Match Column I with Column II

i-d, ii-a, iii-b, iv-c

The correct answer is option 1. i-d, ii-a, iii-b, iv-c.

1. \(\Lambda _{m}\) is the molar conductivity, which is the conductivity of a solution divided by the concentration of the solute. It is an intensive property, which means that it does not depend on the amount of material present. However, the molar conductivity of a solution increases with dilution, because the ions in the solution are more spread out in a dilute solution, which makes them more mobile and able to carry more current. Therefore, the answer for Column II is (d), increases with dilution.

2. \(E^o_{cell}\) is the standard cell potential, which is the cell potential at standard conditions. It is an intensive property, which means that it does not depend on the amount of material present. For example, the standard cell potential for the reaction of zinc and copper is 1.10 volts, regardless of how much zinc or copper is used. Therefore, the answer for Column II is (a), intensive property.

3. \(G^*\) is the molar free energy of activation, which is the free energy required to activate a mole of molecules in a reaction. It is an extensive property, which means that it depends on the amount of material present. For example, the molar free energy of activation for the reaction of zinc and copper is 111 kJ/mol, regardless of how much zinc or copper is used. Therefore, the answer for Column II is (b), depends on number of ions/volume.

4. \(\Delta _r G_{cell}\) is the standard free energy change of a reaction, which is the difference between the free energies of the products and reactants at standard conditions. It is an extensive property, which means that it depends on the amount of material present. For example, the standard free energy change for the reaction of zinc and copper is -177 kJ, regardless of how much zinc or copper is used. Therefore, the answer for Column II is (c), extensive property.