Expressing Concentration of Solutions
We always discuss a solution being diluted or concentrated; this is a qualitative way of expressing the concentration of the solution. A dilute solution means the quantity of solute is relatively very small, and a concentrated solution implies that the solution has a large amount of solute. But these are relative terms and do not give us the quantitative concentration of the solution.
So, to quantitatively describe the concentrations of various solutions around us, we commonly express levels in the following way:

Mass percentage (w/w):
When the concentration is expressed as the percent of one component in the solution by mass it is called mass percentage (w/w). Suppose we have a solution containing component A as the solute and B as the solvent, then its mass percentage is expressed as:
Mass % of A = \( \frac {Mass \space of \space component \space A ~ in ~the ~ solution}{Total ~ mass ~of~ the~ solution } × 100 \)

Volume percentage (V/V):
Sometimes we express the concentration as a percent of one component in the solution by volume, it is then called as volume percentage and is given as:
volume % of A = \( \frac {Volume ~of~ component~ A~ in~ the ~solution}{Total ~ volume ~ of ~ the ~ solution } × 100 \)
For example, if a solution of NaCl in water is said to be 10 % by volume that means a 100 ml solution will contain 10 ml NaCl.

Mass by volume percentage (w/V):
This unit is majorly used in pharmaceutical industry. It is defined as the mass of a solute dissolved per 100mL of the solution.

Molarity (M):
One of the most commonly used methods for expressing the concentrations is molarity. It is the number of moles of solute dissolved in one litre of a solution. Suppose a solution of ethanol is marked 0.25 M, this means that in one litre of the given solution 0.25 moles of ethanol is dissolved.

Molality (m):
Molality represents the concentration regarding moles of solute and the mass of solvent. It is given by moles of solute dissolved per kg of the solvent. The molality formula is as given
\( Molality (m) = \frac {Moles~ of ~solute}{Mass~ of~ solvent~ in~ kg} \)

Mole Fraction:
If the solution has solvent and the solute, mole fraction gives a concentration as the ratio of moles of one component to the total moles present in the solution. It is denoted by x. Suppose we have a solution containing As a solute and B as the solvent. Let n_{A }and n_{B} be the number of moles of A and B present in the solution respectively. So mole fractions of A and B are given as:
\(~~~~~~~~~~~~~~~\)\( x_A = \frac {n_A}{n_A + n_B}\)
\(~~~~~~~~~~~~~~~\)\( x_B = \frac {n_B}{n_A + n_B} \)
The abovementioned methods are commonly used ways of expressing the concentration of solutions. All the methods describe the same thing that is, the concentration of a solution, each of them has their own advantages and disadvantages. Molarity depends on temperature while mole fraction and molality are independent of temperature. All these methods are used on the basis of requirement of expressing the concentrations.
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