Expressing Concentration of Solutions

 

📘 Expressing Concentration of Solutions

The composition of a solution refers to the relative amount of solute and solvent present in it. This composition can be expressed in two main ways:

• Qualitatively

• Quantitatively

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🔹 Qualitative Description

This is a non-numerical way of expressing the concentration. For example:

• A dilute solution has a relatively small amount of solute.

• A concentrated solution has a relatively large amount of solute.

However, qualitative terms are vague and can lead to confusion, especially in scientific or industrial applications. Hence, quantitative expressions of concentration are preferred.

🔹 Quantitative Description

Several methods are used to express the concentration of a solution quantitatively:

(i) Mass Percentage (% w/w)

Definition:

$$\text{Mass \% of a component} = \left( \frac{\text{Mass of the component in the solution}}{\text{Total mass of the solution}} \right) \times 100$$

Example:
A solution of 10% glucose by mass means:

• 10 g of glucose (solute)

• 90 g of water (solvent)
  Total mass = 100 g

Application:
Mass percentage is commonly used in industrial applications.
E.g., Commercial bleaching solution contains 3.62% NaOCl (sodium hypochlorite) by mass.

(ii) Volume Percentage (% v/v)

Definition:

$$\text{Volume \% of a component} = \left( \frac{\text{Volume of the component}}{\text{Total volume of the solution}} \right) \times 100$$

Example:
A 10% ethanol solution by volume means:

• 10 mL ethanol

• Water added to make the total volume = 100 mL

Application:
Used for liquid–liquid solutions like:

• Antifreeze: A 35% (v/v) ethylene glycol solution lowers the freezing point of water to 255.4 K (-17.6°C).

(iii) Mass by Volume Percentage (% w/v)

Definition:

$$\text{Mass by Volume \%} = \left( \frac{\text{Mass of solute in grams}}{\text{Volume of solution in mL}} \right) \times 100$$

Application:
Commonly used in medicine and pharmacy.
E.g., A 5% w/v solution means 5 g of solute in 100 mL of solution.

(iv) Parts per Million (ppm)

Definition:

$$\text{ppm} = \left( \frac{\text{Number of parts of the component}}{\text{Total number of parts of all components}} \right) \times 10^6$$

Application:
Used for very low concentrations (trace quantities), especially in:

• Environmental chemistry

• Pollution analysis
  E.g., Sea water (1030 g) contains 6 × 10⁻³ g of dissolved O₂

$$\text{ppm} = \frac{6 \times 10^{-3}}{1030} \times 10^6 \approx 5.8\ ppm$$

Variants: ppm can be:

• mass to mass

• volume to volume

• mass to volume

(v) Mole Fraction (χ)

Definition:

$$\chi_i = \frac{n_i}{\sum n_i}$$

Where:

• $n_i$ = number of moles of component i

• $\sum n_i$ = total moles of all components

In a binary mixture of components A and B:

$$\chi_A = \frac{n_A}{n_A + n_B}, \quad \chi_B = \frac{n_B}{n_A + n_B}$$ $$\chi_A + \chi_B = 1$$

Application:
Useful in calculating vapor pressure, colligative properties, and gas mixture compositions.

(vi) Molarity (M)

Definition:

$$\text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in litre}}$$

Example:
0.25 M NaOH means 0.25 mol of NaOH is dissolved in 1 litre of solution.

Note:
Temperature-dependent because volume changes with temperature.

(vii) Molality (m)

Definition:

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

Example:
A 1.00 m solution of KCl means 1 mol (74.5 g) of KCl is dissolved in 1 kg of water.

Note:
Independent of temperature because it involves mass, not volume.

📝 Summary Table

Expression	Symbol	Formula	Depends on Temperature?	Typical Use
Mass % (w/w)	—	$\frac{\text{Mass of solute}}{\text{Total mass of solution}} \times 100$	❌ No	Industrial mixtures
Volume % (v/v)	—	$\frac{\text{Volume of solute}}{\text{Total volume of solution}} \times 100$	✅ Yes	Liquid-liquid solutions
Mass/Volume % (w/v)	—	$\frac{\text{Mass of solute}}{\text{Volume of solution in mL}} \times 100$	✅ Yes	Medical & pharmaceutical use
Parts per million (ppm)		$\frac{\text{Part of solute}}{\text{Total parts of solution}} \times 10^6$	❌ No	Environmental concentrations
Mole fraction	$\chi$	$\frac{\text{Moles of component}}{\text{Total moles of solution}}$	❌ No	Gas mixtures, vapor pressure
Molarity	M	$\frac{\text{Moles of solute}}{\text{Volume of solution in litres}}$	✅ Yes	Titrations, lab solutions
Molality	m	$\frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}$	❌ No	Colligative property calculations

🔍 Conclusion

• Each unit has its specific application depending on the accuracy, temperature dependence, and nature of the solution.

• Mass %, ppm, mole fraction, and molality are independent of temperature, making them more reliable in changing environments.

• Molarity, while commonly used, must be handled carefully with temperature-sensitive systems.