Concentrations of Solutions

What is a Solution?

A solution is a homogeneous mixture where one substance (solute) is dissolved in another (solvent). The concentration of a solution refers to how much solute is present in a given volume of the solvent.

• Concentrated solution: Large amount of solute relative to the solvent.
• Dilute solution: Small amount of solute relative to the solvent.

Ways to Express Concentration

Concentration can be expressed in several units depending on the context:

Molarity ($mol\ L^{-1}$)

Molarity (M) measures the number of moles of solute per litre of solution.

$$\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution (L)}}$$

Grams per litre ($g\ L^{-1}$)

This measures the mass of solute in grams per litre of solution.

$$\text{Concentration (g L\(^{-1}\))} = \frac{\text{Mass of solute (g)}}{\text{Volume of solution (L)}}$$

Percentage Concentration

• % (w/v): Grams of solute per 100 mL of solution.
• % (v/v): Volume of solute per 100 mL of solution.
• % (w/w): Grams of solute per 100 g of solution.

Calculations of Molarity from Grams per Litre

You can calculate molarity from the concentration in g/L by converting grams to moles using the molar mass of the solute.

$$\text{Molarity} = \frac{\text{Concentration (g L\(^{-1}\))}}{\text{Molar mass (g mol\(^{-1}\))}}$$

Calculating Moles from Molarity and Volume

You can calculate the number of moles in a solution using molarity and volume:

$$\text{Moles of solute} = \text{Molarity} \times \text{Volume (L)}$$

Percentage Concentration Calculations

To calculate percentage concentrations:

% (w/v)

$$\text{Concentration} = \frac{\text{Mass of solute (g)}}{\text{Volume of solution (mL)}} \times 100$$

% (v/v)

$$\text{Concentration} = \frac{\text{Volume of solute (mL)}}{\text{Volume of solution (mL)}} \times 100$$

Dilution Calculations

When diluting a solution, the number of moles of solute remains the same before and after dilution. The relationship is given by:

$$C_1V_1 = C_2V_2$$

Where:

• $C_1$ and $C_2$ are the initial and final concentrations.
• $V_1$ and $V_2$ are the initial and final volumes.

Colour Intensity and Concentration

In many solutions, the colour intensity is related to concentration. This is due to Beer-Lambert Law, which states that absorbance (colour intensity) is proportional to concentration. As the concentration increases, so does the intensity of the colour.

Primary Standards and Standard Solutions

• A primary standard is a substance that is extremely pure, stable, and has a known concentration. It is used to prepare standard solutions.
• Standard solutions are solutions with a precisely known concentration, used in titrations to determine unknown concentrations.