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Q1.12:
State Henry’s law and mention some important applications.

Solution :

Step 1: Definition and Theoretical Foundation of Henry's Law

Henry’s Law provides a quantitative relationship between the pressure of a gas above a liquid and the concentration of the gas dissolved in that liquid at a constant temperature. It states that: "The partial pressure of the gas in the vapour phase ($p$) is proportional to the mole fraction of the gas ($x$) in the solution."

Mathematically, this is expressed as:

$p = K_H \cdot x$

Where:

  • $p$ = Partial pressure of the gas above the liquid solution.
  • $x$ = Mole fraction of the gas in the solution (representing solubility).
  • $K_H$ = Henry’s Law constant, which is a function of the nature of the gas and the temperature [Per the kinetic theory of gases and intermolecular force analysis].

Note: As $K_H$ increases at a given pressure, the solubility of the gas decreases. Furthermore, since the dissolution of gas in a liquid is an exothermic process, $K_H$ increases with rising temperature, explaining why aquatic species are more comfortable in cold waters.

Step 2: Graphical Representation of Henry's Law

Mole fraction of gas (x) Partial Pressure (p) Slope = $K_H$

Step 3: Important Applications of Henry's Law

Application Area Mechanism and Justification
Carbonated Beverages Bottles of soft drinks and soda are sealed under high pressure to increase the solubility of $CO_2$ in the liquid [Application of the direct proportionality between $p$ and $x$].
Scuba Diving Divers face the "bends" (decompression sickness) due to high external pressure underwater, forcing atmospheric nitrogen to dissolve in blood. Upon ascent, decreasing pressure causes gas bubbles to form, blocking capillaries [Physiological consequence of shifting gas solubility].
High Altitude Physiology At higher altitudes, partial pressure of $O_2$ is lower than at ground level. This leads to low blood oxygen levels in climbers, causing hypoxia and an inability to think clearly [Per Henry's Law, lower $p$ results in lower dissolved $O_2$ in tissues].

Step 4: Summary of Theoretical Significance

Henry's Law is a specific case of Raoult's Law, where the solute is a gas. It serves as a fundamental principle in chemical engineering, environmental science, and human physiology. It dictates that for a given solvent-solute system at constant temperature, the equilibrium state is defined strictly by the pressure head applied to the gas phase.

Final Solution: Henry's Law states $p = K_H \cdot x$. Its critical applications include the pressurization of carbonated drinks, the management of blood gas concentration in scuba diving, and the physiological impact of low atmospheric oxygen at high altitudes.


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