Physical Chemistry PYQ — Page 21

${\mathrm{NO}}_{2}$ required for a reaction is produced by decomposition of ${N}_{2}{O}_{5}$ in ${\mathrm{CCl}}_{4}$ as by equation $2{N}_{2}{O}_{5(g)}\rightarrow 4{\mathrm{NO}}_{2(g)}+{O}_{2(g)}$ The initial concentration of ${N}_{2}{O}_{5}$ is $3\mathrm{mol}{L}^{-1}$ and it is $2.75\mathrm{mol}{L}^{-1}$ after $30$ minutes. The rate of formation of ${\mathrm{NO}}_{2}$ is $x\times {10}^{-3}\mathrm{mol}{L}^{-1}$ $\mathrm{min}-1$, value of $x$ is ________.

The value of Rydberg constant \(\left(R_H\right)\) is \(2.18 \times 10^{-18} \mathrm{~J}\). The velocity of electron having mass \(9.1 \times 10^{-31} \mathrm{~kg}\) in Bohr's first orbit of hydrogen atom \(=\) _______ \(\times 10^5 \mathrm{~ms}^{-1}\) (nearest integer).

For the reaction at $298 \mathrm{~K}, 2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{C} . \Delta \mathrm{H}$ $=400 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta \mathrm{S}=0.2 \mathrm{~kJ} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. The reaction will become spontaneous above $\qquad$ K.

Consider the dissociation of the weak acid \(\mathrm{HX}\) as given below \(\mathrm{HX}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{X}^{-}(\mathrm{aq}), \mathrm{Ka}=1.2 \times 10^{-5}\) \(\left[\mathrm{K}_{\mathrm{a}}\right.\) : dissociation constant \(]\) The osmotic pressure of \(0.03 \mathrm{M}\) aqueous solution of \(\mathrm{HX}\) at \(300 \mathrm{~K}\) is _______ \(\times 10^{-2}\) bar (nearest integer). [Given : \(\mathrm{R}=0.083 \mathrm{~L} \mathrm{bar} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\)]

Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is _______ \(\times 10^{13} \mathrm{~Hz}\) (nearest integer). \(\begin{aligned} & \text { [Given : } \mathrm{R}_{\mathrm{H}}(\text { Rydberg constant })=2.18 \times 10^{-18} \mathrm{~J}, h \text { (Plank's } \\ & \text { constant })=6.6 \times 10^{-34} \mathrm{~J} \text {.s.] } \end{aligned}\)

${\mathrm{KMnO}}_{4}$ decomposes on heating at $513K$ to form ${O}_{2}$ along with

Combustion of glucose \(\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6\right)\) produces \(\mathrm{CO}_2\) and water. The amount of oxygen (in g) required for the complete combustion of \(900 \mathrm{~g}\) of glucose is : [Molar mass of glucose in \(\mathrm{g} \mathrm{mol}^{-1}=180\) ]

An ideal gas undergoes a cyclic transformation starting from the point $A$ and coming back to the same point by tracing the path $A\rightarrow B\rightarrow C\rightarrow A$ as shown in the diagram. The total work done in the process is _____$J$. 

The mass of zinc produced by the electrolysis of zinc sulphate solution with a steady current of $0.015A$ for $15$ minutes is $____\times {10}^{-4}g$. (Atomic mass of zinc $=65.4\mathrm{amu})$

Standard enthalpy of vapourisation for ${\mathrm{CCl}}_{4}$ is $30.5\mathrm{kJ}{\mathrm{mol}}^{-1}$. Heat required for vapourisation of $284g$ of ${\mathrm{CCl}}_{4}$ at constant temperature is __________ $\mathrm{kJ}$. (Given molar mass in ${\mathrm{gmol}}^{-1};C=12,\mathrm{Cl}=35.5$) Round off your answer to the nearest integer.

The standard reduction potentials at \(298 \mathrm{~K}\) for the following half cells are given below : \(\begin{array}{ll} \mathrm{Cr}_2 \mathrm{O}_7^{2-}+14 \mathrm{H}^{+}+6 \mathrm{e}^{-} \rightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_2 \mathrm{O}, \mathrm{E}^{\circ}=1.33 \mathrm{~V} \\ \mathrm{Fe}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Fe} \qquad \mathrm{E}^{\circ}=-0.04 \mathrm{~V} \\ \mathrm{Ni}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Ni} \qquad \mathrm{E}^{\circ}=-0.25 \mathrm{~V} \\ \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow \mathrm{Ag} \quad\qquad \mathrm{E}^{\circ}=0.80 \mathrm{~V} \\ \mathrm{Au}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Au} \qquad \mathrm{E}^{\circ}=1.40 \mathrm{~V} \end{array}\) Consider the given electrochemical reactions, The number of metal(s) which will be oxidized be \(\mathrm{Cr}_2 \mathrm{O}_7^{2-}\), in aqueous solution is ______

Molality of an aqueous solution of urea is \(4.44 \mathrm{~m}\). Mole fraction of urea in solution is \(x \times 10^{-3}\). Value of \(x\) is \(\qquad\) - (Integer answer)

The electronic configuration of Einsteinium is : (Given atomic number of Einsteinium \(=99)\)

The hydrogen electrode is dipped in a solution of $\mathrm{pH}=3$ at $25^{\circ}C$. The potential of the electrode will be $-$______$\times {10}^{-2}V$. $(\frac{2.303\mathrm{RT}}{F}=0.059V)$ Round off the answer to the nearest integer.

One Faraday of electricity liberates $x\times {10}^{–1}$ gram atom of copper from copper sulphate, $x$ is______.

For the electro chemical cell \(\begin{gathered} \text { If } \mathrm{E}_{\left(\mathrm{M}^{2+} / \mathrm{M}\right)}^0=0.46 \mathrm{~V} \text { and } \mathrm{E}_{\left(\mathrm{x} / \mathrm{X}^{2-}\right)}^0=0.34 \mathrm{~V} \text {. } \end{gathered}\) Which of the following is correct?

If a substance $'A'$ dissolves in solution of a mixture of ' $B$' and ' $C$ ' with their respective number of moles as ${n}_{A},{n}_{B}$ and ${n}_{C}$, mole fraction of $C$ in the solution is:

The reaction at cathode in the cells commonly used in clocks involves.

Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter \(10^{-15} \mathrm{~m}\) is ________. \(10^9 \mathrm{~ms}^{-1}\) (nearest integer) [Given : mass of electron \(=9.1 \times 10^{-31} \mathrm{~kg}\), Plank's constant \((h)=6.626 \times 10^{-34} \mathrm{Js}\)] (Value of \(\pi=3.14\))

An organic compound has \(42.1 \%\) carbon, \(6.4 \%\) hydrogen and remainder is oxygen. If its molecular weight is 342, then its molecular formula is :

Consider the following redox reaction: ${\mathrm{MnO}}_{4}^{-}+{H}^{+}+{H}_{2}{C}_{2}{O}_{4}\rightleftharpoons {\mathrm{Mn}}^{2+}+{H}_{2}O+{\mathrm{CO}}_{2}$ The standard reduction potentials are given as below $({E}_{\mathrm{red}}^{\circ})$ ${{E}^{0}}_{{\mathrm{MnO}}_{4}^{-}/{\mathrm{Mn}}^{2+}}=+1.51V$; ${{E}^{0}}_{{\mathrm{CO}}_{2}/{H}_{2}{C}_{2}{O}_{4}}=-0.49V$ If the equilibrium constant of the above reaction is given as ${K}_{\mathrm{eq}}={10}^{x}$, then the value of $x=$ _______ (nearest integer)

Consider the following reaction: $3{\mathrm{PbCl}}_{2}+2{({\mathrm{NH}}_{4})}_{3}{\mathrm{PO}}_{4}\rightarrow {\mathrm{Pb}}_{3}{({\mathrm{PO}}_{4})}_{2}+6{\mathrm{NH}}_{4}\mathrm{Cl}$ If $72\mathrm{mmol}{\mathrm{PbCl}}_{2}$ is mixed with $50\mathrm{mmol}$ of ${({\mathrm{NH}}_{4})}_{3}{\mathrm{PO}}_{4},$ then amount of ${\mathrm{Pb}}_{3}{({\mathrm{PO}}_{4})}_{2}$ formed in $\mathrm{mmol}$. (nearest integer)

Combustion of 1 mole of benzene is expressed at \(\mathrm{C}_6 \mathrm{H}_6(\mathrm{l})+\frac{15}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 6 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \text {. }\) The standard enthalpy of combustion of \(2 \mathrm{~mol}\) of benzene is \(-^{\prime} x^{\prime} \mathrm{kJ}\). \(x=\) ______ Given: 1. standard Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{C}_6 \mathrm{H}_6(\mathrm{l})\), for the reaction \(6 \mathrm{C}\) (graphite) \(+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{C}_6 \mathrm{H}_6(\mathrm{l})\) is \(48.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). 2. Standard Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{CO}_2(\mathrm{~g})\), for the reaction \(\mathrm{C}\) (graphite) \(+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})\) is \(-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). 3. Standard and Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{H}_2 \mathrm{O}(\mathrm{l})\), for the reaction \(\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{l})\) is \(-286 \mathrm{~kJ} \mathrm{~mol}^{-1}\).

Considering acetic acid dissociates in water, its dissociation constant is \(6.25 \times 10^{-5}\). If \(5 \mathrm{~mL}\) of acetic acid is dissolved in 1 litre water, the solution will freeze at \(-x \times 10^{-2}{ }^{\circ} \mathrm{C}\), provided pure water freezes at \(0^{\circ} \mathrm{C}\). \(x=\) ______ . (Nearest integer) Given : \(\begin{aligned} & \left(\mathrm{K}_f\right)_{\text {water }}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \text {. } \\ & \text { density of acetic acid is } 1.2 \mathrm{~g} \mathrm{~mol}^{-1} \text {. } \\ & \text { molar mass of water }=18 \mathrm{~g} \mathrm{~mol}^{-1} \text {. } \\ & \text { molar mass of acetic acid=60 } \mathrm{g} \mathrm{mol}^{-1} \text {. } \\ & \text { density of water }=1 \mathrm{~g} \mathrm{~cm}^{-3} \end{aligned}\) Acetic acid dissociates as \(\mathrm{CH}_3 \mathrm{COOH} \rightleftharpoons \mathrm{CH}_3 \mathrm{COO}^{\ominus}+\mathrm{H}^{\oplus}\)