Physical Chemistry PYQ — Page 55

$5.1 g {\mathrm{NH}}_{4}\mathrm{SH}$ is introduced in $3.0 L$ evacuated flask at ${327}^{o}C$ . $30%$ of the solid ${\mathrm{NH}}_{4}\mathrm{SH}$ is decomposed to ${\mathrm{NH}}_{3}$ and ${H}_{2}S$ as gases. The ${K}_{P}$ of the reaction at ${327}^{o}C$ is $(R=0.082 L \mathrm{atm} {\mathrm{mol}}^{-1}{K}^{-1},\mathrm{Molar} \mathrm{mass} \mathrm{of} S=32 g {\mathrm{mol}}^{-1}, \mathrm{Molar} \mathrm{mass} \mathrm{of} N=14g {\mathrm{mol}}^{-1})$

What are the values of $\frac{{K}_{p}}{{K}_{c}}$ for the following reactions at $300 K$ respectively? (At $300 K, \mathrm{RT}=24.62 {\mathrm{dm}}^{2}\mathrm{atm} {\mathrm{mol}}^{-1}$ ) ${N}_{2}(g)+{O}_{2}(g)\rightleftharpoons 2\mathrm{NO}(g)$ ${N}_{2}{O}_{4}(g)\rightleftharpoons 2\mathrm{NO}(g)$ ${N}_{2}(g)+3{H}_{2}(g)\rightleftharpoons 2{\mathrm{NH}}_{3}(g)$

For the reaction $2A+B\rightarrow C$ , the values of initial rate at different reactant concentrations are given in the table below. The rate law for the reactions is:<table class="pyq-table"><tbody><tr><th>$[A](mol{L}^{-1})$</th><th>$[B](mol{L}^{-1})$</th><th>$Initial Rate$ $(mol{L}^{-1}{s}^{-1})$</th></tr><tr><td>0.05</td><td>0.05</td><td>0.045</td></tr><tr><td>0.10</td><td>0.05</td><td>0.090</td></tr><tr><td>0.20</td><td>0.10</td><td>0.72</td></tr></tbody></table>

The reaction $2 \mathrm{X} \rightarrow \mathrm{B}$ is a zeroth order reaction. If the initial concentration of $\mathrm{X}$ is $0.2 \mathrm{M}$, the half-life is $6 \mathrm{~h}$. When the initial concentration of $X$ is $0.5 \mathrm{M}$, the time required to reach its final concentration of $0.2 \mathrm{M}$ will be

The following results were obtained during kinetic studies of the reaction. $2A+B\rightarrow$ product <table class="pyq-table"><tbody><tr><td>Experiment</td><td>$[A]$ $(\mathrm{in} \mathrm{mol} {L}^{-1})$</td><td>$[B]$ $(in mol {L}^{-1})$</td><td>Initial rate of reaction $(\mathrm{in} \mathrm{mol} {L}^{-1} \mathrm{min}{ }^{-1})$</td></tr><tr><td>$I$</td><td>$0.10$</td><td>$0.20$</td><td>$6.93\times {10}^{-3}$</td></tr><tr><td>$\mathrm{II}$</td><td>$0.10$</td><td>$0.25$</td><td>$6.93\times {10}^{-3}$</td></tr><tr><td>$\mathrm{III}$</td><td>$0.20$</td><td>$0.30$</td><td>$1.386\times {10}^{-2}$</td></tr></tbody></table> The time (in minutes) required to consume half of $\text{A}$ is

The reaction $\mathrm{MgO}(\mathrm{s})+\mathrm{C}(\mathrm{s}) \rightarrow \mathrm{Mg}(\mathrm{s})+\mathrm{CO}(\mathrm{g}),$ for which $\Delta \mathrm{H}^{\circ}=+491.1 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta \mathrm{S}^{\circ}=198.0 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ is not feasible at $298 \mathrm{~K}$. Temperature above which reaction will be feasible is

For a reaction, consider the plot of $ln k$ versus $1/T$ given in the figure. If the rate constant of this reaction at $400 K$ is ${10}^{-5}{s}^{-1}$ , then the rate constant at $500 K$ is: 

If a reaction follows the Arrhenius equation, the plot $\ln k$ vs $\frac{1}{(\mathrm{RT})}$ gives straight line with a gradient $(-\mathrm{y})$ unit. The energy required to activate the reactant is:

The elevation in boiling point for $1$ molal solution of glucose is $2 K$. The depression in freezing point for $2$ molal solution of glucose in the same solvent is $2 K.$ The relation between ${K}_{b}$ and ${K}_{f}$ is:

$8 g$ of $\mathrm{NaOH}$ is dissolved in $18g$ of ${H}_{2}O$. Mole fraction of $\mathrm{NaOH}$ in solution and molality (in $\mathrm{mol} {\mathrm{kg}}^{-1}$) of the solution respectively are:

The entropy change associated with the conversion of $1 kg$ of ice at $273 K$ to water vapours at $383 K$ is: (Specific heat of water liquid and water vapour are $4.2 kJ {K}^{-}$ and $2.0 kJ {K}^{-1}k{g}^{-1}$ ; heat of liquid fusion and vaporization of water are $334 kJ k{g}^{-1}$ and $2491 kJ k{g}^{-1}$ , respectively). ( $log$ $273=2.436,\mathrm{log}⁡373=2.572,\mathrm{log}⁡383=2.583$ )

A process has $\Delta H=200 J mo{l}^{-1}$ and $\Delta S=40 J{K}^{-1}mo{l}^{-1}.$ Out of the values given below choose the minimum temperature above which the process will be spontaneous:

In which one of the following equilibria, ${K}_{p}\neq {K}_{c}?$

The incorrect match in the following is:

The isoelectronic set of ions is:

If the de Broglie wavelength of the electron in ${n}^{th}$ Bohr orbit in a hydrogenic atom is equal to $1.5 \pi {a}_{0}$ $({a}_{0}$ is Bohr radius$)$, then the value of $\frac{n}{z}$ is:

Consider the following statements $(a)$ 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 $1.3.$ $(b)$ Ionic product of water is temperature dependent. $(c)$ A monobasic acid with ${K}_{a}={10}^{-5}$ has a $pH=5$ . The degree of dissociation of this acid is $50%$ . $(d)$ The Le Chatelier's principle is not applicable to common-ion effect. The correct statements are:

What is the work function of the metal if the light of wavelength $4000\overset{o}{A}$ generates photoelectrons of velocity $6\times {10}^{5} {\mathrm{ms}}^{-1}$ from it? (Mass of electron $=9\times {10}^{-31}\mathrm{kg}$, velocity of light $=3\times {10}^{8}{\mathrm{ms}}^{-1}$, Planck's constant $=6.626\times {10}^{-34}\mathrm{Js}$, Charge of electron $=6.626\times {10}^{-34}\mathrm{Js}$)

For any given series of spectral lines of atomic hydrogen, let $\Delta \overset{-}{v}={\overset{-}{v}}_{max}-{\overset{-}{v}}_{min}$ be the difference in maximum and minimum wave number in $c{m}^{-1}$. The ratio $\Delta {\overset{-}{v}}_{Lyman}/\Delta {\overset{-}{v}}_{Balmar}$ is

For the reaction of ${H}_{2}$ with ${I}_{2}$, the rate constant is $2.5\times {10}^{-4} d{m}^{3}mo{l}^{-1}{s}^{-1}$ at ${327}^{o}C$ and $1.0 d{m}^{3} mol-1{s}^{-1}$ at $527^{\circ}C$ . The activation energy for the reaction, in $kJ mol-1$ is: $(R=8.314 J{K}^{-1}mo{l}^{-1})$

If ${K}_{\mathrm{sp}}$ of ${\mathrm{Ag}}_{2}{\mathrm{CO}}_{3}$ is $8\times {10}^{-12}$ , the molar solubility of ${\mathrm{Ag}}_{2}{\mathrm{CO}}_{3}$ in $0.1 M {\mathrm{AgNO}}_{3}$ is:

In an acid-base titration, $0.1 M HCl$ solution was added to the $NaOH$ solution of unknown strength. Which of the following correctly shown the change of $pH$ of the titration mixture in this experiment? 

In a chemical reaction, $A+2B\overset{K}{\rightleftharpoons }2C+D$ , the initial concentration of $B$ was $1.5$ times of the concentration of $A$ , but the equilibrium concentrations of $A$ and $B$ were found to be equal. The equilibrium constant $(K)$ for the chemical reaction is:

The standard Gibbs energy for the given cell reaction in $kJ mo{l}^{-1}$ at $298 K$ is: $Zn(s)+C{u}^{2+}(aq)\longrightarrow Z{n}^{2+}(aq)+Cu(s)$ , ${E}^{0}=2 V at 298 K$ $(Faraday's constant ,F=96000 C mo{l}^{-1})$