Chemical & Ionic Equilibrium · JEE Main previous year questions

At $25^{\circ }\mathrm{C}$, the solubility product of $\mathrm{Mg}(\mathrm{OH}{)}_2$ is $1.0\times 10^{-11}$. At which pH, will $\mathrm{M}{\mathrm{g}}^{2+}$ ions start precipitating in the form of $\mathrm{Mg}(\mathrm{OH}{)}_2$ from a solution of 0.001 M $\mathrm{M}{\mathrm{g}}^{2+}$ ions?

1. A.9
2. B.10
3. C.11
4. D.8

The correct order of increasing basicity of the given conjugate bases ($\mathrm{R}=\mathrm{C}{\mathrm{H}}_3$) is

1. A.$R\mathrm{CO}\overline{\mathrm{O}}<HC\equiv \overline{C}<\overline{R}<\overline{\mathrm{N}}{\mathrm{H}}_2$
2. B.$\overline{R}<HC\equiv \overline{C}<R\mathrm{CO}\overline{\mathrm{O}}<\overline{\mathrm{N}}{\mathrm{H}}_2$
3. C.$R\mathrm{CO}\overline{\mathrm{O}}<\overline{\mathrm{N}}{\mathrm{H}}_2<HC\equiv \overline{C}<\overline{R}$
4. D.$R\mathrm{CO}\overline{\mathrm{O}}<HC\equiv \overline{C}<\overline{\mathrm{N}}{\mathrm{H}}_2<\overline{R}$

Consider the reaction : $\mathrm{C}{\mathrm{l}}_2(\mathrm{aq})+{\mathrm{H}}_2\mathrm{S}(\mathrm{aq})\to \mathrm{S}(\mathrm{s})+2{\mathrm{H}}^{+}(\mathrm{aq})+2C{\mathrm{l}}^{-}(\mathrm{aq})$ The rate equation for this reaction is rate = $\mathrm{k}[\mathrm{C}{\mathrm{l}}_2][{\mathrm{H}}_2\mathrm{S}]$ Which of these mechanisms is/are consistent with this rate equation? (A) $\mathrm{C}{\mathrm{l}}_2+{\mathrm{H}}_2\mathrm{S}\to {\mathrm{H}}^{+}+\mathrm{C}{\mathrm{l}}^{-}+\mathrm{C}{\mathrm{l}}^{+}+\mathrm{H}{\mathrm{S}}^{-}$ (slow) $\mathrm{C}{\mathrm{l}}^{+}+\mathrm{H}{\mathrm{S}}^{-}\to {\mathrm{H}}^{+}+\mathrm{C}{\mathrm{l}}^{-}+\mathrm{S}$ (fast) (B) ${\mathrm{H}}_2\mathrm{S}\iff {\mathrm{H}}^{+}+\mathrm{H}{\mathrm{S}}^{-}$ (fast equilibrium) $\mathrm{C}{\mathrm{l}}_2+\mathrm{H}{\mathrm{S}}^{-}\to 2C{\mathrm{l}}^{-}+{\mathrm{H}}^{+}+\mathrm{S}$ (slow)

1. A.B only
2. B.Both A and B
3. C.Neither A nor B
4. D.A only

Solid $\mathrm{Ba}(\mathrm{N}{\mathrm{O}}_3{)}_2$ is gradually dissolved in a $1.0\times 10^{-4}\mathrm{M}$ $\mathrm{N}{\mathrm{a}}_2\mathrm{C}{\mathrm{O}}_3$ solution. At what concentration of $\mathrm{B}{\mathrm{a}}^{2+}$ will a precipitate begin to form ? (${\mathrm{K}}_{\mathrm{sp}}$ for $\mathrm{BaC}{\mathrm{O}}_3=5.1\times 10^{-9}$)

1. A.$5.1\times 10^{-5}\mathrm{M}$
2. B.$8.1\times 10^{-8}\mathrm{M}$
3. C.$8.1\times 10^{-7}\mathrm{M}$
4. D.$4.1\times 10^{-5}\mathrm{M}$

Phosphorus pentachloride dissociates as follows, in a closed reaction vessel $$\mathrm{PC}{\mathrm{l}}_5(\mathrm{g})\rightleftharpoons \mathrm{PC}{\mathrm{l}}_3(\mathrm{g})+\mathrm{C}{\mathrm{l}}_2(\mathrm{g})$$ If total pressure at equilibrium of the reaction mixture is P and degree of dissociation of $\mathrm{PC}{\mathrm{l}}_5$ is x, the partial pressure of $\mathrm{PC}{\mathrm{l}}_3$ will be

1. A.$(\frac{x}{x+1})P$
2. B.$(\frac{2x}{1-x})P$
3. C.$(\frac{x}{x-1})P$
4. D.$(\frac{x}{1-x})P$

The equilibrium constant for the reaction $$\mathrm{S}{\mathrm{O}}_3(\mathrm{g})\rightleftharpoons \mathrm{S}{\mathrm{O}}_2(\mathrm{g})+\frac{1}{2}{\mathrm{O}}_2(\mathrm{g})$$ is ${\mathrm{K}}_{\mathrm{c}}=4.9\times 10^{-2}$. The value of ${\mathrm{K}}_{\mathrm{c}}$ for the reaction $$2S{\mathrm{O}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\rightleftharpoons 2S{\mathrm{O}}_3(\mathrm{g})$$ will be :

1. A.416
2. B.$9.8\times 10^{-2}$
3. C.$4.9\times 10^{-2}$
4. D.$2.40\times 10^{-3}$

Given the data at $25^{\circ }\mathrm{C}$, $$\mathrm{Ag}+{\mathrm{I}}^{-}\to \mathrm{AgI}+{\mathrm{e}}^{-},{\mathrm{E}}^{\mathrm{o}}=0.152\mathrm{V}$$ $$\mathrm{Ag}\to \mathrm{A}{\mathrm{g}}^{+}+{\mathrm{e}}^{-},{\mathrm{E}}^{\mathrm{o}}=-0.800\mathrm{V}$$ What is the value of $\log {\mathrm{K}}_{\mathrm{sp}}$ for AgI? ($2.303RT/F=0.059\mathrm{V}$)

1. A.$-8.12$
2. B.$+8.612$
3. C.$-37.83$
4. D.$-16.13$

The correct order of increasing acid strength of the compounds (A) $\mathrm{C}{\mathrm{H}}_3\mathrm{C}{\mathrm{O}}_2\mathrm{H}$ (B) $\mathrm{MeOC}{\mathrm{H}}_2\mathrm{C}{\mathrm{O}}_2\mathrm{H}$ (C) $\mathrm{C}{\mathrm{F}}_3\mathrm{C}{\mathrm{O}}_2\mathrm{H}$ (D) $\mathrm{M}{\mathrm{e}}_2\mathrm{CH}-\mathrm{C}{\mathrm{O}}_2\mathrm{H}$

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

If $\alpha$ is the degree of dissociation of $\mathrm{N}{\mathrm{a}}_2\mathrm{S}{\mathrm{O}}_4$, the vant Hoff's factor (i) used for calculating the molecular mass is :

1. A.$1+\alpha$
2. B.$1+2\alpha$
3. C.$1-\alpha$
4. D.$1-2\alpha$

The solubility product of a salt having general formula $\mathrm{M}{\mathrm{X}}_2$, in water is: $4\times 10^{-12}$. The concentration of ${\mathrm{M}}^{2+}$ ions in the aqueous solution of the salt is :

1. A.$2.0\times 10^{-6}\mathrm{M}$
2. B.$4.0\times 10^{-10}\mathrm{M}$
3. C.$1.0\times 10^{-4}\mathrm{M}$
4. D.$1.6\times 10^{-4}\mathrm{M}$

For the reaction $2\mathrm{N}{\mathrm{O}}_2(\mathrm{g})\rightleftharpoons 2NO(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})$, $({\mathrm{K}}_{\mathrm{c}}=1.8\times 10^{-6}\text{ at }184^{\circ }\mathrm{C})$ $(R=0.0831kJ/(mol.\mathrm{K}))$ When ${\mathrm{K}}_{\mathrm{p}}$ and ${\mathrm{K}}_{\mathrm{c}}$ are compared at $184^{\circ }\mathrm{C}$, it is found that :

1. A.${\mathrm{K}}_{\mathrm{p}}$ is greater than ${\mathrm{K}}_{\mathrm{c}}$
2. B.${\mathrm{K}}_{\mathrm{p}}$ is less than ${\mathrm{K}}_{\mathrm{c}}$
3. C.${\mathrm{K}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{c}}$
4. D.Whether ${\mathrm{K}}_{\mathrm{p}}$ is greater than, less than or equal to ${\mathrm{K}}_{\mathrm{c}}$ depends upon the total gas pressure

Hydrogen ion concentration in $\mathrm{mol}/\mathrm{L}$ in a solution of $\mathrm{pH}=5.4$ will be :

1. A.$3.98\times 10^{-6}$
2. B.$3.68\times 10^{-6}$
3. C.$3.88\times 10^6$
4. D.$3.98\times 10^8$

What is the conjugate base of $\mathrm{O}{\mathrm{H}}^{-}$?

1. A.${\mathrm{O}}_2$
2. B.${\mathrm{H}}_2\mathrm{O}$
3. C.${\mathrm{O}}^{-}$
4. D.${\mathrm{O}}^{-2}$

An amount of solid $\mathrm{N}{\mathrm{H}}_4\mathrm{HS}$ is placed in a flask already containing ammonia gas at a certain temperature and $0.50\mathrm{atm}$ pressure. Ammonium hydrogen sulphide decomposes to yield $\mathrm{N}{\mathrm{H}}_3$ and ${\mathrm{H}}_2\mathrm{S}$ gases in the flask. When the decomposition reaction reaches equilibrium, the total pressure in the flask rises to $0.84\mathrm{atm}$. The equilibrium constant for $\mathrm{N}{\mathrm{H}}_4\mathrm{HS}$ decomposition at this temperature is :

1. A.$0.30$
2. B.$0.11$
3. C.$0.17$
4. D.$0.18$

$$\begin{array}{llllll}\text{Electrolyte:}& \mathrm{KCl}& \mathrm{KN}{\mathrm{O}}_3& \mathrm{HCl}& \mathrm{NaOAc}& \mathrm{NaCl}\\ {\wedge }^{\infty }(\mathrm{Sc}{\mathrm{m}}^2\mathrm{mo}{\mathrm{l}}^{-1}):& 149.9& 145& 426.2& 91& 126.5\end{array}$$ Calculate ${\wedge }_{HOAc}^{\infty }$ using appropriate molar conductances of the electrolytes listed above at infinite dilution in ${\mathrm{H}}_2\mathrm{O}$ at $25^{\circ }\mathrm{C}$

1. A.$517.2$
2. B.$552.7$
3. C.$390.7$
4. D.$217.5$

Among the following acids which has the lowest $\mathrm{p}{\mathrm{K}}_{\mathrm{a}}$ value?

1. A.$\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$
2. B.$\mathrm{HCOOH}$
3. C.$(\mathrm{C}{\mathrm{H}}_3{)}_2\mathrm{COOH}$
4. D.$\mathrm{C}{\mathrm{H}}_3\mathrm{C}{\mathrm{H}}_2\mathrm{COOH}$

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

Among $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3,\mathrm{Si}{\mathrm{O}}_2,{\mathrm{P}}_2{\mathrm{O}}_3$ and $\mathrm{S}{\mathrm{O}}_2$ the correct order of acid strength is

1. A.$\mathrm{S}{\mathrm{O}}_2<{\mathrm{P}}_2{\mathrm{O}}_3<\mathrm{Si}{\mathrm{O}}_2<\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$
2. B.$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3<\mathrm{Si}{\mathrm{O}}_2<{\mathrm{P}}_2{\mathrm{O}}_3<\mathrm{S}{\mathrm{O}}_2$
3. C.$\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3<\mathrm{Si}{\mathrm{O}}_2<\mathrm{S}{\mathrm{O}}_2<{\mathrm{P}}_2{\mathrm{O}}_3$
4. D.$\mathrm{Si}{\mathrm{O}}_2<\mathrm{S}{\mathrm{O}}_2<\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3<{\mathrm{P}}_2{\mathrm{O}}_3$

The conjugate base of ${\mathrm{H}}_2\mathrm{P}{\mathrm{O}}_4^{-}$ is :

1. A.$\mathrm{P}{\mathrm{O}}_4^{3-}$
2. B.$\mathrm{HP}{\mathrm{O}}_4^{2-}$
3. C.${\mathrm{H}}_3\mathrm{P}{\mathrm{O}}_4$
4. D.${\mathrm{P}}_2{\mathrm{O}}_5$

What is the equilibrium expression for the reaction ${\mathrm{P}}_4(\mathrm{s})+5{\mathrm{O}}_2\leftrightharpoons {\mathrm{P}}_4{\mathrm{O}}_{10}(\mathrm{s})$?

1. A.$K_c=[{\mathrm{P}}_4{\mathrm{O}}_{10}]/5[{\mathrm{P}}_4][{\mathrm{O}}_2]$
2. B.$K_c=1/[{\mathrm{O}}_2{]}^5$
3. C.$K_c=[{\mathrm{P}}_4{\mathrm{O}}_{10}]/[{\mathrm{P}}_4][{\mathrm{O}}_2{]}^5$
4. D.$K_c=[{\mathrm{O}}_2{]}^5$

The equilibrium constant for the reaction ${\mathrm{N}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\leftrightharpoons 2NO(\mathrm{g})$ at temperature T is $4\times 10^{-4}$. The value of $K_c$ for the reaction $\mathrm{NO}(\mathrm{g})\leftrightharpoons \frac{1}{2}{\mathrm{N}}_2(\mathrm{g})+\frac{1}{2}{\mathrm{O}}_2(\mathrm{g})$ at the same temperature is :

1. A.$2.5\times 10^2$
2. B.$4\times 10^{-4}$
3. C.50
4. D.0.02

The molar solubility (in $\mathrm{mol}{\mathrm{L}}^{-1}$) of a sparingly soluble salt $\mathrm{M}{\mathrm{X}}_4$ is "s". The corresponding solubility product is $K_{sp}$. 's' is given in terms of $K_{sp}$ by the relation :

1. A.$s=(256K_{sp}{)}^{1/5}$
2. B.$s=(128K_{sp}{)}^{1/4}$
3. C.$s=(K_{sp}/128{)}^{1/4}$
4. D.$s=(K_{sp}/256{)}^{1/5}$

The standard e.m.f of a cell, involving one electron change is found to be 0.591 V at $25^{\circ }\mathrm{C}$. The equilibrium constant of the reaction is (F = 96,500 $\mathrm{C}\mathrm{mo}{\mathrm{l}}^{-1}$: R = 8.314 $\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$)

1. A.$1.0\times 10^1$
2. B.$1.0\times 10^{30}$
3. C.$1.0\times 10^{10}$
4. D.$1.0\times 10^5$

The limiting molar conductivities ${\Lambda }^{\circ }$ for NaCl, KBr and KCl are 126, 152 and 150 $\mathrm{S}\mathrm{c}{\mathrm{m}}^2\mathrm{mo}{\mathrm{l}}^{-1}$ respectively. The ${\Lambda }^{\circ }$ for NaBr is

1. A.128 $\mathrm{S}\mathrm{c}{\mathrm{m}}^2\mathrm{mo}{\mathrm{l}}^{-1}$
2. B.278 $\mathrm{S}\mathrm{c}{\mathrm{m}}^2\mathrm{mo}{\mathrm{l}}^{-1}$
3. C.176 $\mathrm{S}\mathrm{c}{\mathrm{m}}^2\mathrm{mo}{\mathrm{l}}^{-1}$
4. D.302 $\mathrm{S}\mathrm{c}{\mathrm{m}}^2\mathrm{mo}{\mathrm{l}}^{-1}$

Species acting as both Bronsted acid and base is :

1. A.$(\mathrm{HS}{\mathrm{O}}_4{)}^{-1}$
2. B.$\mathrm{N}{\mathrm{a}}_2\mathrm{C}{\mathrm{O}}_3$
3. C.$\mathrm{N}{\mathrm{H}}_3$
4. D.$\mathrm{O}{\mathrm{H}}^{-1}$