Question

A solution has 46%(w/w) ethyl alcohol in water.find mole fraction of ethyl alcohol

Answer 1

Given

A solution of ethyl alcohol in water having concentration 45% (w/w).

To Find

Mole fraction of ethyl alcohol.

Formula

• Strength by percentage weight = $\dfrac{\textsf{weight of solute}}{\textsf{weight of solution}} \times 100$

• In solution of A and B, mole fraction of A = $\dfrac{mol_A}{mol_A\:+\:mol_B}$

Solution

Let the weight of the solution be 100 gram.

Using the formula of strength by percentage weight :-

$\dfrac{\textsf{weight of solute}}{100} \times 100\:=\:46\\ \\ \\ =>\: \dfrac{\textsf{weight of solute}}{\cancel{100}} \times \cancel{100}\:=\:46 \\ \\ \\ => \textsf{Weight of solute = 46 gram} \\ \\ \\ => \: \textsf{Weight of solution = Weight of solvent - weight of solute}\\ \\ \\ => \textsf{Weight of solution = 100 - 46 = 54 gram }$

• Molar mass of water is 18 gram.

• Molar mass of ethyl alcohol is 46 gram.

Number of moles of ethyl alcohol =

$\dfrac{\textsf{Given weight}}{\textsf{Molar mass}} \\ \\ \\ => \: \dfrac{46}{46}\: = \:1$

Number of moles of water =

$\dfrac{\textsf{Given weight}}{\textsf{Molar mass}} \\ \\ \\ => \: \dfrac{\cancel{54}}{\cancel{18}}\: = \:3$

Thus, mole fraction of ethyl alchol =

$\dfrac{mol_{ethyl\:alcohol}}{mol_{ethyl\:alcohol}\:+\:mol_{water}}\\ \\ \\ = \dfrac{1}{1\:+\:3}\\ \\ \\ = \dfrac{1}{4}$

$\boxed{\boxed{\green{Thus,\:mole\:fraction\:of\:ethyl\:alcohol\:is\dfrac{1}{4}}}}$