Physical Chemistry PYQ — Page 3

At $\mathrm{T}(\mathrm{K}), 100 \mathrm{~g}$ of $98 \% \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{w} / \mathrm{w})$ aqueous solution is mixed with 100 g of $49 \% \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{w} / \mathrm{w})$ aqueous solution. What is the mole fraction of $\mathrm{H}_{2} \mathrm{SO}_{4}$ in the resultant solution? (Given : Atomic mass $\mathrm{H}=1 \mathrm{u} ; \mathrm{S}=32 \mathrm{u} ; \mathrm{O}=16 \mathrm{u}$). (Assume that temperature after mixing remains constant)

Given below are two statements : Statement I: When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules dissociate and the energetically excited hydrogen atoms produce electromagnetic radiation of discrete frequencies. Statement II: The frequency of second line of Balmer series obtained from $\mathrm{He}^{+}$is equal to that of first line of Lyman series obtained from hydrogen atom. In the light of the above statements, choose the correct answer from the options given below :

Consider the following redox reaction taking place in acidic medium $\mathrm{BH}_{4}^{-}(a q)+\mathrm{ClO}_{3}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{BO}_{3}^{-}(a q)+\mathrm{Cl}^{-}(a q)$ If the Nernst equation for the above balanced reaction is $\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\circ}-\frac{\mathrm{RT}}{\mathrm{nF}} \ln \mathrm{Q}$, then the value of $n$ is $\_\_\_\_$. (Nearest integer)

For the given reaction: $\mathrm{CaCO}_{3}+2 \mathrm{HCl} \longrightarrow \mathrm{CaCl}_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}$ If $90 \mathrm{~g} \mathrm{CaCO}_{3}$ is added to 300 mL of HCl which contains $38.55 \% \mathrm{HCl}$ by mass and has density $1.13 \mathrm{~g} \mathrm{~mL}^{-1}$, then which of the following option is correct ? Given molar mass of $\mathrm{H}, \mathrm{Cl}, \mathrm{Ca}$ and O are 1, 35.5, 40 and $16 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively.

A substance ' X ' (1.5 g) dissolved in 150 g of a solvent ' Y ' (molar mass $=300 \mathrm{~g} \mathrm{~mol}^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent ' Y ' is $\_\_\_\_$ $\times 10^{-2}$. (nearest integer) [Given : $\mathrm{K}_{\mathrm{b}}$ of the solvent $=5.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ ] Assume the solution to be dilute and no association or dissociation of $X$ takes place in solution.

Match List-I with List-II.<table class="pyq-table"><tbody><tr><th>List-I Mass of substance</th><th>List-II Number of atoms</th></tr><tr><td>A. $1.8$ mg water</td><td>I. $2\times 10^{-4}\times N_A$</td></tr><tr><td>B. $9.8$ mg sulphuric acid</td><td>II. $1.5\times 10^{-4}\times N_A$</td></tr><tr><td>C. $1.8$ mg carbon</td><td>III. $3\times 10^{-4}\times N_A$</td></tr><tr><td>D. $5.85$ mg salt (NaCl)</td><td>IV. $7\times 10^{-4}\times N_A$</td></tr></tbody></table>Choose the correct answer from the options given below:

At $T(K)$, the equilibrium constant of $A_2(g) + B_2(g) \rightleftharpoons C(g)$ is $2.7 \times 10^{-5}$. What is the equilibrium constant for $\dfrac{1}{3}A_2(g) + \dfrac{1}{3}B_2(g) \rightleftharpoons \dfrac{1}{3}C(g)$ at the same temperature?

Which of the following contain the same number of atoms ? (Given : Molar mass in g mol$^{-1}$ of H, He, O and S are $1, 4, 16$ and $32$ respectively)<br>A. $2$ g of O$_2$ gas<br>B. $4$ g of SO$_2$ gas<br>C. $1400$ mL of O$_2$ at STP<br>D. $0.05$ L of He at STP<br>E. $0.0625$ mol of H$_2$ gas<br>Choose the correct answer from the options given below :

The first and second ionization constants of $\mathrm{H}_{2} \mathrm{X}$ are $2.5 \times 10^{-8}$ and $1.0 \times 10^{-13}$ respectively. The concentration of $\mathrm{X}^{2-}$ in $0.1 \mathrm{M} \mathrm{H}_{2} \mathrm{X}$ solution is $\_\_\_\_$ $\times 10^{-15} \mathrm{M}$. (Nearest Integer)

Consider the following gas phase reaction being carried out in a closed vessel at $25°C$. $2A(g) \rightarrow 4B(g) + C(g)$ <table class="pyq-table"><tbody><tr><th>time (min)</th><th>total pressure of the system (mm Hg)</th></tr><tr><td>$30$</td><td>$300$</td></tr><tr><td>$\infty$</td><td>$600$</td></tr></tbody></table>The pressure of $C(g)$ at $30$ minutes time interval would be _______ mm Hg. (nearest integer)

$t_{100\%}$ is the time required for the $100\%$ completion of the reaction while $t_{1/2}$ is the time required for $50\%$ of the reaction to be completed. Which of the following option correctly represents the relation between $t_{100\%}$ and $t_{1/2}$ for zero and first order reactions respectively?

Decomposition of A is a first order reaction at $\mathrm{T}(\mathrm{K})$ and is given by $\mathrm{A}(\mathrm{g}) \longrightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$. In a closed 1 L vessel, 1 bar $\mathrm{A}(\mathrm{g})$ is allowed to decompose at $\mathrm{T}(\mathrm{K})$. After 100 minutes, the total pressure was 1.5 bar. What is the rate constant $\left(\mathrm{in} \mathrm{min}^{-1}\right)$ of the reaction ? $(\log 2=0.3)$

Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation energy of second reaction by $20 \mathrm{~kJ} \mathrm{~mol}^{-1}$. If $\mathrm{k}_{1}$ and $\mathrm{k}_{2}$ are the rate constants of first and second reaction respectively at 300 K, then $\ln \frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}$ will be $\_\_\_\_$. (nearest integer) $\left[\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$

Consider the dissociation equilibrium of the following weak acid $\mathrm{HA} \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{A}^{-}(\mathrm{aq})$ If the pKa of the acid is 4, then the pH of 10 mMHA solution is $\_\_\_\_$.(Nearest integer) [Given: The degree of dissociation can be neglected with respect to unity]

Consider the following electrochemical cell at 298 K $\mathrm{Pt}\left|\mathrm{HSnO}_{2}{ }^{-}(\mathrm{aq})\right| \mathrm{Sn}(\mathrm{OH})_{6}{ }^{2-}(\mathrm{aq})\left|\mathrm{OH}^{-}(\mathrm{aq})\right| \mathrm{Bi}_{2} \mathrm{O}_{3}(\mathrm{~s}) \mid \mathrm{Bi}(\mathrm{s})$. If the reaction quotient at a given time is $10^{6}$, then the cell EMF ($\mathrm{E}_{\text {cell }}$) is $\_\_\_\_$ $\times 10^{-1} \mathrm{~V}$ (Nearest integer). Given the standard half-cell reduction potential as $\mathrm{E}_{\mathrm{Bi}_{2} \mathrm{O}_{3} / \mathrm{Bi}, \mathrm{OH}^{-}}^{\circ}=-0.44 \mathrm{~V} \text { and } \mathrm{E}_{\mathrm{Sn}(\mathrm{OH})_{6}^{2-} / \mathrm{HSnO}_{2}^{-}, \mathrm{OH}^{-}}^{\circ}=-0.90 \mathrm{~V}$

The ratio of mass percentage (w/w) of C : H in a hydrocarbon is $12 : 1$. It has two carbon atoms. The weight (in g) of $CO_2(g)$ formed when $3.38$ g of this hydrocarbon is completely burnt in oxygen is : (Given : Molar mass in g mol$^{-1}$ C : 12, H : 1, O : 16)

Consider two Group IV metal ions $\mathrm{X}^{2+}$ and $\mathrm{Y}^{2+}$. A solution containing $0.01 \mathrm{M} \mathrm{X}^{2+}$ and $0.01 \mathrm{M} \mathrm{Y}^{2+}$ is saturated with $\mathrm{H}_{2} \mathrm{~S}$. The pH at which the metal sulphide YS will form as a precipitate is $\_\_\_\_$. (Nearest integer) (Given: $\mathrm{K}_{\mathrm{sp}}(\mathrm{XS})=1 \times 10^{-22}$ at $25^{\circ} \mathrm{C}, \mathrm{K}_{\mathrm{sp}}(\mathrm{YS})=4 \times 10^{-16}$ at $25^{\circ} \mathrm{C}$, $\left[\mathrm{H}_{2} \mathrm{~S}\right]=0.1 \mathrm{M}$ in solution, $\mathrm{K}_{a 1} \times \mathrm{K}_{a 2}\left(\mathrm{H}_{2} \mathrm{~S}\right)=1.0 \times 10^{-21}, \log 2=0.30$, $\log 3=0.48, \log 5=0.70$)

Match the LIST-I with LIST-II \(\begin{array}{|l|l|c|l|} \hline \text{List-I} & \text{Isothermal process} \\ & \text{for ideal gas system} & \text{List-II} & \text{Work done } (V_f > V_i) \\ \hline \text{A.} & \text{Reversible expansion} & \text{I.} & w = 0 \\ \hline \text{B.} & \text{Free expansion} & \text{II.} & w = -nRT \ln \dfrac{V_f}{V_i} \\ \hline \text{C.} & \text{Irreversible expansion} & \text{III.} & w = -p_{\text{ex}}(V_f - V_i) \\ \hline \text{D.} & \text{Irreversible compression} & \text{IV.} & w = -p_{\text{ex}}(V_i - V_f) \\ \hline \end{array}\) Choose the correct answer from the options given below:

The first and second ionization constants of a weak dibasic acid $H_2 A$ are $8.1 \times 10^{-8}$ and $1.0 \times 10^{-13}$ respectively. $0.1$ mol of $H_2 A$ was dissolved in $1$ L of $0.1$ M HCl solution. The concentration of $HA^-$ in the resultant solution is:

Solution A is prepared by dissolving $1$ g of a protein (molar mass $= 50000$ g mol$^{-1}$) in $0.5$ L of water at $300$ K. Its osmotic pressure is $x$ bar. Solution B is made by dissolving $2$ g of same protein in $1$ L of water at $300$ K. Osmotic pressure of solution B is $y$ bar. Entire solution of A is mixed with entire solution of B at same temperature. The osmotic pressure of resultant solution is $z$ bar. $x, y$ and $z$ respectively are: $(R = 0.083$ L bar mol$^{-1}$ K$^{-1})$

An oxide of iron contains $69.9\%$ iron, its empirical formula, is: (Given: Molar mass of Fe and O are $56$ and $16$ g mol$^{-1}$ respectively.)

An organic compound undergoes first order decomposition. The time taken for decomposition to $\left(\frac{1}{8}\right)^{\text {th }}$ and $\left(\frac{1}{10}\right)^{\text {th }}$ of its initial concentration are $\mathrm{t}_{1 / 8}$ and $\mathrm{t}_{1 / 10}$ respectively. What is the value of $\frac{\mathrm{t}_{1 / 8}}{\mathrm{t}_{1 / 10}} \times 10$ ? ($\log 2=0.3$)

Match the LIST-I with LIST-II \(\begin{array}{|c|l|c|c|} \hline & \textbf{List-I (Thermodynamic Process)} & & \textbf{List-II} \\ & & & \textbf{(Magnitude in kJ)} \\ \hline A. & \begin{array}{l} \text{Work done in reversible,} \\ \text{isothermal expansion of }\\ \text{2 mol ideal gas from } 2\,\mathrm{dm}^3 \\ \text{ to } 20\,\mathrm{dm}^3 \text{ at } 300\,\mathrm{K} \end{array} & I. & 4 \\ \hline B. & \begin{array}{l} \text{Work done in irreversible} \\ \text{isothermal expansion of }\\ 1 \text{ mol ideal gas from } 1\,\mathrm{m}^3 \text{ to } 3\,\mathrm{m}^3 \\ \text{at } 300\,\mathrm{K} \text{ against} \\ \text{constant pressure } 3\,\mathrm{kPa} \end{array} & II. & 11.5 \\ \hline C. & \begin{array}{l} \text{Change in internal energy} \\ \text{for adiabatic expansion of }\\ 1 \text{ mol ideal gas, } \Delta T = 320\,\mathrm{K}, \; \\ \overline{C}_V=\dfrac{3}{2}R \end{array} & III. & 6 \\ \hline D. & \begin{array}{l} \text{Change in enthalpy at constant} \\ \text{pressure of }\\ 1 \text{ mol ideal gas, } \Delta T = 337\,\mathrm{K}, \; \\ \overline{C}_p=\dfrac{5}{2}R \end{array} & IV. & 7 \\ \hline \end{array}\) Choose the correct answer from the options given below:

The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below $A(g) \rightleftharpoons B(g) + C(g)$ <table class="pyq-table"><tbody><tr><td>$\dfrac{1}{T}(\text{K}^{-1})$</td><td>$\log_{10} K_p$</td></tr><tr><td>$0.05$</td><td>$3.5$</td></tr><tr><td>$0.06$</td><td>$2.5$</td></tr><tr><td>$0.07$</td><td>$1.5$</td></tr></tbody></table> The magnitude of $\dfrac{\Delta H°}{R}$ calculated from the above data is _____. (Nearest integer)