On decreasing the $p \mathrm{H}$ from 7 to 2 , the solubility of a sparingly soluble salt (MX) of a weak acid (HX) increased from $10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}$ to $10^{-3} \mathrm{~mol} \mathrm{~L}^{-1}$. The $p \mathrm{~K}_{\mathrm{a}}$ of $\mathrm{HX}$ is

Dilution processes of different aqueous solutions, with water, are given in LIST - I. The effects of dilution of the solutions on $$\left[ {{H^ + }} \right]$$ are given in LIST - II

(Note: Degree of dissociation (a) of weak acid and weak base is $$<<1;$$ degree of hydrolysis of salt $$<<1;$$ $$\left[ {{H^ + }} \right]$$ represents the concentration of $${H^ + }$$ ions)

	LIST-I		LIST-II
P.	(10 mL of 0.1 M NaOH + 20 mL of 0.1 M acetic acid) diluted to 60 mL	1.	the value of [H+] does not change on dilution
Q.	(20 mL of 0.1 M NaOH + 20 mL of 0.1 M acetic acid) diluted to 80 mL	2.	the value of [H+] changes to half of its initial value on dilution
R.	(20 mL of 0.1 M HCL + 20 mL of 0.1 M ammonia solution) diluted to 80 mL	3.	the value of [H+] changes to two times of its initial value on dilution
S.	10 mL saturated solution of Ni(OH)2 in equilibrium with excess solid Ni(OH)2 is diluted to 20 mL (solid Ni(OH)2 is still present after dilution).	4.	the value of [H+] changes to $${1 \over {\sqrt 2 }}$$ times of its initial value on dilution
		5.	the value of [H+] changes to $$\sqrt 2 $$ times of its initial value on dilution

Match each process given in LIST-I with one or more effect(s) in LIST-II. The correct option is :

Paragraph
Thermal decomposition of gaseous X₂ to gaseous X at 298 K takes place according to the following equations:
X₂ (g) $$\leftrightharpoons$$ 2X (g)
The standard reaction Gibbs energy, $$\Delta _rG^o$$, of this reaction is positive. At the start of the reaction, there is one mole of X₂ and no X. As the reaction proceeds, the number of moles of X formed is given by $$\beta$$. Thus, $$\beta _{equilibrium}$$ is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given R = 0.083 L bar K^-1 mol^-1)
Question
The equilibrium constant K_p for this reaction at 298 K, in terms of $$\beta _{equilibrium}$$, is

Paragraph
Thermal decomposition of gaseous X₂ to gaseous X at 298 K takes place according to the following equations:
X₂ (g) $$\leftrightharpoons$$ 2X (g)
The standard reaction Gibbs energy, $$\Delta _rG^o$$, of this reaction is positive. At the start of the reaction, there is one mole of X₂ and no X. As the reaction proceeds, the number of moles of X formed is given by $$\beta$$. Thus, $$\beta _{equilibrium}$$ is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given R = 0.083 L bar K^-1 mol^-1)
Question
The INCORRECT statement among the following for this reaction, is