Q.State Henry's law and mention some important applications.

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 at a constant temperature.

Essential reasoning:

1. Mathematically, $p = K_H \cdot x$, where $p$ is the partial pressure of the gas, $x$ is its mole fraction in the solution, and $K_H$ is Henry's constant (specific to the gas–solvent pair at a given temperature).
2. A higher $K_H$ means lower solubility at a given pressure; a lower $K_H$ means higher solubility.

Important applications:

• Carbonated beverages: Bottled under high $CO_2$ pressure to increase solubility; opening the bottle lowers pressure, releasing excess gas as bubbles.
• Deep-sea diving: Divers breathe compressed air; increased pressure dissolves more $N_2$ in blood. Rapid ascent causes decompression sickness (bends) as $N_2$ bubbles form — avoided by diluting the breathing mixture with helium, which is much less soluble in blood than nitrogen (helium's $K_H$ is higher — 144.97 kbar vs 76.48 kbar for $N_2$ — and a higher $K_H$ means lower solubility). …

Understanding Henry's Law

Henry's law is a fundamental principle in physical chemistry that describes how gases dissolve in liquids. The intuition is simple: when you increase the pressure of a gas above a liquid, more gas molecules are forced into the liquid phase. Think of it like squeezing more people into a room — the harder you push (higher pressure), the more people (gas molecules) can fit.

The constant $k_H$ is unique for each gas-liquid system. A higher $k_H$ means the gas is less soluble (you need more pressure to dissolve the same amount), while a lower $k_H$ means the gas dissolves more readily.

Step-by-Step Derivation and Explanation

1. The basic relationship At a fixed temperature, the amount of gas dissolved in a liquid is directly proportional to the pressure of that gas above the liquid. Mathematically:

where $C$ is the concentration of the dissolved gas (often in mol/L or mole fraction), $p$ is the partial pressure, and $k_H$ is Henry's constant. This is the most common form used in problems.

2. Why temperature matters

   Henry's constant $k_H$ is temperature-dependent. As temperature increases, gas solubility generally decreases (think of a warm soda going flat faster). This is because dissolution of a gas is usually exothermic — heat drives the gas out of solution.

3. The mole fraction form

   For precise work, especially in mixtures, we use mole fraction:

Here $x$ is the mole fraction of the gas in the liquid. This form is useful when dealing with multiple gases or when the solvent itself is volatile.

Important Applications

Henry's law explains several everyday phenomena and has critical industrial and biological applications:

1. Carbonated beverages

   Soda and beer are bottled under high $CO_2$ pressure. When you open the bottle, pressure drops suddenly, and $CO_2$ comes out of solution — that's the fizz. The law predicts exactly how much gas remains dissolved at any given pressure.

2. Deep-sea diving

   Divers breathe compressed air at depth. Under high pressure, nitrogen dissolves in the blood. If the diver ascends too quickly, the sudden pressure drop causes nitrogen to form bubbles in the bloodstream — this is decompression sickness ("the bends"). Henry's law governs this process, and divers must ascend slowly to allow nitrogen to leave the blood gradually. …

Henry's Law — Concept & Method

1. State Henry's Law

Henry's Law: At a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid surface.

Mathematically:

Where:

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

2. Important Applications

3. One Clear Solution Method

Method: Direct Substitution in Henry's Law

Concept: When a gas dissolves in a liquid, the mole fraction of the dissolved gas is directly proportional to its partial pressure. Use the formula $p = K_H \cdot x$ to find any one unknown.

Steps:

1. Identify the given quantities — partial pressure ($p$), Henry's constant ($K_H$), or mole fraction ($x$).

2. Write Henry's law equation:

3. Substitute the known values into the equation.

4. Solve for the unknown — rearrange if needed:

   • To find $x$: $\displaystyle x = \frac{p}{K_H}$
   • To find $p$: $p = K_H \cdot x$

5. Check units — ensure pressure units match (atm, bar, or Pa) and $K_H$ has consistent units.

Example Problem …

Henry's Law: Common Mistakes & How to Avoid Them

What Henry's Law Actually Says

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

Where:

• $p$ = partial pressure of the gas above the liquid
• $x$ = mole fraction of the gas in the solution
• $K_H$ = Henry's law constant (depends on gas-solvent pair and temperature)

🚩 Mistake #1: Writing the Formula Backwards

The error: Students write $x = K_H \cdot p$ or $p = \frac{x}{K_H}$, confusing which variable is proportional to which.

Why it happens: Memorizing without understanding the physical meaning.

How to avoid: Remember the physical picture:

• Higher pressure above the liquid → more gas molecules forced into solution → higher solubility
• So pressure ($p$) and solubility ($x$) move in the same direction
• The constant $K_H$ connects them: $p = K_H \cdot x$

Exam tip: If you forget, think: "Pressure pushes gas in" → pressure is on the left side of the equation.

🚩 Mistake #2: Confusing Henry's Constant Units

The error: Using wrong units for $K_H$ or not specifying them in answers.

Why it happens: $K_H$ can be expressed in different forms (atm, bar, Pa, etc.)

How to avoid: Always check:

• If $p$ is in atm → $K_H$ has units of atm
• $K_H$ is not dimensionless — it has pressure units
• Common values: $K_H$ for $O_2$ in water ≈ $4.3 \times 10^4$ atm at 25°C

Remember: $K_H$ is large for less soluble gases (more pressure needed to dissolve the same amount).

🚩 Mistake #3: Forgetting Temperature Dependence

The error: Stating Henry's law without mentioning "at constant temperature."

Why it happens: Students treat it as an absolute law.

How to avoid:

• Always write: "At constant temperature..."
• Know that $K_H$ increases with temperature (solubility decreases as temperature rises)
• This is why cold drinks go flat faster when warm

🚩 Mistake #4: Applying Henry's Law to Wrong Gases

The error: Applying Henry's law to gases that react chemically with the solvent.

Why it happens: Not checking if the gas-solvent interaction is purely physical.

How to avoid: Henry's law applies only to gases that:

• Do not react chemically with the solvent
• Form dilute solutions
• Are at moderate pressures (not too high)

Examples where it fails:

• $NH_3$ in water (reacts to form $NH_4OH$)
• $HCl$ in water (dissociates completely)

Borderline case — do NOT list this as a failure: $CO_2$ in water reacts only slightly (a small fraction forms carbonic acid), so Henry's law still describes its solubility well — that is exactly why carbonated drinks are the flagship Henry's-law application, not an exception.

🚩 Mistake #5: Listing Wrong Applications

The error: Giving vague or incorrect applications.

How to avoid: Memorize these exam-favourite applications:

| Application | Explanation |

|-------------|-------------| …