Equilibrium — JEE Main PYQs

The first and second ionization constants of a weak dibasic acid $\mathrm{H_2A}$ are $8.1 \times 10^{-8}$ and $1.0 \times 10^{-13}$ respectively. 0.1 mol of $\mathrm{H_2A}$ was dissolved in 1 L of 0.1 M HCl solution. The concentration of $\mathrm{HA^-}$ in the resultant solution is :

At 25°C, 20.0 mL of 0.2 M weak monoprotic acid HX is titrated against 0.2 M NaOH. The pH of the solution (a) at the start of the titration (when NaOH has not been added) and (b) when 10 mL of NaOH is added respectively, are :

Given : $K_a = 5 \times 10^{-4}$

$\mathrm{p}K_a = 3.3$

$\alpha << 1$

(a) $\quad$ (b)

At T(K), the equilibrium constant of $\mathrm{A_2(g) + B_2(g) \rightleftharpoons C(g)}$ is $2.7 \times 10^{-5}$. What is the equilibrium constant for $\frac{1}{3}\mathrm{A_2(g)} + \frac{1}{3}\mathrm{B_2(g)} \rightleftharpoons \frac{1}{3}\mathrm{C(g)}$ at the same temperature?

The pH of a solution obtained by mixing 5 mL of 0.1 M $\mathrm{NH_4OH}$ solution with 250 mL of 0.1 M $\mathrm{NH_4Cl}$ solution is ________ $\times\ 10^{-2}$. (Nearest integer) Given: $\mathrm{p}K_b\ (\mathrm{NH_4OH}) = 4.74$

$\log 2 = 0.30$ $\log 3 = 0.48$ $\log 5 = 0.70$

20 mL of a solution of acetic acid required 28.4 mL of 0.1 M NaOH for its neutralization. A solution (X) was prepared by mixing 20 mL of the above acetic acid and 14.2 mL of 0.1 M NaOH solution. What is the pH of the solution (X)? ($\mathrm{p}K_a$ value of acetic acid is 4.75).

For the following reaction at 50 °C and at 2 atm pressure,

$\mathrm{2N_2O_5(g) \rightleftharpoons 2N_2O_4(g) + O_2(g)}$

$\mathrm{N_2O_5}$ is 50% dissociated.

The magnitude of standard free energy change at this temperature is $x$.

$x =$ ________ $\mathrm{J\ mol^{-1}}$ [Nearest integer].

Given : R = 8.314 $\mathrm{J\ mol^{-1}\ K^{-1}}$, log 2 = 0.30, log 3 = 0.48, ln10 = 2.303, °C + 273 = K

$\mathrm{M_3A_2}$ is a sparingly soluble salt of molar mass $y$ $\mathrm{g\ mol^{-1}}$ and solubility $x$ $\mathrm{g\ L^{-1}}$.

The ratio of the molar concentration of the anion ($\mathrm{A^{3-}}$) to the solubility product of the salt is

Arrange the following resultant mixtures in increasing order of their pH values

A. 10 mL 0.2 M $\mathrm{Ca(OH)_2}$ + 25 mL 0.1 M HCl B. 10 mL 0.01 M $\mathrm{H_2SO_4}$ + 10 mL 0.01 M $\mathrm{Ca(OH)_2}$ C. 10 mL 0.1 M $\mathrm{H_2SO_4}$ + 10 mL 0.1 M KOH

Choose the correct answer from the options given below:

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

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

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

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

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

(Assume He, A(g) and B(g) behave as ideal gases)

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

Given is a concentrated solution of a weak electrolyte $\mathrm{A}_x\mathrm{B}_y$ of concentration 'c' and dissociation constant 'K'. The degree of dissociation is given by :

In a closed flask at 600 K, one mole of $\mathrm{X_2Y_4(g)}$ attains equilibrium as given below :

$$\mathrm{X_2Y_4(g) \rightleftharpoons 2XY_2(g)}$$

At equilibrium, 75% $\mathrm{X_2Y_4(g)}$ was dissociated and the total pressure is 1 atm. The magnitude of $\Delta_r G^{\ominus}$ (in kJ mol$^{-1}$) at this temperature is ________. (Nearest Integer)

(Given : $R = 8.3\ \mathrm{J\ mol^{-1}\ K^{-1}}$; $\ln 10 = 2.3$, $\log 2 = 0.3$, $\log 3 = 0.48$, $\log 5 = 0.69$, $\log 7 = 0.84$)

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

$2xy \rightleftharpoons x_2 + y_2 \quad \mathrm{K_1} = 2.5 \times 10^5$

$xy + \frac{1}{2}z_2 \rightleftharpoons xyz \quad \mathrm{K_2} = 5 \times 10^{-3}$

The value of $\mathrm{K_3}$ for the equilibrium $\frac{1}{2}x_2 + \frac{1}{2}y_2 + \frac{1}{2}z_2 \rightleftharpoons xyz$ is :

Solid carbon, CaO and $\mathrm{CaCO_3}$ are mixed and allowed to attain equilibrium at T K.

$\mathrm{CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)} \quad \mathrm{Kp_1} = 0.08\ \mathrm{atm}$

$\mathrm{C(s) + CO_2(g) \rightleftharpoons 2CO(g)} \quad \mathrm{Kp_2} = 2\ \mathrm{atm}$

The partial pressure of CO is __________ $\times 10^{-1}$ atm

If equal volumes of $\mathrm{AB_2}$ and XY (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $\mathrm{AY_2}$ at 300 K ?

(Given $K_{sp}$ (at 300 K) for $\mathrm{AY_2} = 5.2 \times 10^{-7}$)

Consider the following equilibrium,

$$\mathrm{CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)}$$

0.1 mol of CO along with a catalyst is present in a 2 $\mathrm{dm^3}$ flask maintained at 500 K. Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of $\mathrm{CH_3OH}$ is formed. The $K_p^{\theta}$ is __________ $\times 10^{-3}$ (nearest integer).

Given : R = 0.08 $\mathrm{dm^3\ bar\ K^{-1}\ mol^{-1}}$

Assume only methanol is formed as the product and the system follows ideal gas behaviour.

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

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

In the following system, $\mathrm{PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)}$ at equilibrium, upon addition of xenon gas at constant T & p, the concentration of

Given below are two statements:

Statement I : A catalyst cannot alter the equilibrium constant ($K_c$) 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

$x$ mg of $\mathrm{Mg(OH)_2}$ (molar mass = 58) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of $x$ is _________ mg. (Nearest integer)

(Given : $\mathrm{Mg(OH)_2}$ is assumed to dissociate completely in $\mathrm{H_2O}$]

An aqueous solution of HCl with pH 1.0 is diluted by adding equal volume of water (ignoring dissociation of water). The pH of HCl solution would

(Given log 2 = 0.30)

One litre buffer solution was prepared by adding 0.10 mol each of $\mathrm{NH_3}$ and $\mathrm{NH_4Cl}$ in deionised water. The change in pH on addition of 0.05 mol of HCl to the above solution is __________ $\times 10^{-2}$. (Nearest integer)

Given : $\mathrm{p}K_b$ of $\mathrm{NH_3} = 4.745$ and $\log_{10} 3 = 0.477$

The equilibrium constant for decomposition of $\mathrm{H_2O}$ (g)

$$\mathrm{H_2O(g) \rightleftharpoons H_2(g) + \frac{1}{2}O_2(g)} \quad (\Delta G^\circ = 92.34\ \mathrm{kJ\ mol^{-1}})$$

is $8.0 \times 10^{-3}$ at 2300 K and total pressure at equilibrium is 1 bar. Under this condition, the degree of dissociation ($\alpha$) of water is __________ $\times 10^{-2}$ (nearest integer value).

[Assume $\alpha$ is negligible with respect to 1]

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 Kp is :

Which of the following happens when $\mathrm{NH_4OH}$ is added gradually to the solution containing 1M $\mathrm{A^{2+}}$ and 1M $\mathrm{B^{3+}}$ ions?

Given : $\mathrm{K_{sp}[A(OH)_2]} = 9 \times 10^{-10}$ and $\mathrm{K_{sp}[B(OH)_3]} = 27 \times 10^{-18}$ at 298 K.

If 1 mM solution of ethylamine produces $\mathrm{pH} = 9$, then the ionization constant ($\mathrm{K_b}$) of ethylamine is $10^{-x}$. The value of x is _____ (nearest integer).

[The degree of ionization of ethylamine can be neglected with respect to unity.]

Consider the reaction

$$X_2Y(g) \rightleftharpoons X_2(g) + \tfrac{1}{2}Y_2(g)$$

The equation representing correct relationship between the degree of dissociation $(x)$ of $X_2Y(g)$ with its equilibrium constant $K_p$ is ________.

Assume $x$ to be very very small.

pH of water is 7 at $25^{\circ}\mathrm{C}$. If water is heated to $80^{\circ}\mathrm{C}$, it's pH will :

$\mathrm{K_{sp}}$ for $\mathrm{Cr(OH)_3}$ is $1.6 \times 10^{-30}$. What is the molar solubility of this salt in water?

37.8 g $\mathrm{N_2O_5}$ was taken in a 1 L reaction vessel and allowed to undergo the following reaction at 500 K $$\mathrm{2N_2O_{5(g)} \rightleftharpoons 2N_2O_{4(g)} + O_{2(g)}}$$ The total pressure at equilibrium was found to be 18.65 bar. Then, $K_p$ = ______ $\times 10^{-2}$ [nearest integer]

Assume $\mathrm{N_2O_5}$ to behave ideally under these conditions.

Given: R = 0.082 bar L mol$^{-1}$ K$^{-1}$

For the reaction, $$\mathrm{H_2(g) + I_2(g) \rightleftharpoons 2HI(g)}$$ Attainment of equilibrium is predicted correctly by :

[Figure: each option is a plot of molar concentration (y-axis) versus time (x-axis) for the three species $\mathrm{H_2}$, $\mathrm{I_2}$ and $\mathrm{HI}$ approaching equilibrium plateaus]

Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K. If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from following

A weak acid HA has degree of dissociation x. Which of the following options correctly explains ($\mathrm{pH} - \mathrm{p}K_a$)?

Arrange the following in increasing order of solubility product :

$\mathrm{Ca(OH)_2},\ \mathrm{AgBr},\ \mathrm{PbS},\ \mathrm{HgS}$

The equilibrium constant for the reaction

$$\mathrm{SO_3(g) \rightleftharpoons SO_2(g) + \frac{1}{2}\,O_2(g)}$$

is $\mathrm{K_c} = 4.9 \times 10^{-2}$. The value of $\mathrm{K_c}$ for the reaction given below is

$$\mathrm{2\,SO_2(g) + O_2(g) \rightleftharpoons 2\,SO_3(g)}$$

is :

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

$$\mathrm{Fe_2O_{3(s)} + 3CO_{(g)} \rightleftharpoons Fe_{(l)} + 3CO_{2(g)}}$$

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

Given below are two statements :

Statement I : On passing $\mathrm{HCl_{(g)}}$ through a saturated solution of $\mathrm{BaCl_2}$, at room temperature white turbidity appears.

Statement II : When HCl gas is passed through a saturated solution of 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 :

At $-20\ ^{\circ}\mathrm{C}$ and 1 atm pressure, a cylinder is filled with equal number of $\mathrm{H_2}$, $\mathrm{I_2}$ and $\mathrm{HI}$ molecules for the reaction

$\mathrm{H_2(g) + I_2(g) \rightleftharpoons 2HI(g)}$, the $\mathrm{K_p}$ for the process is $x \times 10^{-1}$.

$x =$ ________.

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

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

$$\mathrm{CO_{(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons CO_{2(g)}}$$ is :

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

$\mathrm{X \rightleftharpoons Y;\ K_1 = 1.0}$

$\mathrm{Y \rightleftharpoons Z;\ K_2 = 2.0}$

$\mathrm{Z \rightleftharpoons W;\ K_3 = 4.0}$

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

Given below are two statements :

Statement (I) : A Buffer solution is the mixture of a salt and an acid or a base mixed in any particular quantities.

Statement (II) : Blood is naturally occurring buffer solution whose pH is maintained by $\mathrm{H_2CO_3/HCO_3^{\ominus}}$ concentrations.

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

For a sparingly soluble salt $\mathrm{AB_2}$, the equilibrium concentrations of $\mathrm{A^{2+}}$ ions and $\mathrm{B^-}$ ions are $1.2 \times 10^{-4}$ M and $0.24 \times 10^{-3}$ M, respectively. The solubility product of $\mathrm{AB_2}$ is :

$\mathrm{K_a}$ for $\mathrm{CH_3COOH}$ is $1.8 \times 10^{-5}$ and $\mathrm{K_b}$ for $\mathrm{NH_4OH}$ is $1.8 \times 10^{-5}$. The pH of ammonium acetate solution will be ________.

Solubility of calcium phosphate (molecular mass, M) in water is $\mathrm{W_g}$ per 100 mL at $25\,^\circ\mathrm{C}$. Its solubility product at $25\,^\circ\mathrm{C}$ will be approximately.

Given below are two statements :

Statement (I) : Aqueous solution of ammonium carbonate is basic.

Statement (II) : Acidic/basic nature of salt solution of a salt of weak acid and weak base depends on $\mathrm{K_a}$ and $\mathrm{K_b}$ value of acid and the base forming it.

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

For the reaction $\mathrm{N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}}$, $K_p = 0.492$ atm at 300K. $K_c$ for the reaction at same temperature is ________ $\times 10^{-2}$.

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

The pH at which $\mathrm{Mg(OH)_2}$ $[\mathrm{K_{sp}} = 1 \times 10^{-11}]$ begins to precipitate from a solution containing 0.10 M $\mathrm{Mg^{2+}}$ ions is ________.

The pH of an aqueous solution containing 1M benzoic acid ($\mathrm{pK_a} = 4.20$) and 1M sodium benzoate is 4.5. The volume of benzoic acid solution in 300 mL of this buffer solution is _________ mL. (given : $\log 2 = 0.3$)

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

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

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