C

To determine the molar heat capacities for different thermodynamic processes involving one mole of an ideal monoatomic gas, we can analyze each process:
(i) Isothermal process: For an isothermal process, the molar heat capacity, C, is infinite since the temperature remains constant. We commonly express heat transfer using q=nRT ln(V2/V1). Hence, this is typically not assigned a finite value.
(ii) Isochoric process: In this case, only the internal energy changes, and for a monoatomic ideal gas, C_v = \frac{3}{2}R. Hence, the molar heat capacity is C = C_v = 1.5R.
(iii) Isobaric process: For an isobaric process, we use the relation C = C_p = C_v + R = (\frac{3}{2}R) + R = \frac{5}{2}R.
(iv) Adiabatic process: The relation for a molar heat capacity in an adiabatic process is given as C_{adiabatic} = C_v. Hence the molar heat capacity equals C_v, which is 1.5R.
Thus, matching these with the corresponding options, we find that the correct matching is:
(i) - [A]: Isothermal
(ii) - [D]: Isochoric
(iii) - [B]: Isobaric
(iv) - [C]: Adiabatic
Therefore, the answer is C for the adiabatic process.