Embibe Experts Solutions for Chapter: Equilibrium, Exercise 1: JEE Advanced Paper 2 - 2016

A solution of $0.1 \mathrm{M}$ weak base $\left(\mathrm{B}\right)$ is titrated with $0.1 \mathrm{M}$ of a strong acid $\left(\mathrm{HA}\right)$. The variation of $\mathrm{pH}$ of the solution with the volume of $\mathrm{HA}$ added is shown in the figure below. What is the ${\mathrm{pK}}_{\mathrm{b}}$ of the base? The neutralisation reaction is given by $\mathrm{B}+\mathrm{HA}\to {\mathrm{BH}}^{+}+{\mathrm{A}}^{-}$.

An acidified solution of $0.05 \mathrm{M} {\mathrm{Zn}}^{2+}$ is saturated with $0.1 \mathrm{M} {\mathrm{H}}_2\mathrm{S}$. What is the minimum molar concentration $\left(\mathrm{M}\right)$ of ${\mathrm{H}}^{+}$ required to prevent the precipitation of $\mathrm{ZnS}$? Use ${\mathrm{K}}_{\mathrm{sp}}\left(\mathrm{ZnS}\right)=1.25\times {10}^{-22}$ and overall dissociation constant of ${\mathrm{H}}_2\mathrm{S}, {\mathrm{K}}_{\mathrm{NET}}={\mathrm{K}}_1{\mathrm{K}}_2=1\times {10}^{-21}$

Consider an electrochemical cell: $\mathrm{A}\left(\mathrm{s}\right)\mathrm{ }\left| {\mathrm{A}}^{\mathrm{n}+}\mathrm{ }\left(\mathrm{aq}, 2 \mathrm{M}\right)\mathrm{ }\right|\left| {\mathrm{B}}^{2\mathrm{n}+}\left(\mathrm{aq}, 1 \mathrm{M}\right)\mathrm{ }\right| \mathrm{B}\left(\mathrm{s}\right)$. The value of ${\mathrm{\Delta H}}^{\mathrm{o}}$ for the cell reaction is twice that of ${\mathrm{\Delta G}}^{\mathrm{o}}$ at $300 \mathrm{K}\mathrm{.}$ If the emf of the cell is zero, the magnitude of $\mathrm{\Delta }{\text{S}}^o$ $\left(\mathrm{in} {\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}\right)$ of the cell reaction per mole of $\mathrm{B}$ formed at $300 \mathrm{K}$ is ____ ${\mathrm{Jmol}}^{-1}{\mathrm{K}}^{-1}$. (Give answer after rounding off to the nearest integer value.)
(Given: R $=\hspace{0.33em}8.3\hspace{0.33em}{\mathrm{JK}}^{-\mathrm{1}}{\mathrm{mol}}^{-1}.$ $\mathrm{H},\mathrm{\hspace{0.33em}}\mathrm{S}$ and $\mathrm{G}$ are enthalpy, entropy and Gibbs energy, respectively.)

When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of ${5.7}^{\mathrm{o}}\mathrm{C}$ was measured for the beaker and its contents (Expt.1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant $(-57.0\mathrm{ }\mathrm{k}\mathrm{J}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1})$ , this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid $({\mathrm{K}}_{\mathrm{a}}=2.0\times {10}^{-5})$ was mixed with 100 mL of 1.0 M NaOH (under identical conditions to Expt. 1) where a temperature rise of ${5.6}^{\mathrm{o}}\mathrm{C}$ was measured. (Consider heat capacity of all solutions as $4.2\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{g}}^{-1}\mathrm{ }{\mathrm{K}}^{-1}$ and density of all solutions as $1.0\mathrm{ }\mathrm{g}\mathrm{ }\mathrm{m}{\mathrm{L}}^{-1}$ )

The pH of the solution after Expt. 2 is

Consider the reaction $\mathrm{A}\rightleftharpoons \mathrm{B}$ at $1000 \mathrm{K}$. At the time ${\mathrm{t}}^{\text{'}}$, the temperature of the system was increased to $2000 \mathrm{K}$ and the system was allowed to reach equilibrium. Throughout this experiment the partial pressure of $\mathrm{A}$ was maintained at $1$ bar. Given below is the plot of the partial pressure of $\mathrm{B}$ with time. What is the ratio of the standard Gibbs energy of the reaction at $1000 \mathrm{K}$ to that at $2000 \mathrm{K}$?

Give your answer by multiplying with 100 and rounding off to nearest integer.

For the following reaction, the equilibrium constant ${\mathrm{K}}_{\mathrm{C}}$ at $298\mathrm{ }\mathrm{K}$ is $1.6\times {10}^{17}.$

$\mathrm{F}{{\mathrm{e}}^{2+}}_{\left(\mathrm{aq}\right)}+{{\mathrm{S}}^{2-}}_{\left(\mathrm{aq}\right)}\mathrm{ }\rightleftharpoons \mathrm{F}\mathrm{e}{\mathrm{S}}_{\left(\mathrm{s}\right)}$

When equal volumes of $0.06\mathrm{ }\mathrm{M}\mathrm{ }\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)$ and $0.2\mathrm{ }\mathrm{M}{\mathrm{ }\mathrm{S}}^{2-}\left(\mathrm{a}\mathrm{q}\right)$ solutions are mixed, the equilibrium concentration of $\mathrm{F}{{\mathrm{e}}^{2+}}_{\left(\mathrm{aq}\right)}$ is found to be $\mathrm{Y}\times {10}^{-17}\mathrm{M}.$ The value of $\mathrm{Y}$ is __________ (Answer should be given to the nearest integer value).

The solubility of a salt of weak acid $\left(\mathrm{AB}\right)\mathrm{ }\mathrm{at}\mathrm{ }\mathrm{pH}=3\mathrm{ }\mathrm{is}\mathrm{ }\mathrm{Y}\times {10}^{-3}\mathrm{ }\mathrm{mol}\mathrm{ }{\mathrm{L}}^{-1}$. The value of $\mathrm{Y}$ is ____(Nearest integer). (Given that the value of solubility product of $\mathrm{AB}\left({\mathrm{K}}_{\mathrm{sp}}\right)=2\times {10}^{-10}\mathrm{ }$, and the value of ionisation constant of $\mathrm{HB}\left(\mathrm{Ka}\right)=1\times {10}^{-8}$)

The % yield of ammonia as a function of time in the reaction

${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{N}{\mathrm{H}}_3\left(\mathrm{g}\right),\mathrm{ }\mathrm{\Delta }\mathrm{H}<0$ at $(\mathrm{P},\mathrm{ }{\mathrm{T}}_1)$ is given below.




If this reaction is conducted at $(\mathrm{P},\mathrm{ }{\mathrm{T}}_2)$ with ${\mathrm{T}}_2>{\mathrm{T}}_1$ , the % yield of ammonia as a function of time is represented by: