Passage:
Solubility of gases in liquids is greatly affected by pressure and temperature. Henry gave the quantitative relationship between pressure and solubility of gas in a solvent. According to Henry’s law, partial pressure of a gas above a liquid is directly proportional to its mole fraction in solution and is expressed as \(P = K_H.x\), where \(K_H\) is Henry’s constant and x is mole fraction of gas. \(K_H\) is a function of nature of gas.
F M Raoult gave a quantitative relationship between partial pressures and mole fractions in the binary solution of volatile liquids. Raoult’s law states that for a binary solution of volatile liquids, the partial pressure of each component in the solution is directly proportional to its mole fraction. Thus for a solution of component \(1\) and \(2\), partial pressure of each component \(P_1 = p_1^0x_1\), where \(p_1^0\) is the vapour pressure of pure component \(1\) at the same temperature. Similarly \(P_2 = p_2^0x_2\)
\(K_H\) value for \(Ar(g)\), \(CO_2(g)\), \(HCHO(g)\) and \(CH_4(g)\) are \(40.39\), \(1.67\), \(1.83 × 10^{–5}\) and \(0.413\) respectively. Identify the correct order of their increasing solubility in water
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(Ar < CO_2 < CH_4 < HCHO\)
By Henry’s law, p = KHx. At a given partial pressure,
\( \displaystyle x = \frac{p}{K_H} \)
so the higher the value of KH, the lower the solubility of the gas. KH depends on the nature of the gas.
Ar (KH = 40.39) — first (least soluble): the largest KH.
\( \ce{CO2} \) (1.67) — second.
\( \ce{CH4} \) (0.413) — third.
HCHO (1.83 × 10−5) — last (most soluble): the smallest KH.
Formaldehyde, a polar molecule that forms hydrogen bonds with water, is by far the most soluble.
Shortcut: The largest KH (Ar) is least soluble and the smallest (HCHO) most soluble. Only Option (3) starts with Ar and ends with HCHO.
NCERT (2026-27 edition):
Solubility of a Gas in a Liquid – …
