Various ways to Express Concentration

The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solvent or solution.

A concentrated solution is one that has a relatively large amount of dissolved solute.

A dilute solution is one that has a relatively small amount of dissolved solute.

Percentage

Percentage concentration tells how much solute (the substance dissolved) is present in 100 parts of the total solution or mixture.

It can be expressed in three ways, depending on whether the solute and solvent are solids or liquids.

(a) % w/v — Weight by Volume Percentage

The number of grams of solute present in 100 milliliters of solution.

$\%w/v=\frac{\mathrm{weight of solute}\left(g\right)}{\mathrm{volume of solution}\left(\mathrm{mL}\right)}\times 100$

Example: 5% w/v NaCl solution: Means 5 g of NaCl dissolved in enough water to make 100 mL of solution.

(b) % w/w — Weight by Weight Percentage

The number of grams of solute present in 100 grams of total mixture (solution or semisolid).

$\%w/w=\frac{\mathrm{weight of solute}\left(g\right)}{\mathrm{weight of solution}\left(g\right)}\times 100$

Example: 2% w/w cream: Means 2 g of drug is mixed in 100 g of total cream.

(c) % v/v — Volume by Volume Percentage

The number of milliliters of solute present in 100 milliliters of solution.

$\%v/v=\frac{\mathrm{volume of solute}\left(\mathrm{mL}\right)}{\mathrm{volume of solution}\left(\mathrm{mL}\right)}\times 100$

Example: 70% v/v Alcohol → Means 70 mL of pure alcohol mixed with sufficient water to make 100 mL of total solution.

Molar Concentration

Molar concentration (or Molarity) is the number of moles of solute present in one liter of solution.

It shows how much of a substance (in moles) is dissolved in a given volume of solution. Molarity (M) is expressed as mol/L or simply M.

Example: 1 M NaCl means 1 mole of NaCl in 1 liter of solution.

$$M=\frac{\text{moles of solute}}{\text{volume of solution in liters}}$$

Because $$\text{Moles}=\frac{\text{Weight of solute}}{\text{Molecular weight}}$$

The formula can also be written as

$$M=\frac{\text{weight of solute (g)}}{\text{molecular weight × volume of solution (L)}}$$

ExamplePrepare a 1 M NaOH solution. Or How much NaOH to be dissolved in 1 litre to get 1 Molar solution.

Solution

we know that NaOH = Molecular weight = 40

Volume of solution = 1 liter

Solution to be prepared (Molarity M) = 1 M

So, put these values in the formula

$$M=\frac{\text{weight of solute (g)}}{\text{molecular weight × volume of solution (L)}}$$
$$1=\frac{\text{weight of solute (g)}}{\text{40 × 1 (L)}}$$

Weight of the solute (g) = 1 × 40 × 1 = 40 g

Thus to prepare a 1 M solution of NaOH, we have to dissolve 40 gm of NaOH in 1 litre of water.

Normality

Normality or Normal solution is the amount of gram equivalents of solute are present in 1 liter of solution.

$$\text{Normality (N)}=\frac{\text{Number of Gram Equivalents}}{\text{Volume of the Solution (in liters)}}$$

$$\text{Number of Gram Equivalents =}=\frac{\text{Weight of Solute (in gm)}}{\text{Equivalent Weight of Solute}}$$

Hence,
$$\text{Normality}=\frac{\text{Weight of Solute (in gm)}}{\text{(Equivalent Weight of Solute) × Volume of the Solution (in liters)}}$$

In case of Liquids: Volume can be change into Mass by the formula Volume = Mass X Density

$$\mathrm{Equivalent\; weight\; =}=\frac{\text{Molecular Weight}}{\text{n}}$$
n = number of H⁺ or OH⁻ ions (in acids/bases), or electrons gained/lost (in redox).

H₂SO₄ (sulfuric acid): It gives 2 H⁺ ions → n = 2

NaOH (sodium hydroxide): Gives 1 OH⁻ → n = 1

H₃PO₄ (phosphoric acid): Can donate 3 H⁺ → n = 3

Calculate Equivalent weight of H₂SO₄
Molecular weight of H₂SO₄ = 98

H₂SO₄ (sulfuric acid): It gives 2 H⁺ ions → n = 2

$$\mathrm{Equivalent\; weight\; of\; H₂SO₄}=\frac{\text{98}}{\text{2}}=\; 49$$ This value can be put in the formula of Normality to calculate concentration.

Molal Concentration

A molal solution is a solution in which the concentration of the solute is expressed in moles of solute per kilogram of solvent (not per litre of solution).

Molality depends only on the mass of the solvent, not on the total volume.

$$\mathrm{Molality\; (m)}=\frac{\text{Moles of Solute}}{\text{Mass of solvent in kilograms}}$$

Example

If 1 mole of NaCl is dissolved in 1 kg of water,

then the molality of the solution m = 1 / 1 = 1 mol/kg

Means the solution is 1 Molal = 1 m

Parts Per Million

PPM (Parts Per Million) is a unit used to express very low concentrations of a substance in a solution or mixture.

PPM (parts per million) means 1 part of solute per 1,000,000 parts of solution.

It shows how many parts of a substance are present in one million parts of the total mixture.

$$\text{PPM}=\frac{\text{Mass of solute}}{\text{Mass of solution}}\times {10}^6$$

Example If 5 mg of drug is present in 1 liter of solution, then calculate the concentration in ppm.

Solution Given: 5 mg of drug in 1 liter of solution

1 liter of water = 1000 ml ≈ 1000 g (or 1,000,000 mg)

so, 1 liter = 1,000,000 mg

as per the formula:

$$\text{PPM}=\frac{\text{Mass of solute (5 mg)}}{\text{Mass of solution (1,000,000 mg)}}\times {10}^6$$

$$\text{PPM}=\frac{\text{5}}{\text{1,000,000}}\times {\mathrm{1,000,000}}^{}=\; 5\; ppm$$