# Molarity And Mole Fraction

Majority of reactions happen in solutions and so it is important to understand how the amount of substance is expressed when it is present in the solution. There are many ways in which the amount of substances in solution is expressed:

### Molarity

It is one of the most widely used unit of concentration and is denoted by M. It is defined as no. of moles of solute present in 1 liter of solution. Thus,

$Molarity$ = $\frac{No.~of~moles~of~solute}{Volume~of~solution(in~Litres)}$

### Mass Per Cent or weight percent (w/w %)

It is the ratio of the mass of solute to the mass of solution multiplied by 100 to calculate mass percent. It is also known as weight percent and is represented by (w/w %). You may have seen this symbol on the back of medicines and tablets. It is one of the most commonly used units of representing concentration.

Mathematically,

Mass per cent = $\frac{Mass~of~solute}{Mass~of~solution}~\times~100$

### Molality

It is defined as moles of solute present in 1-kilogram of solvent. It is denoted by m.

Molality, $m$ = $\frac{No.~of~moles~of~solute}{Mass~ of ~solution(in~ kg)}$

### Mole Fraction

The mole fraction or molar fraction (xi) is defined as the amount of a constituent (expressed in moles), ni, divided by the total amount of all constituents in a mixture (also expressed in moles), ntot:

$x_i=\frac{n_i}{n_{tot}}$

The sum of all the mole fractions is equal to 1:

$\sum_{i=1}^{N}n_i=n_{tot};\sum_{i=1}^{N}x_i=1$

#### An indicative example of Molarity

Ques– How much water should be added to 1 liter of 1 M KOH solution to make it 0.2 M KOH solution?

Solution:

1M solution of KOH contains 1 mole of KOH in 1 liter of solution,

So, moles of KOH present in solution = 1 mole

Now we know,

Molarity = $\frac{No.~of~moles~of~solute}{Volume~of~solution(in~Litres)}$

$\Rightarrow~0.2$ = $\frac{1}{x}$

$\Rightarrow~X$ = $\frac{1}{0.2}$

$\Rightarrow~X$ = $5$

Hence if 1 mole of a solution is present in 5 litres of solution, then the molarity of solution will be 0.2 M.

So, extra 4 litres of water should be added to the 1 liter of 1 M KOH solution to make it 0.2 M KOH solution.