The Henry's law constant (\( K_H \)) varies depending on the gas and its temperature. The correct matches are:
- (A) 145 K bar corresponds to CO$_2$ (I), which has the highest Henry's law constant.
- (B) 89 K bar corresponds to He (II), which is less soluble than CO$_2$.
- (C) 76.5 K bar corresponds to N$_2$ at 293 K (III), as nitrogen is less soluble than CO$_2$.
- (D) 1.67 K bar corresponds to N$_2$ at 303 K (IV), as the solubility of gases decreases with increasing temperature.
Thus, the correct answer is (A)-(I), (B)-(II), (C)-(III), (D)-(IV).