Diffusion

1. Overview

Diffusion is the process by which particles spread out and mix with each other without being stirred. It provides essential evidence for the kinetic particle theory, demonstrating that particles in liquids and gases are in constant, random motion. Understanding diffusion is vital for explaining how substances move in biological systems and industrial chemical processes.

---

Key Definitions

• Diffusion: The net movement of particles from a region of their higher concentration to a region of their lower concentration down a concentration gradient, as a result of their random movement.
• Kinetic Particle Theory: The theory that all matter is made up of very small particles (atoms, molecules, or ions) that are in constant motion.
• Concentration Gradient: The difference in the concentration of a substance between two regions.
• Relative Molecular Mass ($M_r$): The average mass of a molecule relative to one-twelfth of the mass of an atom of carbon-12.

---

Core Content

Diffusion and Kinetic Particle Theory

• Random Motion: Particles in liquids and gases move randomly. They collide with each other and the walls of their container, causing them to spread out.
• Concentration: Particles move from where there are many of them (high concentration) to where there are fewer (low concentration) until they are evenly distributed.
• States of Matter:
  • Gases: Diffusion is rapid because particles are far apart and move at high speeds.
  • Liquids: Diffusion is much slower because particles are closer together and have more frequent collisions, which impedes their movement.
  • Solids: Diffusion does not occur in solids because particles are held in fixed positions and can only vibrate.

Factors Affecting the Rate of Diffusion

1. Temperature: As temperature increases, particles gain more kinetic energy and move faster. This leads to an increased rate of diffusion.
2. State of Matter: Gases diffuse faster than liquids due to higher particle speeds and more space between particles.

---

Extended Content (Extended Only)

The Effect of Relative Molecular Mass ($M_r$)

The rate at which a gas diffuses is dependent on its Relative Molecular Mass ($M_r$).

• Lighter particles (lower $M_r$) move faster and diffuse more quickly than heavier particles (higher $M_r$) at the same temperature.

Worked Example: The Ammonia and Hydrogen Chloride Experiment

In this classic experiment, cotton wool soaked in aqueous ammonia and cotton wool soaked in concentrated hydrochloric acid are placed at opposite ends of a glass tube.

The Reaction:

• Word Equation: ammonia + hydrogen chloride → ammonium chloride
• Symbol Equation: $NH_3(g) + HCl(g) \rightarrow NH_4Cl(s)$

Calculating $M_r$:

• $M_r$ of $NH_3$: $14 + (1 \times 3) = 17$
• $M_r$ of $HCl$: $1 + 35.5 = 36.5$

Observation and Explanation:

• A white ring of solid ammonium chloride ($NH_4Cl$) forms inside the tube.
• The ring forms closer to the hydrochloric acid end.
• Reasoning: Because $NH_3$ has a lower $M_r$ (17) than $HCl$ (36.5), the ammonia particles move faster and travel a further distance in the same amount of time.

---

Key Equations

• Relative Molecular Mass ($M_r$): $M_r = \text{Sum of all Relative Atomic Masses } (A_r) \text{ in a molecule}$
• Relationship between Mass and Rate: $\text{Lower } M_r = \text{Faster Diffusion Rate}$ $\text{Higher } M_r = \text{Slower Diffusion Rate}$

---

Common Mistakes to Avoid

• ❌ Wrong: Saying diffusion happens because the particles "want" to fill the space.
• ✓ Right: Diffusion happens due to the random motion of particles.
• ❌ Wrong: Forgetting to include state symbols in the $NH_4Cl$ reaction.
• ✓ Right: Always write $NH_4Cl(s)$, as the white "smoke" is actually tiny particles of solid.
• ❌ Wrong: Claiming that diffusion occurs in solids.
• ✓ Right: Diffusion only occurs in liquids and gases (fluids).
• ❌ Wrong: Thinking heavier molecules diffuse faster because they have more "force."
• ✓ Right: Heavier molecules move more slowly and therefore diffuse more slowly.

---

Exam Tips

• Command Word - "Explain": When asked to explain diffusion, you must mention random motion and movement from high to low concentration.
• Command Word - "State": If asked to state the effect of mass, a simple "The higher the mass, the slower the rate" is sufficient.
• Common Contexts: Look out for questions involving smells (perfume/cooking) or the movement of colored gases ($Br_2$ or $NO_2$) and liquids (ink in water or $KMnO_4$ crystals).
• Calculation Practice: Be prepared to calculate $M_r$ values using the Periodic Table provided in the exam to justify why one gas diffuses faster than another. Common $M_r$ values to recognize include $NH_3$ (17) and $HCl$ (36.5).
• Numerical Values: Be familiar with temperatures used in these experiments (e.g., room temperature is approx. 20-25°C or 293-298K).

---

Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0620 Theory papers.

Exam-Style Question 1 — Short Answer [6 marks]

Question:

A student places a crystal of potassium manganate(VII) at the bottom of a beaker filled with distilled water. After several hours, the purple colour of the potassium manganate(VII) spreads throughout the water.

(a) Define the term diffusion. [2]

(b) Explain why the purple colour spreads throughout the water. Use the kinetic particle theory in your answer. [3]

(c) State one way to increase the rate of diffusion in this experiment. [1]

Worked Solution:

(a)

1. Diffusion is the spreading of particles from an area of high concentration to an area of low concentration. This is the core definition.
2. ...due to their random motion. Completes the definition.

How to earn full marks:

• Mention both movement from high to low concentration AND random motion.

(b)

1. The potassium manganate(VII) crystal dissolves in the water. Initial dissolving is important.
2. Potassium manganate(VII) particles move randomly due to their kinetic energy. Explaining the movement.
3. The potassium manganate(VII) particles collide with water particles and spread throughout the beaker until evenly distributed. Explaining the spreading and even distribution.

How to earn full marks:

• Mention dissolving, random motion, and spreading/collisions for full marks.

(c)

1. Increase the temperature of the water.

How to earn full marks:

• State increasing temperature.
• Do not state "stirring" as stirring is not diffusion.

Common Pitfall: Make sure you include both parts of the definition of diffusion: movement from high to low concentration AND random motion. Also, remember that stirring the solution is NOT diffusion; it's a different process.

Exam-Style Question 2 — Short Answer [5 marks]

Question:

Ammonia gas ($NH_3$) and hydrogen chloride gas ($HCl$) are released simultaneously at opposite ends of a glass tube. A white ring of ammonium chloride ($NH_4Cl$) forms inside the tube closer to the end where the hydrogen chloride gas was released.

(a) Write down the formula to calculate relative molecular mass, $M_r$. [1]

(b) Calculate the $M_r$ of ammonia and hydrogen chloride. [2] [Relative atomic masses: H = 1, N = 14, Cl = 35.5]

(c) Explain why the white ring forms closer to the hydrogen chloride end of the tube. [2]

Worked Solution:

(a)

1. $M_r$ = sum of the relative atomic masses of all the atoms in the molecule. Definition of relative molecular mass.

How to earn full marks:

• State the correct definition including a sum of the Ar values.

(b)

1. $M_r$ of $NH_3$ = 14 + (3 x 1) = 17 Correct calculation of ammonia's Mr.
2. $M_r$ of $HCl$ = 1 + 35.5 = 36.5 Correct calculation of hydrogen chloride's Mr.

How to earn full marks:

• 1 mark for each correct calculation.
• Correct Ar values used.
• Correct Mr values calculated.
• No units required.

(c)

1. Ammonia has a lower $M_r$ than hydrogen chloride. Identifying the difference in Mr.
2. Therefore, ammonia diffuses faster than hydrogen chloride, so the white ring forms closer to the hydrogen chloride end. Linking Mr and diffusion rate.

How to earn full marks:

• Mention that ammonia has lower Mr AND diffuses faster.

Common Pitfall: Remember that gases with lower relative molecular mass diffuse faster. Don't just state that the gases have different Mr values; you need to specify which one is lower and how that affects its diffusion rate.

Exam-Style Question 3 — Extended Response [8 marks]

Question:

A student investigates the diffusion of bromine gas in air. A gas jar of bromine gas and a gas jar of air are connected as shown in the diagram.

(a) State what is observed when the glass plate is removed. [1]

(b) Explain, in terms of the kinetic particle theory, why the bromine gas diffuses into the air. [4]

(c) The student repeats the experiment at a higher temperature. Suggest how the rate of diffusion changes. Explain your answer. [3]

Worked Solution:

(a)

1. The brown bromine gas will spread upwards into the gas jar of air. Describing the observation.

How to earn full marks:

• Mention that the bromine spreads into the air.
• Mention the colour of bromine.

(b)

1. Bromine particles and air particles are in constant, random motion. Stating the motion of particles.
2. Bromine particles collide with air particles. Mentioning collisions.
3. Bromine particles move from an area of high concentration (the bromine gas jar) to an area of low concentration (the air gas jar). Mentioning the concentration gradient.
4. Eventually, the bromine gas and air mixture becomes evenly distributed. Describing the final state.

How to earn full marks:

• Constant random motion, collisions, movement from high to low concentration, and even distribution all needed for full marks.

(c)

1. The rate of diffusion increases. State the change in rate.
2. At a higher temperature, the bromine and air particles have more kinetic energy. Linking temperature to kinetic energy.
3. This means they move faster and collide more frequently, so the bromine gas diffuses faster. Linking kinetic energy to speed and collisions.

How to earn full marks:

• Mention that the rate increases, particles have more kinetic energy, and move faster/collide more.

Common Pitfall: Be sure to link the increase in temperature directly to an increase in kinetic energy of the particles. Then, explain how this increased kinetic energy leads to faster movement and more frequent collisions, resulting in a higher rate of diffusion.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

A student carries out an experiment to investigate the effect of relative molecular mass ($M_r$) on the rate of diffusion. The student sets up the following apparatus in a fume cupboard.

When the cotton wool plugs are put in place, the ammonia and hydrochloric acid react in the tube to form a white ring of ammonium chloride.

(a) Write the balanced chemical equation for the reaction between ammonia ($NH_3$) and hydrochloric acid ($HCl$). [2]

(b) Explain why the experiment should be carried out in a fume cupboard. [2]

(c) After 10 minutes, the white ring forms 28.0 cm from the hydrochloric acid end of the tube. The total length of the tube is 50.0 cm.

(i) Calculate the distance the ammonia has diffused. [1]

(ii) Calculate the ratio of the distance diffused by ammonia to the distance diffused by hydrogen chloride. [2]

(d) The $M_r$ of ammonia is 17 and the $M_r$ of hydrogen chloride is 36.5. Explain how the results of the experiment support the kinetic particle theory regarding the effect of $M_r$ on the rate of diffusion. [2]

Worked Solution:

(a)

1. $NH_3(g) + HCl(g) \rightarrow NH_4Cl(s)$ Correct reactants and products.
2. Balanced equation. Correct balancing.

How to earn full marks:

• Correct formula for all substances AND balanced equation.
• State symbols are not required.

(b)

1. Ammonia and hydrogen chloride are corrosive/irritant/toxic gases. Identifying the hazard.
2. The fume cupboard removes these gases, preventing them from being inhaled or causing harm. Explaining the safety precaution.

How to earn full marks:

• Identify the hazard AND explain why a fume cupboard is necessary.

(c) (i)

1. Distance diffused by $NH_3$ = 50.0 cm - 28.0 cm = 22.0 cm Subtracting the known distance from the total distance. $\boxed{22.0 \text{ cm}}$

How to earn full marks:

• Correct subtraction.
• Correct answer with correct units.

(ii)

1. Distance of $HCl$ = 28.0 cm Stating the distance diffused by HCl.
2. Ratio = Distance of $NH_3$ / Distance of $HCl$ = 22.0 cm / 28.0 cm = 0.79 Dividing the distances.
3. Ratio is 0.79:1 Expressing the ratio in the correct form. $\boxed{0.79:1}$

How to earn full marks:

• Correct division of distances.
• Correct ratio.

(d)

1. Ammonia has a smaller $M_r$ than hydrogen chloride. Identifying the difference in Mr.
2. Ammonia diffuses a greater distance than hydrogen chloride in the same time, showing that gases with a lower $M_r$ diffuse faster. Linking Mr, distance, and diffusion rate.

How to earn full marks:

• Mention the difference in Mr AND link the distance diffused to the rate of diffusion.

Common Pitfall: When calculating the ratio, make sure you divide the distances in the correct order (ammonia distance / HCl distance). Also, remember to relate the distances diffused back to the relative molecular masses of the gases to explain the observed result.