Physical Chemistry PYQ — Page 5

Given below are two statements : Statement (I) : 1,2,3-Trihydroxypropane can be separated from water by simple distillation. Statement (II) : An azeotropic mixture cannot be separated by fractional distillation. In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :  Statement I : H$_2$O molecules move from the chamber $1$ to chamber $2$. Statement II : The osmotic pressure of a solution prepared by dissolving $50$ mg of potassium sulphate (molar mass $= 174$ g/mol) in $2$ L of water (at $27°$C) is $0.0107$ bar. (Given : R $= 0.083$ dm$^3$ bar K$^{-1}$ mol$^{-1}$ and assume complete dissociation of electrolyte) In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements: $R=8.314$ J K$^{-1}$ mol$^{-1}$ and $1$ cal $=4.2$ J Statement I: When $E_a=12.6$ kcal/mol, the room temperature rate constant is doubled by a $10\,^\circ$C increase in temperature ($298$ K to $308$ K) Statement II: For a first order reactions A $\rightarrow$ B,  Here $[A]_o$ is the initial concentration of A and $t_{1/2}$ is half life of reaction. In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements: Given: Molar mass of C, H, O, Cl are $12, 1, 16$ and $35.5$ g mol$^{-1}$, respectively. Statement I: In $30\%$ (w/w) solution of methanol in CCl$_4$ (at T K), the mole fraction of CCl$_4$ is equal to $0.33$. Statement II: Mixture of methanol and CCl$_4$ shows positive deviation from Raoult's law. In the light of the above statements, choose the correct answer from the options given below:

Given at $298$ K: $E^{\ominus}_{Fe^{2+}/Fe} = X$ Volt; $E^{\ominus}_{Fe^{3+}/Fe} = Y$ Volt. The $E^{\ominus}_{Fe^{3+}/Fe^{2+}}$ in Volt at $298$ K is given by:

Given, (A) $\mathrm{n}=5, \mathrm{~m}_{1}=-1$ (B) $\mathrm{n}=3, \mathrm{l}=2, \mathrm{~m}_{1}=-1, \mathrm{~m}_{\mathrm{s}}=+\frac{1}{2}$ The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) respectively are :

Gas 'A' undergoes change from state 'X' to state 'Y'. In this process, the heat absorbed and work done by the gas is $10$ J and $18$ J respectively. Now gas is brought back to state 'X' by another process during which $6$ J of heat is evolved. In the reverse process of 'Y' to 'X',

$19.5$ g of fluoro acetic acid (molar mass $= 78$ g mol$^{-1}$) is dissolved in $500$ g of water at $298$ K. The depression in the freezing point of water was $1°$C. What is $K_a$ of fluoro acetic acid? (For water, $K_f = 1.86$ K kg mol$^{-1}$). Assume molarity and molality to have same values.

For the thermal decomposition of reactant $\mathrm{AB}(\mathrm{g})$, the following plot is constructed.  The half life of the reaction is ' $x^{\prime} \min$. $x=$ $\_\_\_\_$ min. (Nearest integer)

For the reaction, $\mathrm{N}_{2} \mathrm{O}_{4} \rightleftharpoons 2 \mathrm{NO}_{2}$, graph is plotted as shown below. Identify correct statements. A. Standard free energy change for the reaction is $-5.40 \mathrm{~kJ} \mathrm{~mol}^{-1}$. B. As $\Delta \mathrm{G}^{\ominus}$ in graph is positive, $\mathrm{N}_{2} \mathrm{O}_{4}$ will not dissociate into $\mathrm{NO}_{2}$ at all. C. Reverse reaction will go to completion. D. When 1 mole of $\mathrm{N}_{2} \mathrm{O}_{4}$ changes into equilibrium mixture, value of $\Delta \mathrm{G}^{\ominus}=-0.84 \mathrm{~kJ} \mathrm{~mol}^{-1}$ E. When 2 mole of $\mathrm{NO}_{2}$ changes into equilibrium mixture, $\Delta \mathrm{G}^{\ominus}$ for equilibrium mixture is $-6.24 \mathrm{~kJ} \mathrm{~mol}^{-1}$.  Choose the correct answer from the options given below :

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.

For the given reaction:<br>$\mathrm{CaCO}_{3}+2 \mathrm{HCl} \longrightarrow \mathrm{CaCl}_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}$<br>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 ?<br>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.

For the following reaction at $50°$C and at $2$ atm pressure, $2N_2O_5(g) \rightleftharpoons 2N_2O_4(g)+O_2(g)$ $N_2O_5$ is $50\%$ dissociated. The magnitude of standard free energy change at this temperature is $x$. $x=$ ______ J mol$^{-1}$ [Nearest integer]. Given: $R=8.314$ J mol$^{-1}$ K$^{-1}$, $\log 2=0.30$, $\log 3=0.48$, $\ln 10=2.303$, $°C+273=K$

For the following gas phase equilibrium reaction at constant temperature, $\mathrm{NH}_{3}(\mathrm{~g}) \rightleftharpoons 1 / 2 \mathrm{~N}_{2}(\mathrm{~g})+3 / 2 \mathrm{H}_{2}(\mathrm{~g})$ if the total pressure is $\sqrt{3} \mathrm{~atm}$ and the pressure equilibrium constant $\left(\mathrm{K}_{\mathrm{p}}\right)$ is 9 atm, then the degree of dissociation is given as $\left(x \times 10^{-2}\right)^{-1 / 2}$. The value of $x$ is $\_\_\_\_$. (nearest integer)

For strong electrolyte $\Lambda_{\mathrm{m}}$ increases slowly with dilution and can be represented by the equation $\Lambda_{\mathrm{m}}=\Lambda_{\mathrm{m}}^{\circ}-\mathrm{Ac}^{1 / 2}$ Molar conductivity values of the solutions of strong electrolyte AB at $18^{\circ} \mathrm{C}$ are given below : \(\begin{array}{|l|c|c|c|c|} \hline \mathrm{c}\;[\mathrm{mol\,L^{-1}}] & 0.04 & 0.09 & 0.16 & 0.25 \\ \hline \Lambda_{\mathrm{m}}\;[\mathrm{S\,cm^{2}\,mol^{-1}}] & 96.1 & 95.7 & 95.3 & 94.9 \\ \hline \end{array}\) The value of constant A based on the above data $\left[\right.$ in $\left.\mathrm{S} \mathrm{cm}^{2} \mathrm{~mol}^{-1} /(\mathrm{mol} / \mathrm{L})^{1 / 2}\right]$ unit is $\_\_\_\_$.

For reaction $A \rightarrow P$, rate constant $k = 1.5 \times 10^3$ s$^{-1}$ at $27°$C. If activation energy for the above reaction is $60$ kJ mol$^{-1}$, then the temperature (in $°$C) at which rate constant, $k = 4.5 \times 10^3$ s$^{-1}$ is _______. (Nearest integer) Given : $\log 2 = 0.30$, $\log 3 = 0.48$, $R = 8.3$ J K$^{-1}$ mol$^{-1}$, $\ln 10 = 2.3$

For a reaction $A \rightarrow P$ at $T\text{ K}$, the half life $(t_{1/2})$ is plotted as a function of initial concentration $[A]_0$ of $A$ as given below.  The value of $x$ in the given figure is _______ s (Nearest integer)

For a general redox reaction Anode : $\text{Red}_1 \rightarrow \text{Ox}_1^{n_1^+} + n_1 e^-$ Cathode : $\text{Ox}_2 + n_2 e^- \rightarrow \text{Red}_2^{n_2^-}$ Which of the following statement is incorrect ?

For a first order reaction $A \rightarrow B$ <table class="pyq-table"><tbody><tr><th>$t/\text{min}$</th><th>$[A]/M$</th></tr><tr><td>$0$</td><td>$0.6500$</td></tr><tr><td>$x$</td><td>$0.0650$</td></tr><tr><td>$20$</td><td>$0.00065$</td></tr></tbody></table> $x=$ ______ min. (Nearest integer)

For a closed circuit Daniell cell, which of the following plots is the accurate one at a given temperature?

$\mathrm{A} \longrightarrow \mathrm{B}$ (first reaction) $\mathrm{C} \longrightarrow \mathrm{D}$ (second reaction) Consider the above two first-order reactions. The rate constant for first reaction at 500 K is double of the same at 300 K. At $500 \mathrm{~K}, 50 \%$ of the reaction becomes complete in 2 hour. The activation energy of the second reaction is half of that of first reaction. If the rate constant at 500 K of the second reaction becomes double of the rate constant of first reaction at the same temperature; then rate constant for the second reaction at 300 K is $\_\_\_\_$ $\times 10^{-1}$ hour $^{-1}$ (nearest integer).

First order gas phase reaction $A \rightarrow B + C$ $p_i =$ initial pressure of gas A, $p_t =$ total pressure of the reaction mixture at time $t$ Expression of rate constant ($k$) is

Elements P and Q form two types of non-volatile, non-ionizable compounds PQ and $\mathrm{PQ}_{2}$. When 1 g of PQ is dissolved in 50 g of solvent ${ }^{\prime} \mathrm{A}^{\prime}, \Delta \mathrm{T}_{\mathrm{b}}$ was 1.176 K while when 1 g of $\mathrm{PQ}_{2}$ is dissolved in 50 g of solvent ${ }^{\prime} \mathrm{A}^{\prime}, \Delta \mathrm{T}_{\mathrm{b}}$ was 0.689 K. ($\mathrm{K}_{\mathrm{b}}$ of ' $\mathrm{A}^{\prime}=5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$). The molar masses of elements P and Q (in $\mathrm{g} \mathrm{mol}^{-1}$) respectively, are :

Electricity is passed through an acidic solution of $\mathrm{Cu}^{2+}$ till all the $\mathrm{Cu}^{2+}$ was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current of 600 mA was continued to pass through the same solution for another 28 minutes by keeping the total volume of the solution fixed at 200 mL. The total volume of oxygen evolved at STP during the entire process is $\_\_\_\_$ mL. (Nearest integer) [Given: $\mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Cu}(\mathrm{s}) \mathrm{E}_{\text {red }}^{\mathrm{o}}=+0.34 \mathrm{~V}$ $\mathrm{O}_{2}(\mathrm{~g})+4 \mathrm{H}^{+}+4 \mathrm{e}^{-} \rightarrow 2 \mathrm{H}_{2} \mathrm{O} \mathrm{E}_{\text {red }}^{\mathrm{o}}=+1.23 \mathrm{~V}$ Molar mass of $\mathrm{Cu}=63.54 \mathrm{~g} \mathrm{~mol}^{-1}$ Molar mass of $\mathrm{O}_{2}=32 \mathrm{~g} \mathrm{~mol}^{-1}$ Faraday Constant $=96500 \mathrm{C} \mathrm{mol}^{-1}$ Molar volume at $\mathrm{STP}=22.4 \mathrm{~L}$]