Q.(a) Explain the following phenomena with the help of Henry's law.

Concept: Henry’s Law — the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid ($p = K_H \cdot x$).

(a) (i) Bends: When a diver ascends quickly, the external pressure drops sharply. The dissolved nitrogen (highly soluble at high underwater pressure) comes out of solution rapidly, forming gas bubbles in the blood and tissues. These bubbles block capillaries, causing severe joint pain — the bends.

(ii) High-altitude weakness: At high altitude, atmospheric pressure is low. The partial pressure of oxygen is reduced, so less oxygen dissolves in the blood. This leads to hypoxia — weakness, breathlessness, and discomfort. …

The Core Idea: Henry’s Law

Henry’s law is simple but powerful: at a constant temperature, the amount of gas that dissolves in a liquid is proportional to the pressure of that gas above the liquid. Mathematically:

What this means physically: if you increase the pressure above a liquid, more gas gets forced into solution. If you suddenly drop the pressure, the dissolved gas comes rushing out — like bubbles in a soda bottle. This same principle explains all three phenomena below.

(a)(i) The Bends (Decompression Sickness)

1. What happens underwater: When a diver descends, the pressure of water increases. To breathe, the diver inhales compressed air (mostly nitrogen and oxygen) at high pressure. According to Henry’s law, the high partial pressure of nitrogen in the lungs forces more nitrogen to dissolve into the blood and body tissues.

2. The danger during ascent: If the diver rises too quickly, the external pressure drops rapidly. The solubility of nitrogen in blood decreases sharply — the gas can no longer stay dissolved. Nitrogen comes out of solution as tiny bubbles in the bloodstream and joints.

3. The painful result: These gas bubbles block blood vessels, cause severe joint pain (the “bends”), and can damage nerves or organs. It’s exactly like opening a fizzy drink too fast — except the “fizz” is inside your body.

(a)(ii) High-Altitude Breathing Difficulty

1. The pressure drop: At high altitudes (mountains, aircraft), the atmospheric pressure is much lower than at sea level. The partial pressure of oxygen in the air is correspondingly reduced.

2. Henry’s law in the lungs: Oxygen dissolves into the blood in the alveoli (air sacs of the lungs). The amount that dissolves is proportional to its partial pressure in the inhaled air. At high altitude, the partial pressure of oxygen is low, so less oxygen enters the bloodstream.

3. The feeling of weakness: The blood carries less oxygen to tissues, causing hypoxia — a shortage of oxygen at the cellular level. This leads to breathlessness, weakness, dizziness, and fatigue. It’s not that the air has less oxygen percentage-wise (it’s still ~21%), but the pressure is lower, so Henry’s law says less dissolves. …

Henry's Law — Concept & Application

Henry's Law states:

At constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.

Mathematically:

where

• $p$ = partial pressure of the gas
• $K_H$ = Henry's constant (depends on gas & temperature)
• $x$ = mole fraction of the gas in the solution

Key idea: More pressure → more gas dissolves. Less pressure → gas escapes.

(a) Explanation of Phenomena using Henry's Law

(i) Painful condition known as bends (decompression sickness)

Method: Apply Henry's Law to gas solubility under pressure changes.

Steps:

1. Deep-sea divers breathe compressed air at high pressure.
   • High pressure → large amount of nitrogen ($N_2$) dissolves in blood and tissues (Henry's Law: $p \uparrow \Rightarrow x \uparrow$).
2. When diver ascends rapidly, external pressure drops suddenly.
   • Solubility of $N_2$ decreases sharply → dissolved nitrogen comes out of solution.
3. Gas bubbles form in blood and joints → causes severe pain, known as bends.
4. Prevention: Ascend slowly or use helium-oxygen mixture (He has lower solubility in blood).

Key result: Rapid pressure drop → gas comes out of solution → bubble formation → pain.

(ii) Feeling of weakness and discomfort in breathing at high altitude

Method: Apply Henry's Law to oxygen partial pressure.

Steps:

1. At high altitude, atmospheric pressure is low.
   • Partial pressure of oxygen ($p_{O_2}$) is significantly reduced.
2. According to Henry's Law:

• Lower $p_{O_2}$ → less oxygen dissolves in blood.

3. Result: Tissues receive insufficient oxygen → hypoxia → weakness, dizziness, breathlessness.
4. Body adapts over time by producing more red blood cells (acclimatization).

Key result: Low atmospheric pressure → low $p_{O_2}$ → low dissolved oxygen in blood → discomfort.

(b) Why soda water bottle fizzes on opening?

Method: Apply Henry's Law to $CO_2$ solubility under pressure release.

Steps: …

Here is a breakdown of the common mistakes students make on this Henry's Law question, along with the correct conceptual understanding and exam-smart strategies to avoid them.

Part (a)(i): The Bends (Decompression Sickness)

Common Mistake 1: Reversing the cause and effect.

Students often say, "When a diver comes up too fast, the pressure increases, causing nitrogen to dissolve." This is wrong.

• Why it's wrong: Pressure decreases as the diver ascends. Henry's Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.
• The Correct Concept:
  • At depth: High pressure → High solubility of $N_2$ in blood.
  • During rapid ascent: Pressure drops rapidly → Solubility of $N_2$ drops sharply → Gas comes out of solution, forming painful bubbles in blood and joints.
• How to avoid: Always link pressure change to solubility change in the correct direction. Write the sequence clearly:

  High $P$ (deep sea) → High solubility → $N_2$ dissolves in blood.

  Rapid decrease in $P$ (ascent) → Low solubility → $N_2$ bubbles out.

Common Mistake 2: Mentioning the wrong gas.

Some students say "oxygen bubbles" cause the bends.

• Why it's wrong: Oxygen is metabolized by the body. It is the inert gas nitrogen ($N_2$) that is not used up and accumulates in tissues.
• How to avoid: Memorize: Nitrogen is the culprit for the bends. Oxygen is consumed; $CO_2$ is buffered; $N_2$ is the problem.

Part (a)(ii): High Altitude Breathing

Common Mistake 3: Confusing "low oxygen" with "low solubility".

Students say, "At high altitude, the solubility of oxygen in blood decreases, so we feel weak."

• Why it's wrong: Henry's Law is about the amount of gas dissolved at a given partial pressure. At high altitude, the partial pressure of oxygen in the air is low. Therefore, the concentration of $O_2$ dissolved in blood is low. The solubility constant ($K_H$) of $O_2$ in blood does not change.
• The Correct Concept:

  $P_{O_2}$ (in air) is low at high altitude.

  By Henry's Law: $C_{O_2} = K_H \times P_{O_2}$.

  Therefore, $C_{O_2}$ (in blood) is low → hypoxia (weakness, discomfort).

• How to avoid: Never say "solubility decreases." Say "partial pressure of oxygen in the atmosphere is lower, so the concentration of dissolved oxygen in blood is lower."

Part (b): Soda Water Fizzing

Common Mistake 4: Forgetting the pressure change upon opening.

Students say, "The bottle fizzes because $CO_2$ reacts with water."

• Why it's wrong: The fizzing is a physical phenomenon, not a chemical reaction (though some $CO_2$ does form carbonic acid, that's not the cause of the fizz).
• The Correct Concept:
  • Before opening: Bottle is under high pressure of $CO_2$ gas. High $P_{CO_2}$ → High solubility of $CO_2$ in the liquid. …