\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.
Step 1: Understanding the Concept:
Match fundamental chemical and physical laws from different chapters (Solutions, Thermodynamics, Electrochemistry) to their standard governing mathematical formulas. Step 2: Key Formula or Approach:
Recall the specific equations. Henry's relates gas pressure to solubility ($K_H$), Raoult's relates solution vapor pressure to pure solvent ($P^0$), First law represents energy conservation, and Kohlrausch's law sums limiting molar conductivities. Step 3: Detailed Explanation:
(a) Henry's Law: States that the partial pressure of a gas in the vapour phase ($p$) is directly proportional to the mole fraction of the gas ($x$) in the solution. Formula: $p = K_{H} \cdot x$. (a $\rightarrow$ ii)
(b) Raoult's Law: For a solution containing volatile liquids, the partial vapour pressure of a component ($P_{1}$) is proportional to its mole fraction in the liquid phase ($x_{1}$) multiplied by its pure vapour pressure ($P_{1}^{0}$). Formula: $P_{1} = x_{1}P_{1}^{0}$. (b $\rightarrow$ i)
(c) First Law of Thermodynamics: The law of conservation of energy expressed mathematically as the change in internal energy ($\Delta U$) equals heat added ($q$) plus work done ($w$). Formula: $\Delta U = q + w$. (c $\rightarrow$ iv)
(d) Kohlrausch's Law of Independent Migration of Ions: The limiting molar conductivity of a strong electrolyte ($\Lambda_{m}^{0}$) is the sum of the individual ionic contributions ($\lambda_{+}^{0}, \lambda_{-}^{0}$) scaled by their stoichiometric coefficients ($\nu_{+}, \nu_{-}$). Formula: $\Lambda_{m}^{0} = \nu_{+}\lambda_{+}^{0} + \nu_{-}\lambda_{-}^{0}$. (d $\rightarrow$ iii) Step 4: Final Answer:
Matching sequence is a-ii, b-i, c-iv, d-iii.
