JEE Main 2014 — Physical Chemistry

A current of $10.0A$ flows for $2.00h$ through an electrolytic cell containing a molten salt of metal $X$. This results in the decomposition of $0.250\mathrm{mol}$ of metal $X$ at the cathode. The oxidation state of $X$ in the molten salt is: $(F=96,500C)$

A gaseous compound of nitrogen and hydrogen contains $12.5 \%$ (by mass) of hydrogen. The density of the compound relative to hydrogen is 16. The molecular formula of the compound is:

Assuming that the degree of hydrolysis is small, the $\mathrm{pH}$ of $0.1 \mathrm{M}$ solution of sodium acetate $\left(\mathrm{K}_{\mathrm{a}}=1.0 \times 10^{-5}\right)$ will be:

At a certain temperature, only 50% HI is dissociated into H$_{2}$ and I$_{2}$ at equilibrium. The equilibrium constant is :

Based on the equation: $$ \Delta \mathrm{E}=-2.0 \times 10^{-18} \mathrm{~J}\left(\frac{1}{\mathrm{n}_2^2}-\frac{1}{\mathrm{n}_1^2}\right) $$ the wavelength of the light that must be absorbed to excite hydrogen electron from level $n=1$ to level $\mathrm{n}=2$ will be: $\left(\mathrm{h}=6.625 \times 10^{-34} \mathrm{Js}, \mathrm{C}=3 \times 10^8 \mathrm{~ms}^{-1}\right)$

Choose the correct statement with respect to the vapour pressure of a liquid among the following :

Consider separate solutions of $0.500M{C}_{2}{H}_{5}\mathrm{OH}(\mathrm{aq}),0.100M{\mathrm{Mg}}_{3}{({\mathrm{PO}}_{4})}_{2}(\mathrm{aq}),0.250M\mathrm{KBr}(\mathrm{aq})$ and $0.125M{\mathrm{Na}}_{3}{\mathrm{PO}}_{4}(\mathrm{aq})$ at $25^{\circ}C$. Which statement is true about these solutions, assuming all salts to be strong electrolytes?

Consider the following equilibrium $$ \mathrm{AgCl} \downarrow+2 \mathrm{NH}_3 \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_3 2_2\right]^{+}+\mathrm{Cl}^{-}\right. $$ White precipitate of $\mathrm{AgCl}$ appears on adding which of the following?

Consider the reaction : ${\text{H}}_{2} {\text{SO}}_{ 3 ( \text{aq} ) } + {\text{Sn}}_{( \text{aq} )}^{ 4 + } + {\text{H}}_{2} {\text{O}}_{( l⁡ )} \rightarrow {\text{Sn}}_{( \text{aq} )}^{ 2 + } + {\text{HSO}}_{ 4 ( \text{aq} ) }^{-} + 3 {\text{H}}_{( \text{aq} )}^{+}$ Which of the following statements is correct ?

Dissolving 120 g of a compound of (mol. wt. 60) in 1000 g of water gave a solution of density 1.12 g/mL. The molarity of the solution is :

Excited hydrogen atom emits light in the ultraviolet region at $2.47 \times 10^{15} \mathrm{~Hz}$. With this frequency, the energy of a single photon is: $\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\right)$

For an ideal solution of two components $A&B$, which of the following is true?

For complete combustion of ethanol, ${\text{C}}_{2} {\text{H}}_{5} \text{OH} ( \text{l} ) + 3 {\text{O}}_{2} ( \text{g} ) \rightarrow 2 {\text{CO}}_{2} ( \text{g} ) + 3 {\text{H}}_{2} \text{O} ( \text{l} )$, the amount of heat produced as measured in bomb calorimeter, is ${\text{1364.47 kJ mol}}^{-1}$ at $2 5 ℃$. Assuming ideality the Enthalpy of combustion, ${\Delta }_{\text{c}} \text{H}$, for the reaction will be: $( \text{R} = {\text{8.314 kJ mol}}^{-1} )$

For the decomposition of the compound, represented as ${\text{NH}}_{2} {\text{COONH}}_{4} ( \text{s} ) \rightleftharpoons 2 {\text{NH}}_{3} ( \text{g} ) + {\text{CO}}_{2} ( \text{g} )$ the ${K}_{p}=2.9\times {10}^{-5}{atm}^{3}$. If the reaction is started with 1 mole of the compound, the total pressure at equilibrium would be :

For the non-stoichiometry reaction, $2 \text{A} + \text{B} \rightarrow \text{C} + \text{D}$, the following kinetic data were obtained in three separate experiments, all at $298K$.<table class="pyq-table"><tbody><tr><th>Initial Concentration (A)</th><th>Initial Concentration (B)</th><th>Initial rate of formation of C $( {\text{mol L}}^{-} {S}^{-} )$</th></tr><tr><td>$\text{0.1 M}$</td><td>$\text{0.1 M}$</td><td>$\text{1.2} \times 1 {0}^{ - 3 }$</td></tr><tr><td>$\text{0.1 M}$</td><td>$\text{0.2 M}$</td><td>$\text{1.2} \times 1 {0}^{ - 3 }$</td></tr><tr><td>$\text{0.2 M}$</td><td>$\text{0.1 M}$</td><td>$\text{2.4} \times 1 {0}^{ - 3 }$</td></tr></tbody></table> The rate law for the formation of $C$ is

For the reaction ${ \text{SO}}_{2} (\text{g})+\frac{1}{2} {\text{O}}_{2} (\text{g})\rightleftharpoons { \text{SO}}_{3} (\text{g})$ , if ${\text{K}}_{\text{P}} = {\text{K}}_{\text{C}} { ( \text{RT} ) }^{x}$ where the symbols have usual meaning then the value of $x$ is: (assuming ideality)

For the reaction, $\text{3A} + \text{2B} \rightarrow \text{C} + \text{D}$, the differential rate law can be written as :

For the reaction, $2 \mathrm{~N}_2 \mathrm{O}_5 \rightarrow 4 \mathrm{NO}_2+\mathrm{O}_2$, the rate equation can be expressed in two ways $-\frac{\mathrm{d}\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\mathrm{dt}}=\mathrm{k}\left[\mathrm{N}_2 \mathrm{O}_5 \quad\right] n \mathrm{nd}$ $+\frac{\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}}=\mathrm{k}^{\prime}\left[\mathrm{N}_2 \mathrm{O}_5\right]$ $\mathrm{k}$ and $\mathrm{k}^{\prime}$ are related as:

Given below are the half - cell reactions : $\begin{matrix} {\text{Mn}}^{ 2 + } + 2 {\text{e}}^{-} \rightarrow \text{Mn} ; & {\text{E}}^{\circ } = - \text{1.18 V} \\ 2 ( {\text{Mn}}^{ 3 + } + {\text{e}}^{-} \rightarrow {\text{Mn}}^{ 2 + } ) ; & {\text{E}}^{\circ } = + \text{1.51 V} \end{matrix}$ The ${\text{E}}^{\circ }$ for $3 {\text{Mn}}^{ 2 + } \rightarrow \text{Mn} + 2 {\text{Mn}}^{ 3 + }$ will be :

Given $$ \mathrm{Fe}^{3+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq}) ; \mathrm{E}^0=+0.77 \mathrm{~V} $$ $$ \begin{aligned} &\mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Al}(\mathrm{s}) ; \mathrm{E}^0=-1.66 \mathrm{~V} \\ &\mathrm{Br}_2(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{Br}^{-} ; \mathrm{E}^0=+1.09 \mathrm{~V} \end{aligned} $$ Considering the electrode potentials, which of the following represents the correct order of reducing power?

How many electrons are involved in the following redox reaction ? ${\text{Cr}}_{2} {\text{O}}_{7}^{ 2 - } + {\text{Fe}}^{ 2 + } + {\text{C}}_{2} {\text{O}}_{4}^{ 2 - } \rightarrow {\text{Cr}}^{3 +} + {\text{Fe}}^{ 3 + } + {\text{CO}}_{2}$ (Unbalanced)

How many electrons would be required to deposit $6.35 \mathrm{~g}$ of copper at the cathode during the electrolysis of an aqueous solution of copper sulphate? (Atomic mass of copper $=63.5 \mathrm{u}, \mathrm{N}_{\mathrm{A}}=$ Avogadro's constant):

If $m$ and $e$ are the mass and charge of the revolving electron in the orbit of radius $r$ for hydrogen atom, the total energy of the revolving electron will be:

If $\lambda_0$ and $\lambda$ be threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is:

In some solutions, the concentration of $\mathrm{H}_3 \mathrm{O}^{+}$ remains constant even when small amounts of strong acid or strong base are added to them. These solutions are known as:

In the reaction of formation of sulphur trioxide by contact process $2 \mathrm{SO}_2+\mathrm{O}_2 \rightleftharpoons 2 \mathrm{SO}_3$ the rate of reaction was measured as $\frac{\mathrm{d}\left[\mathrm{O}_2\right]}{\mathrm{dt}}=-2.5 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$. The rate of reaction is terms of $\left[\mathrm{SO}_2\right]$ in $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}$ will be:

Resistance of 0.2 M solution of an electrolyte is $5 0 \Omega$. The specific conductance of the solution is ${\text{1.4 S m}}^{-1}$. The resistance of 0.5 M solution of the same electrolyte is $28 0 \Omega$. The molar conductivity of 0.5 M solution of the electrolyte in ${\text{S m}}^{2} {mol}^{-1}$ is :

The amount of $\mathrm{BaSO}_4$ formed upon mixing 100 $\mathrm{mL}$ of $20.8 \% \mathrm{BaCl}_2$ solution with $50 \mathrm{~mL}$ of $9.8 \%$ $\mathrm{H}_2 \mathrm{SO}_4$ solution will be: $(\mathrm{Ba}=137, \mathrm{Cl}=35.5, \mathrm{~S}=32, \mathrm{H}=1$ and $\mathrm{O}=16$ )

The amount of oxygen in $3.6$ moles of water is:

The conjugate base of hydrazoic acid is:

The correct set of four quantum numbers for the valence electrons of rubidium atom $(Z=37)$ is

The de-Broglie wavelength of a particle of mass $6.63 \mathrm{~g}$ moving with a velocity of $100 \mathrm{~ms}^{-1}$ is:

The energy of an electron in first Bohr's orbit of H atom is $-13.6 \text{eV}\text{.}$ The energy value of electron in the first excited state of ${ \text{Li}}^{ \text{2+}}$ is :

The equivalent conductance of $\mathrm{NaCl}$ at concentration C and at infinite dilution are ${\lambda }_{\text{C}}$ and ${\lambda }_{\infty }$, respectively. The correct relationship between ${\lambda }_{\text{C}}$ and ${\lambda }_{\infty }$ is given as : (where the constant B is positive)

The half-life period of a first-order reaction is $15\text{minutes}$. The amount of substance left after one hour will be

The ionization energy of gaseous $\mathrm{Na}$ atoms is $495.5\mathrm{kJ}{\mathrm{mol}}^{-1}$. The lowest possible frequency of light that ionizes a sodium atom is $(\text{h}=\text{6.626}\times 1{0}^{-34}Js,{N}_{\text{A}}=\text{6.022}\times 1{0}^{23}{mol}^{-1})$

The metal that cannot be obtained by the electrolysis of an aqueous solution of its salt is

The molar heat capacity $\left(\mathrm{C}_{\mathrm{p}}\right)$ of $\mathrm{CD}_2 \mathrm{O}$ is 10 cals at $1000 \mathrm{~K}$. The change in entropy associated with cooling of $32 \mathrm{~g}$ of $\mathrm{CD}_2 \mathrm{O}$ vapour from $1000 \mathrm{~K}$ to $100 \mathrm{~K}$ at constant pressure will be: $(\mathrm{D}=$ deuterium, atomic mass $=2 \mathrm{u})$

The observed osmotic pressure for a $0.10M$ solution of $\mathrm{Fe}({\mathrm{NH}}_{4}{)}_{2}({\mathrm{SO}}_{4}{)}_{2}$ at $25^{\circ}C$ is $10.8\mathrm{atm}$. The expected and experimental (observed) values of Van't Hoff factor '$i$' will be respectively; $(R=0.082L\mathrm{atm}{k}^{-}{\mathrm{mol}}^{-1})$

The $\left(\mathrm{S}^{\circ}\right)$ of the following substances are: $\left.\mathrm{CH}_4 \mathrm{~g}\right) 186.2 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ $\mathrm{O}_2$ (g) $205.2 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ $\mathrm{CO}_2(\mathrm{~g}) 213.6 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ $\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ 69.9.JK ${ }^{-1} \mathrm{~mol}^{-1}$ The entropy change $\left(\Delta \mathrm{S}^{\circ}\right)$ for the reaction $\mathrm{CH}_4(\mathrm{~g})+2 \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}$ (l) is:

The rate coefficient $(k)$ for a particular reactions is $1.3 \times 10^{-4} \mathrm{M}^{-1} \mathrm{~s}^{-1}$ at $100^{\circ} \mathrm{C}$, and $1.3 \times 10^{-3}$ $\mathrm{M}^{-1} \mathrm{~s}^{-1}$ at $150^{\circ} \mathrm{C}$. What is the energy of activation $\left(\mathrm{E}_{\mathrm{A}}\right)$ (in $\left.\mathrm{kJ}\right)$ for this reaction? $(\mathrm{R}=$ molar gas constant $=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ )

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecules is:

The standard electrode potentials $( {\text{E}}_{ {\text{M}}^{+} / \text{M} }^{\text{o}} )$ of four metals $\text{A,} \text{B,} \text{C}$ and $\text{D}$ are $-\text{1}\text{.2} \text{V,}$$\text{0}\text{.6} \text{V}$, $\text{0}\text{.85} \text{V}$ and $-\text{0}\text{.76} \text{V}$, respectively. The sequence of deposition of metals on applying potential is

The standard enthalpy of formation $\left(\Delta_f \mathrm{H}^{\circ}{ }_{298}\right)$ for methane, $\mathrm{CH}_4$ is $-74.9 \mathrm{~kJ} \mathrm{~mol}^{-1}$. In order to calculate the average energy given out in the formation of a $\mathrm{C}-\mathrm{H}$ bond from this it is necessary to know which one of the following?

The standard enthalpy of formation of${\mathrm{NH}}_{3}$ is $-46.0\mathrm{kJ}/\mathrm{mol}$. If bond enthalpy of ${H}_{2}$ is $-436\mathrm{kJ}/\mathrm{mol}$ and that of ${N}_{2}$ is $-712\mathrm{kJ}/\mathrm{mol}$ , the average bond enthalpy of $N-H$ bond in ${\mathrm{NH}}_{3}$ is :

What happens when an inert gas is added to an equilibrium keeping volume unchanged?

Zirconium phosphate $[{\mathrm{Zr}}_{3}{({\mathrm{PO}}_{4})}_{4}]$ dissociates into three zirconium cations of charge $+4$ and four phosphate anions of charge $-3$. If molar solubility of zirconium phosphate is denoted by $s$ and its solubility product by ${K}_{\mathrm{sp}}$ then which of the following relationship between $s$ and ${K}_{\mathrm{sp}}$ is correct ?