \;(solute)= 6.0\;mol
Moles  of  water  (solvent)=3.0  molMoles\; of\; water\; (solvent)= 3.0\;mol
So, the mole fraction of methanol will be:
Mole  fraction  of  Methanol=moles of methanol(solute)moles of methanol(solute)+moles of water(solvent)Mole\;fraction\;of\;Methanol = \dfrac{moles\text{ }of\text{ }methanol\left( solute \right)}{moles\text{ }of\text{ }methanol\left( solute \right)+moles\text{ }of\text{ }water\left( solvent \right)}
Mole  fraction  of  Methanol=6.06.0+3.0Mole\; fraction\; of\; Methanol = \dfrac{6.0}{6.0+3.0} molmol\dfrac{mol}{mol}
Mole  fraction  of  Methanol=0.67Mole\; fraction\; of\; Methanol = 0.67

Note:
-For a given mixture the sum of all the mole fractions will always equal to one.
-If we multiply the mole fraction by hundred, it will give the mole percentage.
-Mole fraction does not have a unit. It is also dimensionless.