Question

Match List - I (Laws) with the List - II (Mathematical expressions):

Codes:

• A. a - i, b – ii, c - iii, d - iv
• B. a - ii, b – i, c - iii, d - iv
• C. a - ii, b – i, c – iv, d – iii
• D. a – i, b – ii, c – iv, d - iii

Hint:

It is crucial to be precise with the notation in physical chemistry laws:

• \textbf{Raoult's Law (P\(_1\) = x\(_1\)P\(_1\)\(^0\)):} The superscript '0' denotes the pure component.
• \textbf{Henry's Law (p = K\(_H\)x):} K\(_H\) is the constant for the gas-solvent pair.
• \textbf{Kohlrausch's Law:} \(\Lambda_m^0\) refers to limiting molar conductivity (at infinite dilution).
• \textbf{First Law of Thermodynamics:} Pay attention to the sign convention for work (w). \(\Delta U = q+w\) means w is work done *on* the system. \(\Delta U = q-w\) means w is work done *by* the system. Both forms are valid if the convention is stated.

Answer 1

The Correct Option is C

Step 1: Match each law with its mathematical expression.
(a) Henry's law: This law relates the partial pressure of a gas above a liquid to the concentration of the gas dissolved in the liquid. The mathematical form is \( p = K_H x \), where p is the partial pressure of the gas, x is its mole fraction in the solution, and K\(_H\) is Henry's law constant. This matches with (ii). So, a \(\rightarrow\) ii.
(b) Raoult's law: This law states that for a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction. The expression is \( P_1 = x_1 P_1^0 \), where P\(_1\) is the partial pressure of component 1, x\(_1\) is its mole fraction, and P\(_1\)\(^0\) is the vapour pressure of the pure component. This matches with (i). So, b \(\rightarrow\) i.
(c) First law of thermodynamics: This law is a statement of the conservation of energy. It states that the change in internal energy of a system (\(\Delta\)U) is equal to the heat supplied to the system (q) plus the work done on the system (w). The equation is \( \Delta U = q + w \). This matches with (iv). So, c \(\rightarrow\) iv.
(d) Kohlrausch's law: This law of independent migration of ions states that the limiting molar conductivity of an electrolyte (\(\Lambda^0_m\)) can be represented as the sum of the individual contributions of the anion and cation of the electrolyte. The expression is \( \Lambda^0_m = \nu_+ \lambda^0_+ + \nu_- \lambda^0_- \), where \(\nu_+\) and \(\nu_-\) are the number of cations and anions per formula unit, and \(\lambda^0_+\) and \(\lambda^0_-\) are their limiting molar conductivities. This matches with (iii). So, d \(\rightarrow\) iii.
Step 2: Compile the matches.
The correct matches are: a \(\rightarrow\) ii, b \(\rightarrow\) i, c \(\rightarrow\) iv, d \(\rightarrow\) iii.
Step 3: Final Answer.
This combination corresponds to option (C).