 # Expression of 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:

## Concentration

It is the amount of solute present in one liter of solution. It is denoted by C or S.

$C or S = \frac{Weight\ of\ solute\ in\ grams}{Volume\ in\ liters}$

## Recommended Videos ## 1. Concentration in Parts Per Million (ppm)

The parts of a component per million parts (106) of the solution.

$ppm(A) = \frac{Mass\ of\ A}{Total\ mass\ of\ the\ solution}\times {10}^6$

## 2. 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 = $\frac {Mass \space of \space component \space A ~ in ~the ~ solution}{Total ~ mass ~of~ the~ solution } × 100$

## 3. 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.

## 4. Mass by Volume Percentage (w/V):

This unit is majorly used in the pharmaceutical industry. It is defined as the mass of a solute dissolved per 100mL of the solution.

## 5. 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.

## 6. 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 solventThe molality formula is as given-

$Molality (m) = \frac {Moles~ of ~solute}{Mass~ of~ solvent~ in~ kg}$

## 7. Normality

It is the number of gram equivalents of solute present in one liter of the solution and it is denoted by N.

$N = \frac{Weight\ of\ solute\ in\ grams}{Equivalent\ mass \times Volume\ in\ liter}$

The relation between normality and molarity.

• N x Eq.Wt = Molarity x Molar mass
• N = Molarity x Valency
• N = Molarity x Number of H+ or OH– ion.

## 8. Formality

It is the number of gram formula present in one litre of solution. It is denoted by F.

$F = \frac{Weight\ of\ solute\ in\ gram}{Formula\ wt \times Volume\ in\ liter}$

It is applicable in the case of ionic solids like NaCl.

## 9. Mole Fraction:

If the solution has a solvent and the solute, a 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 nA and nB 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 above-mentioned 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 its 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 the requirement of expressing the concentrations.

## Solutions of Solids in Liquids

1. A saturated solution is a solution that remains in contact with an excess of solute.
2. The amount of solute dissolved per 100g of solvent in a saturated solution at a specific temperature represents the solubility of the solute.
3. For exothermic substances such as KOH, CaO, Ca(OH)2, M2CO3, M2SO4, etc, solubility is inversely proportional to temperature.
4. For endothermic substances such as NaCl, KNO3, NaNO3, glucose, etc., solubility is directly proportional to temperature.

## Solubility of Gases

The solubility of gases is mostly expressed in terms of the absorption coefficient,k that is the volume of the gas dissolved by unit volume of solvent at 1 atm pressure and a specific temperature.

The solubility of a gas in a liquid depends upon

1. Temperature solubility is inversely proportional to temperature as the dissolution of gas is exothermic in most cases.
2. Nature of gas – Gases having a higher value of van der Waals force of attraction that is gases that are more easily liquefied are more soluble. For example, SO2 and CO2 are more soluble in water than O2, N2, and H2.
3. Nature of solvent – Gases which can ionize in aqueous solution are more stable in water as compared to the other solvents.

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