Core Syllabus Module

Ionic Equilibrium

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Chapter Elite-20 Challenge Zone

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JEE Advanced 2025

LEVELJEE Advanced

At $2 5^{\circ} C$ , the concentration of $H^{+}$ ions in $1.00 \times 1 0^{- 3} M$ aqueous solution of a weak monobasic acid having acid dissociation constant $(K_{a}) = 4.00 \times 1 0^{- 11}$ is $X \times 1 0^{- 7} M$ . The value of $X$ is _______. Use: Ionic product of water $(K_{w}) = 1.00 \times 1 0^{- 14}$ at $2 5^{\circ} C$

JEE Advanced 2023

LEVELJEE Advanced

On decreasing the pH from 7 to 2, the solubility of a sparingly soluble salt (MX) of a weak acid (HX) increased from $1 0^{- 4} mol L^{- 1}$ to $1 0^{- 3} mol L^{- 1}$ . The $p K_{a}$ of HX is:

Dilution process of different aqueous solutions; with water, are given in List-I. The effects of dilution of the solutions on $[H^{+}]$ are given in List-II. (Note : Degree of dissociation ( $α$ ) of weak acid and weak base is $<< 1$ ; degree of hydrolysis of salt $<< 1$ ; $[H^{+}]$ represents the concentration of $H^{+}$ ions)

List-I

(P)

(10 mL of 0.1 M NaOH + 20 mL of 0.1 M acetic acid) diluted to 60 mL

(Q)

(20 mL of 0.1 M NaOH + 20 mL of 0.1 M acetic acid) diluted to 80 mL

(R)

(20 mL of 0.1 M HCl + 20 mL of 0.1 M ammonia solution) diluted to 80 mL

(S)

10 mL saturated solution of

N i (O H)_{2}

in equilibrium with excess solid

N i (O H)_{2}

is diluted to 20 mL (solid

N i (O H)_{2}

is still present after dilution).

List-II

(1)

the value of

[H^{+}]

does not change on dilution

(2)

the value of

[H^{+}]

changes to half of its initial value on dilution

(3)

the value of

[H^{+}]

changes to two times of its initial value on dilution

(4)

the value of

[H^{+}]

changes to

\frac{1}{2}

times of its initial value on dilution

(5)

the value of

[H^{+}]

changes to

2

times of its initial value on dilution

JEE Advanced 2018

LEVELJEE Advanced

The solubility of a salt of weak acid(AB) at pH 3 is $Y \times 1 0^{- 3} mol L^{- 1}$ . The value of Y is_______. (Given that the value of solubility product of AB ( $K_{s p}$ ) = $2 \times 1 0^{- 10}$ and the value of ionization constant of HB( $K_{a}$ ) = $1 \times 1 0^{- 8}$ )

JEE Advanced 2022

LEVELJEE Advanced

Concentration of $H_{2} SO_{4}$ and $Na_{2} SO_{4}$ in a solution is $1 M$ and $1.8 \times 1 0^{- 2} M$ , respectively. Molar solubility of $PbSO_{4}$ in the same solution is $X \times 1 0^{- Y} M$ (expressed in scientific notation). The value of $Y$ is _________. [Given: Solubility product of $PbSO_{4}$ ( $K_{sp}$ ) = $1.6 \times 1 0^{- 8}$ . For $H_{2} SO_{4}$ , $K_{a 1}$ is very large and $K_{a 2} = 1.2 \times 1 0^{- 2}$ ]

JEE Main 2020

LEVELJEE Advanced

A soft drink was bottled with a partial pressure of $CO_{2}$ of 3 bar over the liquid at room temperature. The partial pressure of $CO_{2}$ over the solution approaches a value of 30 bar when 44 g of $CO_{2}$ is dissolved in 1 kg of water at room temperature. The approximate pH of the soft drink is ...... $\times 1 0^{- 1}$ . (First dissociation constant of $H_{2} CO_{3} = 4.0 \times 1 0^{- 7}$ ) $lo g 2 = 0.3$ ; density of the soft drink $= 1 g mL^{- 1}$ )

JEE Main 2020

LEVELJEE Advanced

3 g of acetic acid is added to 250 mL of 0.1 M HCl and the solution made up to 500 mL. To 20 mL of this solution $\frac{1}{2}$ mL of 5 M NaOH is added. The pH of the solution is ………… [Given : $p K_{a}$ of acetic acid = 4.75, molar mass of acetic acid = 60 g/mol, $lo g 3 = 0.4771$ ] Neglect any changes in volume.

JEE Main 2021

LEVELJEE Advanced

The solubility of $AgCN$ in a buffer solution of $pH = 3$ is $x$ . The value of $x$ is...... . [Assume : No cyano complex is formed; $K_{s p} (AgCN) = 2.2 \times 1 0^{- 16}$ and $K_{a} (HCN) = 6.2 \times 1 0^{- 10}$ ]

(A)

0.625 \times 1 0^{- 6}

(B)

1.6 \times 1 0^{- 6}

(C)

2.2 \times 1 0^{- 16}

(D)

1.9 \times 1 0^{- 5}

JEE Advanced 2025

LEVELJEE Advanced

The solubility of barium iodate in an aqueous solution prepared by mixing $200 mL$ of $0.010 M$ barium nitrate with $100 mL$ of $0.10 M$ sodium iodate is $X \times 1 0^{- 6} mol dm^{- 3}$ . The value of $X$ is _______. Use: Solubility product constant ( $K_{s p}$ ) of barium iodate = $1.58 \times 1 0^{- 9}$

JEE Advanced 2020

LEVELJEE Advanced

An acidified solution of $0.05 M$ $Zn^{2 +}$ is saturated with $0.1 M$ $H_{2} S$ . What is the minimum molar concentration (M) of $H^{+}$ required to prevent the precipitation of $ZnS$ ? [Use $K_{sp} (ZnS) = 1.25 \times 1 0^{- 22}$ and Overall dissociation constant of $H_{2} S$ , $K_{NET} = K_{1} K_{2} = 1 \times 1 0^{- 21}$ ]

JEE Advanced 2015

LEVELJEE Advanced

Comprehension Passage

When

100 mL

1.0 M

HCl

was mixed with

100 mL

1.0 M

NaOH

in an insulated beaker at constant pressure, a temperature increase of

5.7^{\circ} C

was measured for the beaker and its contents. (Expt-1). Because the enthalpy of neutralisation of a strong acid with a strong base is a constant (

- 57.0 kJ mol^{- 1}

), this experiment could be used to measure the calorimeter constant. In a second experiment (Expt-2),

100 mL

2.0 M

acetic acid (

K_{a} = 2.0 \times 1 0^{- 5}

) was mixed with

100 mL

1.0 M

NaOH

(under identical conditions to (Expt-1)) where a temperature rise of

5.6^{\circ} C

was measured. (Consider heat capacity of all solutions as

4.2 J g^{- 1} K^{- 1}

and density of all solutions as

1.0 g mL^{- 1}

)

Question 1:

Enthalpy of dissociation (in $kJ mol^{- 1}$ ) of acetic acid obtained from the Expt-2 is

The $pH$ of the solution after Expt-2

For the following reaction, the equilibrium constant $K_{c}$ at 298 K is $1.6 \times 1 0^{17}$ . $Fe^{2 +} (aq) + S^{2 -} (aq) ⇌ FeS(s)$ When equal volumes of 0.06 M $Fe^{2 +} (aq)$ and 0.2 M $S^{2 -} (aq)$ solutions are mixed, the equilibrium concentration of $Fe^{2 +} (aq)$ is found to be $Y \times 1 0^{- 17}$ M. The value of Y is ______.

JEE Advanced 2022

LEVELJEE Advanced

A solution is prepared by mixing $0.01 mol$ each of $H_{2} CO_{3}$ , $NaHCO_{3}$ , $Na_{2} CO_{3}$ , and $NaOH$ in $100 mL$ of water. pH of the resulting solution is ______. [Given : $p K_{a 1}$ and $p K_{a 2}$ of $H_{2} CO_{3}$ are $6.37$ and $10.32$ , respectively ; $lo g 2 = 0.30$ ]

JEE Main 2018

LEVELJEE Advanced

An aqueous solution contains an unknown concentration of $Ba^{2 +}$ . When $50 mL$ of a $1 M$ solution of $Na_{2} SO_{4}$ is added, $BaSO_{4}$ just begins to precipitate. The final volume is $500 mL$ . The solubility product of $BaSO_{4}$ is $1 \times 1 0^{- 10}$ . What is the original concentration of $Ba^{2 +}$ ?

(A)

5 \times 1 0^{- 9} M

(B)

2 \times 1 0^{- 9} M

(C)

1.1 \times 1 0^{- 9} M

(D)

1.0 \times 1 0^{- 10} M

JEE Main 2019

LEVELJEE Advanced

What is the molar solubility of $Al(OH)_{3}$ in $0.2 M NaOH$ solution? Given that, solubility product of $Al(OH)_{3} = 2.4 \times 1 0^{- 24}$

(A)

3 \times 1 0^{- 19}

(B)

12 \times 1 0^{- 21}

(C)

3 \times 1 0^{- 22}

(D)

12 \times 1 0^{- 23}

JEE Main 2019

LEVELJEE Advanced

20 mL of 0.1 M $H_{2} SO_{4}$ solution is added to 30 mL of 0.2 M $NH_{4} OH$ solution. The pH of the resultant mixture is [ $pK_{b}$ of $NH_{4} OH = 4.7$ ]

The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively :

(A)

X_{2} Y, 2 \times 1 0^{- 9} M^{3}

(B)

X Y, 2 \times 1 0^{- 6} M^{3}

(C)

X Y_{2}, 1 \times 1 0^{- 9} M^{3}

(D)

X Y_{2}, 4 \times 1 0^{- 9} M^{3}

JEE Main 2021

LEVELJEE Advanced

The solubility of $CdSO_{4}$ in water is $8.0 \times 1 0^{- 4} mol L^{- 1}$ . Its solubility in $0.01 M H_{2} SO_{4}$ solution is ……… $\times 1 0^{- 6} mol L^{- 1}$ . (Round off to the nearest integer) (Assume that, solubility is much less than $0.01 M$ )

JEE Main 2019

LEVELJEE Advanced

The molar solubility of $Cd(OH)_{2}$ is $1.84 \times 1 0^{- 5} m$ in water. The expected solubility of $Cd(OH)_{2}$ in a buffer solution of $pH = 12$ is

(A)

1.84 \times 1 0^{- 9} M

(B)

\frac{2.49}{1.84} \times 1 0^{- 9} M

(C)

6.23 \times 1 0^{- 11} M

(D)

2.49 \times 1 0^{- 10} M

JEE Main 2021

LEVELJEE Advanced

Sulphurous acid ( $H_{2} SO_{3}$ ) has $K_{a_{1}} = 1.7 \times 1 0^{- 2}$ and $K_{a_{2}} = 6.4 \times 1 0^{- 8}$ . The pH of $0.588 M$ is …… (Round off to the nearest integer)

Micro-Topic Strategy Matrix

Ostwald's Dilution Law

Acid Base Concepts

Solubility Product and Common Ion Effect

pH, Buffer and Indicator

Hydrolsis of Salts

Chapter Elite-20 Challenge Zone

List-I

List-II

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Enthalpy of dissociation (in kJ mol−1) of acetic acid obtained from the Expt-2 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The pH of the solution after Expt-2

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } What is the molar solubility of Al(OH)3​ in 0.2 M NaOH solution? Given that, solubility product of Al(OH)3​=2.4×10−24

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 20 mL of 0.1 M H2​SO4​ solution is added to 30 mL of 0.2 M NH4​OH solution. The pH of the resultant mixture is [pKb​ of NH4​OH=4.7]

The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The molar solubility of Cd(OH)2​ is 1.84×10−5 m in water. The expected solubility of Cd(OH)2​ in a buffer solution of pH=12 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Sulphurous acid (H2​SO3​) has Ka1​​=1.7×10−2 and Ka2​​=6.4×10−8. The pH of 0.588 M is …… (Round off to the nearest integer)

Enthalpy of dissociation (in $kJ mol^{- 1}$ ) of acetic acid obtained from the Expt-2 is

The $pH$ of the solution after Expt-2

What is the molar solubility of $Al(OH)_{3}$ in $0.2 M NaOH$ solution? Given that, solubility product of $Al(OH)_{3} = 2.4 \times 1 0^{- 24}$

20 mL of 0.1 M $H_{2} SO_{4}$ solution is added to 30 mL of 0.2 M $NH_{4} OH$ solution. The pH of the resultant mixture is [ $pK_{b}$ of $NH_{4} OH = 4.7$ ]

The molar solubility of $Cd(OH)_{2}$ is $1.84 \times 1 0^{- 5} m$ in water. The expected solubility of $Cd(OH)_{2}$ in a buffer solution of $pH = 12$ is

Sulphurous acid ( $H_{2} SO_{3}$ ) has $K_{a_{1}} = 1.7 \times 1 0^{- 2}$ and $K_{a_{2}} = 6.4 \times 1 0^{- 8}$ . The pH of $0.588 M$ is …… (Round off to the nearest integer)