JEE Main 2014 — Physical Chemistry

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

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 :

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 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 :

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:

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 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 :

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 :

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: $\left(\mathrm{h}=6.625 \times 10^{-34} \mathrm{Js}, \mathrm{C}=3 \times 10^8 \mathrm{~ms}^{-1}\right)$

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 $=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ )

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

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

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 :

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

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):

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

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?

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:

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 ?

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: $\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\right)$

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

The conjugate base of hydrazoic acid 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)

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 $=2 \mathrm{u})$

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

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:

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 ?

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 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)

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

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: $(F=96,500C)$

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:

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)

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?

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:

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

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

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

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: $( \text{R} = {\text{8.314 kJ mol}}^{-1} )$

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 :

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?

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

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?

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