Physical Chemistry PYQ — Page 3

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 :

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',

Which of the following statements regarding the energy of the stationary state is true in the following one - electron systems ?

$x \mathrm{mg}$ of pure HCl was used to make an aqueous solution. 25.0 mL of $0.1 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}$ solution is used when the HCl solution was titrated against it. The numerical value of $x$ is $\_\_\_\_$ $\times 10^{-1}$. (Nearest integer) Given : Molar mass of HCl and $\mathrm{Ba}(\mathrm{OH})_{2}$ are 36.5 and $171.0 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively.

Consider $\mathrm{A} \xrightarrow{\mathrm{k}_{1}} \mathrm{~B}$ and $\mathrm{C} \xrightarrow{\mathrm{k}_{2}} \mathrm{D}$ are two reactions. If the rate constant $\left(\mathrm{k}_{1}\right)$ of the $\mathrm{A} \longrightarrow \mathrm{B}$ reaction can be expressed by the following equation $\log _{10} \mathrm{k}=14.34-\frac{1.5 \times 10^{4}}{\mathrm{~T} / \mathrm{K}}$ and activation energy of $C \longrightarrow D$ reaction $\left(E a_{2}\right)$ is $\frac{1}{5}$ th of the $A \longrightarrow B$ reaction $\left(E a_{1}\right)$, then the value of $\left(E a_{2}\right)$ is $\_\_\_\_$ $\mathrm{kJ} \mathrm{mol}^{-1}$. (Nearest Integer)

An electrochemical cell, consist of the following two redox couples, $M^{x+}(aq)/M(s)$ $[E_{red}^\ominus=+0.15\text{ V}]$ and $Fe^{3+}(aq)/Fe(s)$ $[E_{red}^\ominus=-0.036\text{ V}]$. The cell EMF $(E_{cell})$ is recorded to be $0.2057$ V. If the reaction quotient of the electrochemical reaction is found to be $10^{-2}$, then the value of $x$ is ______. (Nearest integer) [Given: M is a p-block metal and $\dfrac{2.303RT}{F}=0.059$ V]

Given below are two statements: Statement I: The Henry's law constant $\mathrm{K}_{\mathrm{H}}$ is constant with respect to variations in solution's concentration over the range for which the solution is ideally dilute. Statement II: $\mathrm{K}_{\mathrm{H}}$ does not differ for the same solute in different solvents. In the light of the above statements, choose the correct answer from the options given below

Consider the following spectral lines for atomic hydrogen : A. First line of Paschen series B. Second line of Balmer series C. Third line of Paschen series D. Fourth line of Bracket series. The correct arrangement of the above lines in ascending order of energy is :

Which of the following statement(s) is/are true ? A. If two orbitals have the same value of $(n + l)$, the orbital with lower value of $n$ will have lower energy. B. Energies of the orbitals in the same subshell increase with increase in atomic number. C. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital. D. Among $5f$, $6s$, $4d$, $5p$ and $5d$ orbitals, none of the orbitals have $2$ radial nodes. 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:

Two liquids A and B form an ideal solution at temperature T K. At T K, the vapour pressures of pure A and B are 55 and $15 \mathrm{kN} \mathrm{m}^{-2}$ respectively. What is the mole fraction of $A$ in solution of $A$ and $B$ in equilibrium with a vapour in which the mole fraction of A is 0.8 ?

Which one of the following graphs accurately represents the plot of partial pressure of $\mathrm{CS}_{2}$ vs its mole fraction in a mixture of acetone and $\mathrm{CS}_{2}$ at constant temperature?

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:

At $298\text{ K}$, the molar conductivity of $x\%$ (w/w) $MX$ solution (aqueous) is $123.5\text{ S cm}^2\text{ mol}^{-1}$. The conductance of same solution is $1.9 \times 10^{-3}\text{ S}$. The value of $x$ is _______ $\times 10^{-2}$. (Given : cell constant $= 1.3\text{ cm}^{-1}$; molar mass of $MX$ is $75\text{ g mol}^{-1}$, density of aqueous solution of $MX$ at $298\text{ K}$ is $1.0\text{ g mL}^{-1}$)

An electrochemical cell is constructed using half cells in the direction of spontaneous change $Fe(OH)_2(s) + 2e^- \rightarrow Fe(s) + 2OH^-(aq) \quad E^\theta = -0.88$ V and $AgBr(s) + e^- \rightarrow Ag(s) + Br^-(aq) \quad E^\theta = +0.07$ V Which of the following option is correct?

Molar conductivity of a weak acid HQ of concentration 0.18 M was found to be $1 / 30$ of the molar conductivity of another weak acid HZ with concentration of 0.02 M. If $\lambda^{\circ} \mathrm{Q}^{-}$happened to be equal with $\lambda^{\circ} \mathrm{Z}^{-}$, then the difference of the $\mathrm{pK}_{\mathrm{a}}$ values of the two weak acids $\left(\mathrm{pK}_{\mathrm{a}}(\mathrm{HQ})-\mathrm{pK}_{\mathrm{a}}(\mathrm{HZ})\right)$ is $\_\_\_\_$ (Nearest integer). [Given: degree of dissociation $(\alpha) \ll 1$ for both weak acids, $\lambda^{\circ}$ : limiting molar conductivity of ions]

In the given electrochemical cell, $\mathrm{Ag}(\mathrm{s})|\mathrm{AgCl}(\mathrm{s})| \mathrm{FeCl}_{2}(\mathrm{aq}), \mathrm{FeCl}_{3}(\mathrm{aq}) \mid \mathrm{Pt}(\mathrm{s})$ at 298 K, the cell potential $\left(\mathrm{E}_{\text {cell }}\right)$ will increase when : A. Concentration of $\mathrm{Fe}^{2+}$ is increased. B. Concentration of $\mathrm{Fe}^{3+}$ is decreased. C. Concentration of $\mathrm{Fe}^{2+}$ is decreased. D. Concentration of $\mathrm{Fe}^{3+}$ is increased. E. Concentration of $\mathrm{Cl}^{-}$is increased. Choose the correct answer from the options given below :

The pH and conductance of a weak acid (HX) was found to be 5 and $4 \times 10^{-5} \mathrm{~S}$, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of $1 \mathrm{~cm}^{2}$ were at a distance of 15 cm apart. The value of the limiting molar conductivity is $\_\_\_\_$ $\mathrm{S} \mathrm{m}^{2} \mathrm{~mol}^{-1}$. (nearest integer) (Given : degree of dissociation of the weak acid $(\alpha) \ll 1$)

In a closed flask at $600$ K, one mole of X$_2$Y$_4$(g) attains equilibrium as given below : $\text{X}_2\text{Y}_4(g) \rightleftharpoons 2\text{XY}_2(g)$ At equilibrium, $75\%$ X$_2$Y$_4$(g) was dissociated and the total pressure is $1$ atm. The magnitude of $\Delta_r G^{\ominus}$ (in kJ mol$^{-1}$) at this temperature is __________. (Nearest Integer) (Given : R $= 8.3$ J mol$^{-1}$ K$^{-1}$; $\ln 10 = 2.3$, $\log 2 = 0.3$, $\log 3 = 0.48$, $\log 5 = 0.69$, $\log 7 = 0.84$)

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:

$20.0 \mathrm{dm}^{3}$ of an ideal gas ' X ' at 600 K and 0.5 MPa undergoes isothermal reversible expansion until pressure of the gas is 0.2 MPa. Which of the following option is correct? (Given: $\log 2=0.3010$ and $\log 5=0.6989$)

Consider the following data for the reaction $X_2(g) + Y_2(g) \rightleftharpoons 2XY(g)$ at $600\text{ K}$. The $\Delta_r G^\circ$ (in kJ mol$^{-1}$) for the reaction is : <table class="pyq-table"><tbody><tr><th>Compound</th><th>$\Delta_f H^\circ_{600K}$ (kJ mol$^{-1}$)</th><th>$S^\circ_{600K}$ (J mol$^{-1}$ K$^{-1}$)</th></tr><tr><td>$XY(g)$</td><td>$42$</td><td>$200$</td></tr><tr><td>$X_2(g)$</td><td>$8$</td><td>$140$</td></tr><tr><td>$Y_2(g)$</td><td>$80$</td><td>$250$</td></tr></tbody></table>

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 :