State and explain Henry's law

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Q. State and explain Henry's law

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Concept understanding — Henrys Law

Henry's Law: The Physics of "Fizz"

Imagine you open a cold bottle of soda. You hear that familiar psshhht sound. Bubbles rush out. Now think: why were those bubbles inside the bottle in the first place? The liquid wasn't boiling. The answer is Henry's Law.

The Intuition: Gas Wants to Dissolve

Gases are just molecules flying around. When a gas touches a liquid, some of those molecules get "trapped" inside the liquid — they dissolve. But here's the key: the more you push on the gas, the more of it gets forced into the liquid.

Think of a crowded bus. If you push more people toward the door (higher pressure), more people get squeezed inside. If you let the pressure off (open the bottle), people rush out. That's exactly what happens with gas and liquid.

In the soda bottle, carbon dioxide gas is pumped in at high pressure. That pressure forces a huge amount of CO₂ to dissolve into the liquid. When you open the bottle, the pressure above the liquid drops to normal air pressure. Suddenly, the liquid can't hold all that CO₂ anymore — so it escapes as bubbles. That's the fizz.

The Precise Statement

Henry's Law says:

C = k_H \cdot P

Where:

$C$ = concentration of the dissolved gas in the liquid (usually mol/L or g/L)
$P$ = partial pressure of that gas above the liquid (usually atm or kPa)
$k_H$ = Henry's law constant — a number that depends on the specific gas, the liquid, and the temperature

In words: At a constant temperature, the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid.

What the Constant $k_H$ Tells You

$k_H$ is not universal. It's different for every gas-liquid pair. For example:

CO₂ in water has a certain $k_H$
O₂ in water has a different $k_H$ (smaller — oxygen doesn't dissolve as easily)

Temperature matters too. Higher temperature means lower $k_H$ — gases become less soluble in hot liquids. That's why a warm soda goes flat faster than a cold one.

Watch out

Henry's Law works only for dilute solutions and non-reacting gases. If the gas reacts chemically with the liquid (like HCl gas dissolving in water to form hydrochloric acid), Henry's Law does not apply — the concentration will be much higher than predicted.

Real-Life Examples

Situation	What Henry's Law explains
Soda fizz	High pressure forces CO₂ in; releasing pressure lets it out
Scuba diving	At depth, high pressure forces more N₂ into blood; rising too fast causes decompression sickness ("the bends")
Fish breathing	Oxygen dissolves in water at the surface (where partial pressure is highest); deeper water has less dissolved O₂
Altitude sickness	At high altitude, lower atmospheric pressure means less O₂ dissolves in your blood

The Key Takeaway

Important

Henry's Law is a proportionality: double the pressure above the liquid → double the gas dissolved in the liquid (at constant temperature). It's why carbonated drinks are bottled under pressure, why deep-sea divers must ascend slowly, and why a warm drink loses its carbonation faster.

The law is simple, but its consequences are everywhere — from the soda in your hand to the air you breathe at different altitudes.

Henry's law is a key quantitative concept in the NCERT/CBSE Class 12 Chemistry chapter on Solutions, and ‘Henry's law formula’ or ‘Henry's law numericals’ are common important-question searches for board exams, JEE Main and NEET. Its real-world applications, like gas solubility in carbonated drinks and blood at altitude, make it a favourite for application-based competitive-exam questions.

Why this formula?

Henry's Law: Why the Formula Holds

Henry's Law describes the solubility of a gas in a liquid at a constant temperature. The key formula is:

P = k_H \cdot x

Where:

$P$ = partial pressure of the gas above the liquid
$x$ = mole fraction of the gas dissolved in the liquid
$k_H$ = Henry's constant (depends on gas, liquid, and temperature)

Why This Linear Relationship Exists

1. Dynamic Equilibrium at the Interface

Imagine a gas above a liquid. At the molecular level:

Gas molecules constantly strike the liquid surface and dissolve
Dissolved molecules constantly escape back into the gas phase

At equilibrium, the rate of dissolution equals the rate of escape. This is a dynamic balance, not a static one.

2. The Driving Force for Dissolution

The rate at which gas molecules enter the liquid depends on:

How many gas molecules hit the surface — this is proportional to the partial pressure $P$ of the gas
How easily they dissolve — this is captured by $k_H$

So:

\text{Rate}_{\text{dissolve}} \propto P

3. The Driving Force for Escape

The rate at which dissolved molecules leave the liquid depends on:

How many dissolved molecules are near the surface — this is proportional to the mole fraction $x$ of the gas in the liquid
How easily they escape — also captured by $k_H$

So:

\text{Rate}_{\text{escape}} \propto x

4. Equating the Two Rates

At equilibrium:

\text{Rate}_{\text{dissolve}} = \text{Rate}_{\text{escape}}

Therefore:

P \propto x

Introducing the proportionality constant $k_H$ :

P = k_H \cdot x

Why It's Linear (Not Exponential or Logarithmic)

The linearity arises because:

No saturation effects at low concentrations — the molecules don't "crowd" each other
Ideal behavior is assumed — gas molecules don't interact strongly with each other or with the solvent
Temperature is constant — $k_H$ doesn't change

This is analogous to Raoult's Law for ideal solutions, but for a solute gas rather than a solvent.

Key Exam Points

Henry's Law works best for dilute solutions (low $x$ )
$k_H$ increases with temperature — gases become less soluble as temperature rises
$k_H$ is different for each gas-liquid pair — e.g., $CO_2$ in water vs $O_2$ in water
The law fails if the gas reacts chemically with the solvent (e.g., $HCl$ in water)

Quick Example

If $k_H = 3.0 \times 10^4 \text{ atm}$ for $O_2$ in water at 25°C, and the partial pressure of $O_2$ in air is 0.21 atm:

x = \frac{P}{k_H} = \frac{0.21}{3.0 \times 10^4} = 7.0 \times 10^{-6}

This tiny mole fraction explains why fish need gills to extract enough oxygen from water!

Bottom line: Henry's Law is a direct consequence of dynamic equilibrium at the gas-liquid interface, where the rates of dissolution and escape balance each other linearly.

Step 1. Statement. Henry's law states that, at low concentrations, the partial pressure of a gas in the vapour phase above a solution (its vapour pressure) is directly proportional to the mole fraction of that gaseous solute dissolved in the solution.

Step 2. Mathematical form. $p_{solute}\propto x_{solute\ in\ solution}$ , i.e. $p_{solute}=K_H\,x_{solute\ in\ solution}$ , where $K_H$ (Henry's law constant) is an empirical constant with the dimensions of pressure, whose value depends on the identity of both the gas and the solvent.

Step 3. Explanation. A plot of $p_{solute}$ against $x_{solute}$ is a straight line through the origin, of slope $K_H$ . A gas with a LARGER $K_H$ is LESS soluble (a given mole fraction produces a larger pressure); a gas with a SMALLER $K_H$ is MORE soluble. The law breaks down at high pressure/temperature, for gases that chemically react with the solvent (e.g. NH $_3$ or HCl with water), and for gases that associate or dissociate while dissolving.

✓Final answer

p_{solute}=K_H\,x_{solute\ in\ solution}

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