Consider the following gaseous equilibrium in a closed container of volume ' $V$ ' at $\mathrm{T}(\mathrm{K})$.

$ \mathrm{P}_2(\mathrm{~g})+\mathrm{Q}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{PQ}(\mathrm{~g}) $

2 moles each of $\mathrm{P}_2(\mathrm{~g}), \mathrm{Q}_2(\mathrm{~g})$ and $\mathrm{PQ}(\mathrm{g})$ are present at equilibrium. Now one mole each of ' $\mathrm{P}_2$ ' and ' $\mathrm{Q}_2$ ' are added to the equilibrium keeping the temperature at $\mathrm{T}(\mathrm{K})$. The number of moles of $\mathrm{P}_2, \mathrm{Q}_2$ and PQ at the new equilibrium, respectively, are

Consider the general reaction given below at 400 K

$ x \mathrm{~A}(\mathrm{~g}) \rightleftharpoons y \mathrm{~B}(\mathrm{~g}) . $

The values of $K_p$ and $K_c$ are studied under the same condition of temperature but variation in $x$ and $y$.

(i) $\mathrm{K}_{\mathrm{p}}=85.87$ and $\mathrm{K}_{\mathrm{c}}=2.586$ appropriate units

(ii) $\mathrm{K}_{\mathrm{p}}=0.862$ and $\mathrm{K}_{\mathrm{c}}=28.62$ appropriate units

The values of $x$ and $y$ in (i) and (ii) respectively are :

Consider the following reactions in which all the reactants and products are present in gaseous state

$ \begin{aligned} & 2 x y \rightleftharpoons x_2+y_2 \,\,\mathrm{~K}_1=2.5 \times 10^5 \\ & x y+\frac{1}{2} z_2 \rightleftharpoons x y z \,\,\mathrm{~K}_2=5 \times 10^{-3} \end{aligned} $

The value of $\mathrm{K}_3$ for the equilibrium $\frac{1}{2} x_2+\frac{1}{2} y_2+\frac{1}{2} z_2 \rightleftharpoons x y z$ is :

One mole each of He and $\mathrm{A}(\mathrm{g})$ are taken in a 10 L closed flask and heated to 400 K to establish the following equilibrium.

$ \mathrm{A}(\mathrm{~g}) \rightleftharpoons \mathrm{B}(\mathrm{~g}) $

$\mathrm{K}_{\mathrm{c}}$ for this reaction at 400 K is 4.0 . The partial pressures (in atm) of He and B(g) are respectively (at equilibrium)

(Assume $\mathrm{He}, \mathrm{A}(\mathrm{g})$ and $\mathrm{B}(\mathrm{g})$ behave as ideal gases)

(Given : $\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ )

The reaction $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ was initiated with the amount ' a ' of $\mathrm{A}(\mathrm{g})$. At equilibrium it is found that the amount of $\mathrm{A}(\mathrm{g})$ remaining is ( $\mathrm{a}-x$ ) at a total pressure of p .

The equilibrium constant Kp of the reaction can be calculated from the expression :

At $\mathrm{T}(\mathrm{K})$, the equilibrium constant of

$\mathrm{A}_2(g)+\mathrm{B}_2(g) \rightleftharpoons \mathrm{C}(g)$ is $2.7 \times 10^{-5}$.

What is the equilibrium constant for

$\frac{1}{3} \mathrm{~A}_2(\mathrm{~g})+\frac{1}{3} \mathrm{~B}_2(\mathrm{~g}) \rightleftharpoons \frac{1}{3} \mathrm{C}(\mathrm{g})$ at the same temperature?

Given below are two statements :

Statement I : A catalyst cannot alter the equilibrium constant $\left(\mathrm{K}_{\mathrm{c}}\right)$ of the reaction, temperature remaining constant.

Statement II : A homogenous catalyst can change the equilibrium composition of a system, temperature remaining constant.

In the light of the above statements, choose the correct answer from the options given below

Consider the following chemical equilibrium of the gas phase reaction at a constant temperature : $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$

If $p$ being the total pressure, $K_p$ is the pressure equilibrium constant and $\alpha$ is the degree of dissociation, then which of the following is true at equilibrium?

Consider the equilibrium

$ \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_4(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{~g}) $

If the pressure applied over the system increases by two fold at constant temperature then

(A) Concentration of reactants and products increases.

(B) Equilibrium will shift in forward direction.

(C) Equilibrium constant increases since concentration of products increases.

(D) Equilibrium constant remains unchanged as concentration of reactants and products remain same.

Choose the correct answer from the options given below :

At temperature T, compound $AB_{2(g)}$ dissociates as $AB_{2(g)} \rightleftharpoons AB_{(g)} + \frac{1}{2} B_{2(g)}$ having degree of dissociation $ x $ (small compared to unity). The correct expression for $ x $ in terms of $ K_p $ and $ p $ is:

For the reaction,

$\mathrm{H}_2(\mathrm{~g})+\mathrm{I}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{~g})$

Attainment of equilibrium is predicted correctly by :

Consider the reaction

$\mathrm{X}_2 \mathrm{Y}(\mathrm{~g}) \rightleftharpoons \mathrm{X}_2(\mathrm{~g})+\frac{1}{2} \mathrm{Y}_2(\mathrm{~g})$

The equation representing correct relationship between the degree of dissociation (x) of $\mathrm{X}_2 \mathrm{Y}(\mathrm{g})$ with its equilibrium constant Kp is __________.

Assume $x$ to be very very small.

A vessel at 1000 K contains $\mathrm{CO}_2$ with a pressure of 0.5 atm . Some of $\mathrm{CO}_2$ is converted into CO on addition of graphite. If total pressure at equilibrium is 0.8 atm , then K_p is :

For the given hypothetical reactions, the equilibrium constants are as follows :

$\begin{aligned} & \mathrm{X} \rightleftharpoons \mathrm{Y} ; \mathrm{K}_1=1.0 \\ & \mathrm{Y} \rightleftharpoons \mathrm{Z} ; \mathrm{K}_2=2.0 \\ & \mathrm{Z} \rightleftharpoons \mathrm{W} ; \mathrm{K}_3=4.0 \end{aligned}$

The equilibrium constant for the reaction $\mathrm{X} \rightleftharpoons \mathrm{W}$ is

The ratio $\frac{K_P}{K_C}$ for the reaction :

$\mathrm{CO}_{(\mathrm{g})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})} \rightleftharpoons \mathrm{CO}_{2(\mathrm{~g})}$ is :

At $-20^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ pressure, a cylinder is filled with equal number of $\mathrm{H}_2, \mathrm{I}_2$ and $\mathrm{HI}$ molecules for the reaction $\mathrm{H}_2(\mathrm{~g})+\mathrm{I}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})$, the $\mathrm{K}_{\mathrm{p}}$ for the process is $x \times 10^{-1}$.

$\mathrm{x}=$ __________.

[Given : $\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$]

Given below are two statements :

Statement I : On passing $\mathrm{HCl}_{(\mathrm{g})}$ through a saturated solution of $\mathrm{BaCl}_2$, at room temperature white turbidity appears.

Statement II : When $\mathrm{HCl}$ gas is passed through a saturated solution of $\mathrm{NaCl}$, sodium chloride is precipitated due to common ion effect.

In the light of the above statements, choose the most appropriate answer from the options given below :

The following reaction occurs in the Blast furnance where iron ore is reduced to iron metal

$\mathrm{Fe}_2 \mathrm{O}_{3(s)}+3 \mathrm{CO}_{(g)} \rightleftharpoons \mathrm{Fe}_{(\mathrm{l})}+3 \mathrm{CO}_{2(g)}$

Using the Le-chatelier's principle, predict which one of the following will not disturb the equilibrium.

The equilibrium constant for the reaction

$\mathrm{SO}_3(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g})$

is $\mathrm{K}_{\mathrm{c}}=4.9 \times 10^{-2}$. The value of $\mathrm{K}_{\mathrm{c}}$ for the reaction given below is $2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_3(\mathrm{~g})$ is :

$\mathrm{A}_{(\mathrm{g})} \rightleftharpoons \mathrm{B}_{(\mathrm{g})}+\frac{\mathrm{C}}{2}(\mathrm{g})$ The correct relationship between $\mathrm{K}_{\mathrm{P}}, \alpha$ and equilibrium pressure $\mathrm{P}$ is

For the given reaction, choose the correct expression of $\mathrm{K}_{\mathrm{C}}$ from the following :-

$\mathrm{Fe}_{(\mathrm{aq})}^{3+}+\mathrm{SCN}_{(\mathrm{aq})}^{-} \rightleftharpoons(\mathrm{FeSCN})_{(\mathrm{aq})}^{2+}$

For a concentrated solution of a weak electrolyte ($\mathrm{K}_{\text {eq }}=$ equilibrium constant) $\mathrm{A}_{2} \mathrm{B}_{3}$ of concentration '$c$', the degree of dissociation '$\alpha$' is :

The effect of addition of helium gas to the following reaction in equilibrium state, is :

$\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})$

The equilibrium constant for the reversible reaction

2A(g) $\rightleftharpoons$ 2B(g) + C(g) is K₁

${3 \over 2}$A(g) $\rightleftharpoons$ ${3 \over 2}$B(g) + ${3 \over 4}$C(g) is K₂.

K₁ and K₂ are related as :

4.0 moles of argon and 5.0 moles of PCl₅ are introduced into an evacuated flask of 100 litre capacity at 610 K. The system is allowed to equilibrate. At equilibrium, the total pressure of mixture was found to be 6.0 atm. The K_p for the reaction is :

[Given : R = 0.082 L atm K^$-$1 mol^$-$1]

For a reaction at equilibrium

A(g) $\rightleftharpoons$ B(g) + ${1 \over 2}$ C(g)

the relation between dissociation constant (K), degree of dissociation ($\alpha$) and equilibrium pressure (p) is given by :