Given below are two statements:
Assertion A: Amongst He, Ne, Ar and Kr; 1 g of activated charcoal adsorbs more of Kr.
Reason R: The critical volume V$$_c$$ (cm$$^3$$ mol$$^{-1}$$) and critical pressure P$$_c$$ (atm) is highest for Krypton but the compressibility factor at critical point Z$$_c$$ is lowest for Krypton.

Activated charcoal adsorbs a gas more strongly when the attractive van der Waals forces between its molecules are larger. For the noble gases those forces grow with increasing ease of liquefaction, or equivalently with higher critical temperature $$T_c$$. The critical temperatures are:

He : 5.2 K < Ne : 44.4 K < Ar : 150.9 K < Kr : 209.4 K.

Since krypton has the highest $$T_c$$, 1 g of activated charcoal will adsorb the greatest quantity of Kr. Hence Assertion A is true.

The Reason states that krypton has the highest critical volume $$V_c$$ and critical pressure $$P_c$$, but the lowest compressibility factor at the critical point $$Z_c$$. Experimental critical constants are:

He : $$P_c=2.3\ \text{atm},\;V_c=57\ \text{cm}^3\ \text{mol}^{-1},\;T_c=5.2\ \text{K}$$
Ne : $$P_c=26.3\ \text{atm},\;V_c=41\ \text{cm}^3\ \text{mol}^{-1},\;T_c=44.4\ \text{K}$$
Ar : $$P_c=48.3\ \text{atm},\;V_c=74.6\ \text{cm}^3\ \text{mol}^{-1},\;T_c=150.9\ \text{K}$$
Kr : $$P_c=55.0\ \text{atm},\;V_c=92.0\ \text{cm}^3\ \text{mol}^{-1},\;T_c=209.4\ \text{K}$$

Thus Kr indeed has the highest $$P_c$$ and $$V_c$$ among the four gases. However, the compressibility factor at the critical point is

$$Z_c=\frac{P_cV_c}{RT_c}$$

Using the data above gives $$Z_c\,$$: He 0.302, Ne 0.296, Ar 0.291, Kr 0.294. Krypton does not possess the lowest $$Z_c$$; argon’s value is slightly lower. Therefore the statement “$$Z_c$$ is lowest for krypton” is false, rendering Reason R false.

A true Assertion with a false Reason matches Option A.

Final answer : Option A.