What is a Solution?

A solution is a homogeneous mixture of a solute (the substance dissolved) in a solvent (the substance doing the dissolving). In chemistry, the most common solvent is water, making aqueous solutions.

Solute

The substance being dissolved. Usually present in a smaller amount (e.g. NaCl in saltwater).

Solvent

The substance that dissolves the solute. Usually present in greater amount (e.g. water).

Concentration

The amount of solute per unit volume of solution. Commonly expressed as mol/L (molarity, M).

Formula: Concentration (c) = moles of solute (n) ÷ volume of solution in litres (V). Written as c = n / V or n = c × V.

Molarity and Calculations

Molarity (M) is the most common unit of concentration in chemistry. It is defined as the number of moles of solute per litre of solution. To perform calculations, you also need the formula: n = m / M_r (moles = mass ÷ molar mass).

The Concentration Triangle

n

(moles)

c

(mol/L)

V

(litres)

n = c × V | c = n / V | V = n / c

Unit check: Always convert volume to litres before using the formula. 250 mL = 0.250 L. Also ensure mass is in grams for calculating moles with molar mass (g/mol).

Dilution and Standard Solutions

Dilution involves adding more solvent to reduce the concentration of a solution. The number of moles of solute remains constant. The dilution equation is: c₁V₁ = c₂V₂.

Preparing a Standard Solution

1. Calculate

Determine the mass of solute needed using n = c × V and m = n × M_r

↓

2. Weigh

Weigh the solute accurately on an electronic balance

↓

3. Dissolve

Dissolve in a beaker with a small amount of distilled water; stir

↓

4. Transfer and Fill

Pour into a volumetric flask; rinse beaker; fill to the calibration line with distilled water

Solubility

Solubility is the maximum amount of solute that dissolves in a given volume of solvent at a specific temperature. A solution at its maximum is saturated. Solubility of most solids in water increases with temperature, while solubility of gases in water decreases with temperature.

Key Vocabulary

Molarity (M)

The concentration of a solution measured in moles of solute per litre of solution (mol/L or mol L^-1).

Standard Solution

A solution of precisely known concentration, prepared by dissolving an accurately weighed amount of solute in a volumetric flask.

Dilution

The process of reducing a solution's concentration by adding more solvent, while keeping the amount of solute constant.

Saturated Solution

A solution containing the maximum amount of dissolved solute at a given temperature. No more solute can dissolve.

Worked Examples

1

What is the concentration of a solution containing 0.50 mol of NaCl dissolved in 250 mL of solution?

Step 1: Convert volume: 250 mL = 0.250 L.

Step 2: Apply c = n / V = 0.50 / 0.250.

Answer: c = 2.0 mol/L (2.0 M).

2

What mass of NaOH (M_r = 40.0 g/mol) is needed to prepare 500 mL of a 0.10 M solution?

Step 1: Find moles: n = c × V = 0.10 × 0.500 = 0.050 mol.

Step 2: Find mass: m = n × M_r = 0.050 × 40.0.

Answer: m = 2.0 g of NaOH.

3

25.0 mL of 2.0 M HCl is diluted to 500 mL. What is the new concentration?

Step 1: Use c₁V₁ = c₂V₂. Substitute: 2.0 × 0.0250 = c₂ × 0.500.

Step 2: 0.050 = c₂ × 0.500.

Answer: c₂ = 0.050 / 0.500 = 0.10 M.

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

What is the concentration (in mol/L) of a solution with 0.20 mol of solute in 500 mL?

0.10 M 0.20 M 2.5 M 0.40 M

Question 2

In the dilution equation c₁V₁ = c₂V₂, what quantity stays constant?

Moles of solute Volume Concentration Temperature

Question 3

A volumetric flask is used when preparing a standard solution because it:

Heats the solution evenly Measures volume very accurately Weighs the solute precisely Filters impurities

Question 4

How many moles of KOH are in 2.0 L of a 0.50 M solution?

0.25 mol 4.0 mol 1.0 mol 0.50 mol

Question 5

As temperature increases, the solubility of most solid solutes in water:

Decreases First increases then decreases Stays the same Increases

Solutions and Concentration

What is a Solution?

Solute

Solvent

Concentration

Molarity and Calculations

The Concentration Triangle

Dilution and Standard Solutions

Preparing a Standard Solution

Solubility

Key Vocabulary

Molarity (M)

Standard Solution

Dilution

Saturated Solution

Worked Examples

What is the concentration of a solution containing 0.50 mol of NaCl dissolved in 250 mL of solution?

What mass of NaOH (M_r = 40.0 g/mol) is needed to prepare 500 mL of a 0.10 M solution?

25.0 mL of 2.0 M HCl is diluted to 500 mL. What is the new concentration?

Knowledge Check

Key Concepts Summary

Solutions and Concentration

What is a Solution?

Solute

Solvent

Concentration

Molarity and Calculations

The Concentration Triangle

Dilution and Standard Solutions

Preparing a Standard Solution

Solubility

Key Vocabulary

Molarity (M)

Standard Solution

Dilution

Saturated Solution

Worked Examples

What is the concentration of a solution containing 0.50 mol of NaCl dissolved in 250 mL of solution?

What mass of NaOH (Mr = 40.0 g/mol) is needed to prepare 500 mL of a 0.10 M solution?

25.0 mL of 2.0 M HCl is diluted to 500 mL. What is the new concentration?

Knowledge Check

Key Concepts Summary

What mass of NaOH (M_r = 40.0 g/mol) is needed to prepare 500 mL of a 0.10 M solution?