Chemical & Ionic Equilibrium · JEE Main previous year questions

Consider two Group IV metal ions ${\mathrm{X}}^{2+}$ and ${\mathrm{Y}}^{2+}$. A solution containing $0.01\mathrm{M}{\mathrm{X}}^{2+}$ and $0.01\mathrm{M}{\mathrm{Y}}^{2+}$ is saturated with ${\mathrm{H}}_2\mathrm{S}$. The pH at which the metal sulphide YS will form as a precipitate is ____ . (Nearest integer) (Given: ${\mathrm{K}}_{\mathrm{sp}}(\mathrm{XS})=1\times 10^{-22}$ at $25^{\circ }\mathrm{C}$, ${\mathrm{K}}_{\mathrm{sp}}(\mathrm{YS})=4\times 10^{-16}$ at $25^{\circ }\mathrm{C}$, $[{\mathrm{H}}_2\mathrm{S}]=0.1M$ in solution, ${\mathrm{K}}_{a1}\times {\mathrm{K}}_{a2}({\mathrm{H}}_2\mathrm{S})=1.0\times 10^{-21}$, $\log 2=0.30$, $\log 3=0.48$, $\log 5=0.70$)

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 :

1. A.(i) 1, 2; (ii) 2, 1
2. B.(i) 1, 3; (ii) 2, 1
3. C.(i) 3, 1; (ii) 3, 1
4. D.(i) 4, 1; (ii) 4, 1

1. A.208
2. B.228
3. C.146
4. D.301

For the following gas phase equilibrium reaction at constant temperature, ${\mathrm{NH}}_3(\text{g})\rightleftharpoons 1/2{\mathrm{N}}_2(\text{g})+3/2{\mathrm{H}}_2(\text{g})$ if the total pressure is $\sqrt{3}\text{ atm}$ and the pressure equilibrium constant ($K_p$) is $9\text{ atm}$ , then the degree of dissociation is given as $(x\times 10^{-2}{)}^{-1/2}$. The value of $x$ is ____ . (nearest integer)

It is noticed that ${\text{Pb}}^{2+}$ is more stable than ${\text{Pb}}^{4+}$ but ${\text{Sn}}^{2+}$ is less stable than ${\text{Sn}}^{4+}$. Observe the following reactions. ${\text{PbO}}_2+\text{Pb}\to 2\text{PbO};{\Delta }_r{\text{G}}^{\circ }(1)$ ${\text{SnO}}_2+\text{Sn}\to 2\text{SnO};{\Delta }_r{\text{G}}^{\circ }(2)$ Identify the correct set from the following

1. A.${\Delta }_r{G}^{\circ }(1)>0;{\Delta }_r{G}^{\circ }(2)<0$
2. B.${\Delta }_r{G}^{\circ }(1)<0;{\Delta }_r{G}^{\circ }(2)>0$
3. C.${\Delta }_r{G}^{\circ }(1)<0;{\Delta }_r{G}^{\circ }(2)<0$
4. D.${\Delta }_r{G}^{\circ }(1)>0;{\Delta }_r{G}^{\circ }(2)>0$

1. A.I < II < III < IV
2. B.II < I < III < IV
3. C.III < I < II < IV
4. D.IV < III < II < I

A first row transition metal $(\mathrm{M})$ does not liberate ${\mathrm{H}}_2$ gas from dilute HCl .1 mol of aqueous solution of $\mathrm{MS}{\mathrm{O}}_4$ is treated with excess of aqueous KCN and then ${\mathrm{H}}_2\mathrm{S}(\mathrm{g})$ is passed through the solution. The amount of MS (metal sulphide) formed from the above reaction is ____ mol.

1. A.1
2. B.2
3. C.0
4. D.3

1. A.
2. B.
3. C.
4. D.

Dissociation of a gas ${\mathrm{A}}_2$ takes place according to the following chemical reaction. At equilibrium, the total pressure is 1 bar at 300 K . ${\mathrm{A}}_2(\mathrm{g})\rightleftharpoons 2\mathrm{A}(\mathrm{g})$ The standard Gibbs energy of formation of the involved substances has been provided below: $$\begin{array}{cc}\text{Substance}& \Delta {\mathrm{G}}_{\mathrm{f}}^{\circ }/kJ\mathrm{mo}{\mathrm{l}}^{-1}\\ {\mathrm{A}}_2& -100.00\\ \mathrm{A}& -50.832\end{array}$$ The degree of dissociation of ${\mathrm{A}}_2(\mathrm{g})$ is given by ${\left(x\times 10^{-2}\right)}^{1/2}$ where $x=$ ____. (Nearest integer). [ Given : $\mathrm{R}=8\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1},\log 2=0.3010,\log 3=0.48$ ] Assume degree of dissociation is not negligible.

Consider the following reactions. $\underset{\text{(Hot solution)}}{\mathrm{PbC}{\mathrm{l}}_2}+{\mathrm{K}}_2\mathrm{Cr}{\mathrm{O}}_4\to A+2\mathrm{KCl}$ $A+\mathrm{NaOH}\rightleftharpoons \mathrm{B}+\mathrm{N}{\mathrm{a}}_2\mathrm{Cr}{\mathrm{O}}_4$ $\mathrm{PbS}{\mathrm{O}}_4+4\mathrm{C}{\mathrm{H}}_3\mathrm{COON}{\mathrm{H}}_4\to (\mathrm{N}{\mathrm{H}}_4{)}_2\mathrm{S}{\mathrm{O}}_4+\mathrm{X}$ In the above reactions, A, B and X are respectively.

1. A.$\mathrm{N}{\mathrm{a}}_2[\mathrm{Pb}(\mathrm{OH}{)}_2],\mathrm{PbCr}{\mathrm{O}}_4$ and $[\mathrm{Pb}(\mathrm{N}{\mathrm{H}}_3{)}_4]\mathrm{S}{\mathrm{O}}_4$
2. B.$\mathrm{N}{\mathrm{a}}_2[\mathrm{Pb}(\mathrm{OH}{)}_2],\mathrm{PbCr}{\mathrm{O}}_4$ and $(\mathrm{N}{\mathrm{H}}_4{)}_2[\mathrm{Pb}(\mathrm{C}{\mathrm{H}}_3\mathrm{COO}{)}_4]$
3. C.$\mathrm{PbCr}{\mathrm{O}}_4,\mathrm{N}{\mathrm{a}}_2[\mathrm{Pb}(\mathrm{OH}{)}_4]$ and $(\mathrm{N}{\mathrm{H}}_4{)}_2[\mathrm{Pb}(\mathrm{C}{\mathrm{H}}_3\mathrm{COO}{)}_4]$
4. D.$\mathrm{PbCr}{\mathrm{O}}_4,\mathrm{N}{\mathrm{a}}_2[\mathrm{Pb}(\mathrm{OH}{)}_4]$ and $[\mathrm{Pb}(\mathrm{N}{\mathrm{H}}_3{)}_4]\mathrm{S}{\mathrm{O}}_4$

Given below are two statements : Statement I : The number of pairs among $[\mathrm{Si}{\mathrm{O}}_2,\mathrm{C}{\mathrm{O}}_2],[\mathrm{SnO},\mathrm{Sn}{\mathrm{O}}_2],[\mathrm{PbO},\mathrm{Pb}{\mathrm{O}}_2]$ and $[\mathrm{GeO},\mathrm{Ge}{\mathrm{O}}_2]$, which contain oxides that are both amphoteric is 2 . Statement II : $\mathrm{B}{\mathrm{F}}_3$ is an electron deficient molecule, can act as a Lewis acid, forms adduct with $\mathrm{N}{\mathrm{H}}_3$ and has a trigonal planar geometry. In the light of the above statements, choose the correct answer from the options given below :

1. A.Both Statement I and Statement II are false
2. B.Statement I is false but Statement II is true
3. C.Both Statement I and Statement II are true
4. D.Statement I is true but Statement II is false

1. A.C and E only
2. B.D and E only
3. C.A and D only
4. D.B and C only

$$\text{Nitrobenzene}\underset{\begin{array}{c}(4)\mathrm{B}{\mathrm{r}}_2/{\mathrm{H}}_2\mathrm{O}\\ (5)\mathrm{NaN}{\mathrm{O}}_2/HBr,0-5^{\circ }\mathrm{C}\\ (6)CuBr/NaBr\end{array}}{\overset{\begin{array}{c}(1)\mathrm{B}{\mathrm{r}}_2/FeB{\mathrm{r}}_3/\Delta \\ (2)Sn/HCl/\Delta \\ (3)\text{pH neutralisation}\end{array}}{\to }}\text{Major Product (P)}$$ Consider the above sequence of reactions. The number of bromine atom(s) in the final product (P) will be :

1. A.6
2. B.5
3. C.1
4. D.3

The correct order of reactivity of the following benzyl halides towards reaction with KCN is : a: 4-hydroxybenzyl bromide $(\mathrm{BrC}{\mathrm{H}}_2-{\mathrm{C}}_6{\mathrm{H}}_4-\mathrm{OH}$, para$)$ b: 4-aminobenzyl bromide $(\mathrm{BrC}{\mathrm{H}}_2-{\mathrm{C}}_6{\mathrm{H}}_4-\mathrm{N}{\mathrm{H}}_2$, para$)$ c: 4-nitrobenzyl bromide $(\mathrm{BrC}{\mathrm{H}}_2-{\mathrm{C}}_6{\mathrm{H}}_4-\mathrm{N}{\mathrm{O}}_2$, para$)$ d: 3-nitrobenzyl bromide $(\mathrm{BrC}{\mathrm{H}}_2-{\mathrm{C}}_6{\mathrm{H}}_4-\mathrm{N}{\mathrm{O}}_2$, meta$)$

1. A.a > b > c > d
2. B.b > a > d > c
3. C.b > a > c > d
4. D.a > b > d > c

MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K. $\mathrm{MX}(\mathrm{s})\rightleftharpoons {\mathrm{M}}^{+}(\mathrm{aq})+{\mathrm{X}}^{-}(\mathrm{aq});{\mathrm{K}}_{\mathrm{sp}}=10^{-10}$ If the standard reduction potential for ${\mathrm{M}}^{+}(\mathrm{aq})+{\mathrm{e}}^{-}\to \mathrm{M}(\mathrm{s})$ is $\left({\mathrm{E}}_{{\mathrm{M}}^{+}/M}^{\ominus }\right)=0.79\mathrm{V}$, then the value of the standard reduction potential for the metal/metal insoluble salt electrode ${\mathrm{E}}_{{\mathrm{X}}^{-}/MX(\mathrm{s})/M}^{\ominus }$ is ____ mV. (nearest integer) [Given: $\frac{2.303RT}{F}=0.059$ V]

1. A.
2. B.
3. C.
4. D.

Consider the following half cell reaction $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_7^{2-}(\mathrm{aq})+6{\mathrm{e}}^{-}+14{\mathrm{H}}^{+}(\mathrm{aq})\to 2C{\mathrm{r}}^{3+}(\mathrm{aq})+7{\mathrm{H}}_2\mathrm{O}(\mathrm{\ell })$ The reaction was conducted with the ratio of $\frac{[{\mathrm{Cr}}^{3+}{]}^2}{[{\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}]}=10^{-6}$. The pH value at which the EMF of the half cell will become zero is ____ . (nearest integer value) $[\text{Given: standard half cell reduction potential }{E}_{\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_7^{2-},{\mathrm{H}}^{+}/C{\mathrm{r}}^{3+}}^{\circ }=1.33\mathrm{V},\frac{2.303RT}{F}=0.059V.]$

The equilibrium constant for decomposition of ${\mathrm{H}}_2\mathrm{O}(\mathrm{g})$ ${\mathrm{H}}_2\mathrm{O}(\mathrm{g})\rightleftharpoons {\mathrm{H}}_2(\mathrm{g})+\frac{1}{2}{\mathrm{O}}_2(\mathrm{g})(\Delta G^{\circ }=92.34\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1})$ is $8.0\times 10^{-3}$ at $2300\mathrm{K}$ 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]

The pH of a 0.01 M weak acid HX (${\mathrm{K}}_a=4\times 10^{-10}$) is found to be 5 . Now the acid solution is diluted with excess of water so that the pH of the solution changes to 6 . The new concentration of the diluted weak acid is given as $x\times 10^{-4}\mathrm{M}$. The value of $x$ is ____ (nearest integer)

The molar conductance of an infinitely dilute solution of ammonium chloride was found to be $185{\mathrm{S}\mathrm{cm}}^2{\mathrm{mol}}^{-1}$ and the ionic conductance of hydroxyl and chloride ions are $170$ and $70{\mathrm{S}\mathrm{cm}}^2{\mathrm{mol}}^{-1}$, respectively. If molar conductance of $0.02\mathrm{M}$ solution of ammonium hydroxide is $85.5{\mathrm{S}\mathrm{cm}}^2{\mathrm{mol}}^{-1}$, its degree of dissociation is given by $x\times 10^{-1}$. The value of $x$ is $\underline{}$. (Nearest integer)

$x\mathrm{mg}$ of ${\mathrm{Mg}(\mathrm{OH})}_2(\text{molar mass}=58)$ is required to be dissolved in $1.0\mathrm{L}$ of water to produce a $\mathrm{pH}$ of $10.0$ at $298\mathrm{K}$. The value of $x$ is $\underline{}\mathrm{mg}$. (Nearest integer) (Given : ${\mathrm{Mg}(\mathrm{OH})}_2$ is assumed to dissociate completely in ${\mathrm{H}}_2\mathrm{O}$ )

In the following system, $\mathrm{PC}{\mathrm{l}}_5(\mathrm{g})\rightleftharpoons \mathrm{PC}{\mathrm{l}}_3(\mathrm{g})+\mathrm{C}{\mathrm{l}}_2(\mathrm{g})$ at equilibrium, upon addition of xenon gas at constant $T$ and $p$, the concentration of

1. A.$\mathrm{PC}{\mathrm{l}}_5$, $\mathrm{PC}{\mathrm{l}}_3$ and $\mathrm{C}{\mathrm{l}}_2$ remain constant
2. B.$\mathrm{PC}{\mathrm{l}}_3$ will increase
3. C.$\mathrm{C}{\mathrm{l}}_2$ will decrease
4. D.$\mathrm{PC}{\mathrm{l}}_5$ will increase

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 homogeneous 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

1. A.Statement I is true but Statement II is false
2. B.Statement I is false but Statement II is true
3. C.Both Statement I and Statement II are true
4. D.Both Statement I and Statement II are false

Given below are two statements: Statement I : When a system containing ice in equilibrium with water (liquid) is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted. Statement II : At melting point of ice, there is absorption of heat in order to overcome intermolecular forces of attraction within the molecules of water in ice and kinetic energy of molecules is not increased at melting point. In the light of the above statements, choose the correct answer from the options given below

1. A.Both Statement I and Statement II are false
2. B.Statement I is true but Statement II is false
3. C.Both Statement I and Statement II are true
4. D.Statement I is false but Statement II is true

If equal volumes of $A{B}_2$ and $XY$ (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $A{Y}_2$ at $300\text{ K}$ ? (Given ${\mathrm{K}}_{\mathrm{sp}}$ ( at $300\text{ K}$ ) for $A{Y}_2=5.2\times 10^{-7}$ )

1. A.$2.0\times 10^{-4}\text{ M }A{B}_2,0.8\times 10^{-3}\text{ M }XY$
2. B.$2.0\times 10^{-2}\text{ M }A{B}_2,2.0\times 10^{-2}\text{ M }XY$
3. C.$1.5\times 10^{-4}\text{ M }A{B}_2,1.5\times 10^{-3}\text{ M }XY$
4. D.$3.6\times 10^{-3}\text{ M }A{B}_2,5.0\times 10^{-4}\text{ M }XY$