Equilibrium practice · Hard

Assertion :- At $25^{\circ} \mathrm{C}$ the pH of $10^{-8} \mathrm{~M} \, {HCl}$ is 8.

Reason :- pH of acidic solution is always below 7 at $25^{\circ} \mathrm{C}.$

Acetic acid and propionic acid have ${K_a}$ values $1.75 \times {10^{ - 5}}$ and $1.3 \times {10^{ - 5}}$ respectively at a certain temperature. An equimolar solution of a mixture of the two acids is partially neutralized by$\mathrm{NaOH}\mathrm{.}$. How is the ratio of the contents of acetate and propionate ions related to the ${K_a}$ values and the molarity?

${K_{SP}}$ of $M{X_4}$ and solubility of $M{X_4}$ (S mol/L), is related by

If $K_{s p}$ of $\mathrm{ZnS}$ is $1.0 \times 10^{-21}$, the minimum volume of water is required for the dissolution of $0.097 \mathrm{~g} \mathrm{~ZnS}$ is :

For the reaction taking place at certain temperature $\mathrm{NH}_2 \mathrm{COONH}_4(\mathrm{s}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{g})+\mathrm{CO}_2(\mathrm{g})$ If equilibrium pressure os $3 \mathrm{X}$ bar then $\Delta_\mathrm{t} \mathrm{G}^{\circ}$ would be

$A\left( g \right) + 3B\left( g \right) \rightleftharpoons 4C\left( g \right)$ starting concentration of $A$ is equal to $B$, equilibrium concentration of $A$ and $C$ are same then ${K_C} =$

Assertion :- Boric acid behaves as a weak monobasic acid.

Reason :- Boric acid contains hydrogen bonds in its structure.

What mass of 95% pure $CaC{O_3}$ will be required to neutralise 50 mL of 0.5 m HCl solution according to the following reaction?
$CaC{O_3} + 2HC{l_{(aq)}} \to CaC{l_{2(aq)}} + C{O_{2(g)}} + 2{H_2}{O_{(l)}}$
[Calculate upto second place of decimal point]

The silver ion in a solution is precipitated by the addition of
chloride ion.
$\mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{AgCl}(s), K=1 \times 10^{10}$.
The final volume of the solution is $500 \mathrm{~mL}$. At a point when not more than $0.10 \mathrm{~mg}$ of $\mathrm{Ag}^{+}$ion remains unprecipitated $[\mathrm{Cl^-}]$ ion is

In a $10.0 \mathrm{~L}$ container, an equilibrium was established between $\mathrm{SO}_3, \mathrm{SO}_2$ and $\mathrm{O}_2$ gases, by starting with $\mathrm{SO}_3$ only. The density of equilibrium mixture was found to be $16 \mathrm{~g/litre}$ at a temperature of $\frac{900}{0.0821} \mathrm{~K}.$ If the degree of dissociation of $\mathrm{SO}_3$ is $40 \%,$ then the value of $K_{{P}}$ (in atm) for the reaction $2 \mathrm{SO}_3(\mathrm{g})\rightleftharpoons 2 \mathrm{SO}_2(\mathrm{g})+\mathrm{O}_2(\mathrm{g})$ is

A buffer solution is $0.25 \mathrm{~M}-\mathrm{CH}_3 \mathrm{COOH}+0.15 \mathrm{~M}-\mathrm{CH}_3 \mathrm{COONa},$ saturated in $\mathrm{H}_2 \mathrm{S}(0.1 \mathrm{~M})$ and has $\left[\mathrm{Mn}^{2+}\right]=0.04 \mathrm{~M}, K_{\mathrm{a}}\left(\mathrm{CH}_3 \mathrm{COOH}\right)=2.0 \times 10^{-5},$ $K_{\mathrm{a}}\left(\mathrm{H}_2 \mathrm{S}\right)=1.0 \times 10^{-21}$ and $K_{\mathrm{sp}}(\mathrm{MnS})=2.5 \times 10^{-13}.$
Which buffer component should be increased in concentration and to which minimum value to just start precipitation of $\mathrm{MnS}?$

At $700 \mathrm{~K}$ and 350 bar, a $1: 3$ mixture of $\mathrm{N}_2(g)$ and $\mathrm{H}_2(g)$ reacts to form an equilibrium mixture containing $X\left(\mathrm{NH}_3\right)=0.50$. Assuming ideal behaviour $K_p$ for the equilibrium reaction, $\mathrm{N}_2(g)+3 \mathrm{H}_2(g) \rightleftharpoons 2 \mathrm{NH}_3(g)$ is

$2 A=B, K_{\text {eq }}=X$
$2 B \rightleftharpoons C ; K_{\text {eq }}=Y$
$D\rightleftharpoons C, {K}_{\text {eq }}=Z$
Equilibrium constant for the reaction $D \rightleftharpoons 4 A$ is

Benzoic acid $\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{COOH}, 12 \mathrm{~g} \mathrm{~mol}^{-1}\right)$ forms dimer in benzene solvent
$\mathrm{C}_6 \mathrm{H}_5 \mathrm{COOH} \rightleftharpoons \frac{1}{2}\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{COOH}\right)_2$
Vapour density of a mixture of $A$ and $B$ is found to be 91.5 . If to initially $(A)=1.0 \mathrm{M}, K_c$ at equilibrium is

An amount of $2.0 \mathrm{~M}$ solution of $\mathrm{Na}_2 \mathrm{CO}_3$ is boiled in a closed container with excess of $\mathrm{CaF}_2.$ Very little amount of $\mathrm{CaCO}_3$ and $\mathrm{NaF}$ are formed. If the solubility product of $\mathrm{CaCO}_3$ is '$x$' and the molar solubility of $\mathrm{CaF}_2$ is '$y$', the molar concentration of $\mathrm{F}^{-}$in the resulting solution after equilibrium is attained is

If solubility product of $Z{r_3}{(P{O_4})_4}$ is denoted by ${K_{sp}}$ and its molar solubility is denoted by $S$, then which of the following relation between $S$ and ${K_{sp}}$ is correct?

A volume of $1.0 \mathrm{~L}$ of solution which was in equilibrium with solid mixture of ${AgCl}$ and ${Ag}_2 {CrO}_4$ was found to contain $1 \times 10^{-4}$ moles of ${Ag}^{+}$ ions, $1.0 \times 10^{-6}$ moles of ${Cl}^{-}$ ions and $8.0 \times 10^{-4}$ moles of ${CrO}_4{ }^{2-}$ ions. The ${Ag}^{+}$ ions are added slowly to the above mixture (keeping the volume constant) till $8.0 \times 10^{-7}$ moles of ${AgCl}$ got precipitated. How many moles of ${Ag}_2 {CrO}_4$ were precipitated simultaneously?

Given below are two statements: One is labelled as Assertion A and the other labelled as Reason R.
Assertion A: During the boiling of water having temporary hardness, $Mg{(HC{O_3})_2}$ is converted to $MgC{O_3}$.
Reason R The solubility product of $Mg{(OH)_2}$ is greater than that of $MgC{O_3}$.
In the light of the above statements, choose the most appropriate answer from the options given below

At a certain temperature, $K_{\mathrm{P}}$ for the dissociation of solid $\mathrm{CaCO}_3$ is $4.5 \times 10^{-2}$ atm and for the reaction $\mathrm{C}(\mathrm{s})+\mathrm{CO}_2(\mathrm{g}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{g}),$ the $K_{\mathrm{P}}$ value is $2.0 \mathrm{~atm}.$ The pressure of carbon monoxide at this temperature, when solid carbon $\mathrm{CaO}$ and $\mathrm{CaCO}_3$ are mixed together and allowed to attain equilibrium is

$\mathrm{SO}_3(g)$ is partially dissociated into $\mathrm{SO}_2(g)$ and $\mathrm{O}_2(g)$ at $900 \mathrm{~K}$ and $1 \mathrm{~atm}$ as:
$\mathrm{SO}_3(g) \rightleftharpoons \mathrm{SO}_2(g)+\frac{1}{2} \mathrm{O}_2(g)$

The density of the equilibrium mixture was found to be $0.866 \mathrm{~g} \mathrm{~dm}^{-3}$. Thus, degree dissociation of $\mathrm{SO}_3(\mathrm{~g})$. is

Equilibrium constants ${K_1}$ and ${K_2}$  for the following equilibria are related as :
$\mathrm{NO}\left( \mathrm{g} \right) + \frac{1}{2}{\mathrm{O}_2}\left( \mathrm{g} \right)\leftrightharpoons\mathrm{N}{\mathrm{O}_2}\left( \mathrm{g} \right);{K_1}$
$2\mathrm{N}{\mathrm{O}_2}\left( \mathrm{g} \right)\leftrightharpoons2\mathrm{NO}\left( \mathrm{g} \right) + {\mathrm{O}_2}\left( \mathrm{g} \right);{K_2}$

Solid ${Ca}\left({HCO}_3\right)_2$ decomposes as
${Ca}\left({HCO}_3\right)_2({~s}) \rightleftharpoons {CaCO}_3({~s})+{CO}_2({~g})+{H}_2 {O}({g})$

If the total pressure is 0.2 bar at $420 {~K}$, what is the standard free energy change for the given reaction $\left(\Delta_r G^{\circ}\right)$ ?

The solubility product of $Cr{\left( {OH} \right)_3}$ at 298 K is $6.0 \times {10^{ - 31}}$. The concentration of hydroxide ions in a saturated solution of $Cr{\left( {OH} \right)_3}$ will be

$\mathrm{pH}$ of a saturated solution of silver salt of monobasic acid $\mathrm{HA}$ is found to be 9. Select the option(s) which is / are correct. Given : $\mathrm{K}_{\mathrm{a}}(\mathrm{HA})=10^{-10}$
I) Solubility of the silver salt is $1.1 \times 10^{-5} \mathrm{~mol} /$ lit
II) Solubility product of the silver salt is $1.1 \times 10^{-11} \mathrm{~M}^2$
III) Concentration of $\mathrm{Ag}^{+}$ in the solution will be greater than that of $\mathrm{A}^{-}$

The acid ionization constant of ${Zn}^{2+}$ is $2.0 \times 10^{-10}.$ What is the $\mathrm{pH}$ of $0.001 \mathrm{~M}$ solution of ${ZnCl}_2?$ $(\log 2=0.3)$

The solubility product of $\mathrm{SrF}_2$ in water is $8 \times 10^{-10}$. Find its solubility in $0.1 \mathrm{~M} \mathrm{~NaF}$ aqueous solution.

What is the molarity of $\mathrm{F}^{-}$in a saturated solution of $\operatorname{InF}_3$ ? $\left(K_{s p}=7.9 \times 10^{-10}\right)$

Consider the following statements.
I) The pH of a mixture containing 400 mL of $\;0.1\;M\;{H_2}S{O_4}$ and 400 mL of $\;0.1\;M\;NaOH$ will be approximately 1.3
II) Ionic product of water is temperature dependent.
III) A monobasic acid with ${K_a} = {10^{ - 5}}$ has a $pH = 5.$ The degree of dissociation of this acid is 50%.
IV) The Le-Chatelier’s principle is not applicable to common-ion effect.
The correct statements are