Physical Chemistry PYQ — Page 15

Given below are two statements : Statement I : Mohr's salt is composed of only three types of ions-ferrous, ammonium and sulphate. Statement II : If the molar conductance at infinite dilution of ferrous, ammonium and sulphate ions are $\mathrm{x}_1, \mathrm{x}_2$ and $\mathrm{x}_3 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$, respectively then the molar conductance for Mohr's salt solution at infinite dilution would be given by $\mathrm{x}_1+\mathrm{x}_2+2 \mathrm{x}_3$ In the light of the given statements, choose the correct answer from the options given below :

For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant n ? [E: Energy of the stationary state, Z : atomic number, $\mathrm{n}=$ principal quantum number]

$\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ is a first order reaction. $\begin{array}{|l|l|l|}\hline \text{Time} & T & \infty \\\hline \mathbf{P}_{\text {system }} & \mathrm{P}_{\mathrm{t}} & \mathrm{P}_{\infty} \\\hline\end{array}$ The reaction was started with reactant A only. Which of the following expression is correct for rate constant k ?

Standard electrode potentials for a few half cells are mentioned below : $\begin{aligned} & \mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{\circ}=0.34 \mathrm{~V}, \mathrm{E}_{\mathrm{Zn}^{2+} / \mathrm{Zn}}^{\circ}=-0.76 \mathrm{~V} \\ & \mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^{\circ}=0.80 \mathrm{~V}, \mathrm{E}_{\mathrm{Mg}^{2+} / \mathrm{Mg}}^{\circ}=-2.37 \mathrm{~V} \end{aligned}$ Which one of the following cells gives the most negative value of $\Delta \mathrm{G}^{\circ}$ ?

A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2 A . The amount of the aluminium deposited at the cathode is [Given : molar mass of aluminium and chlorine are $27 \mathrm{~g} \mathrm{~mol}^{-1}$ and $35.5 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively. Faraday constant $\left.=96500 \mathrm{C} \mathrm{mol}^{-1}\right]$

Consider a binary solution of two volatile liquid components 1 and $2 . x_1$ and $y_1$ are the mole fractions of component 1 in liquid and vapour phase, respectively. The slope and intercept of the linear plot of $\frac{1}{x_1}$ vs $\frac{1}{y_1}$ are given respectively as:

 An ideal gas undergoes a cyclic transformation starting from the point $A$ and coming back to the same point by tracing the path $\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{D} \rightarrow \mathrm{A}$ as shown in the three cases above. Choose the correct option regarding $\Delta \mathrm{U}$ :

Mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dil. HCl is Given : Molar mass of Mg is $24 \mathrm{~g} \mathrm{~mol}^{-1}$.

The percentage dissociation of a salt $\left(\mathrm{MX}_3\right)$ solution at given temperature (van't Hoff factor $\mathrm{i}=$ 2) is ______ % (Nearest integer)

Ice at $-5^{\circ} \mathrm{C}$ is heated to become vapor with temperature of $110^{\circ} \mathrm{C}$ at atmospheric pressure. The entropy change associated with this process can be obtained from

Reaction $\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})$ is a first order reaction. It was started with pure A  Which of the following option is incorrect?

Arrange the following in order of magnitude of work done by the system / on the system at constant temperature : (a) $\left|\mathrm{w}_{\text {reversible }}\right|$ for expansion in infinite stage. (b) $\left|w_{\text {irreversible }}\right|$ for expansion in single stage. (c) $\left|w_{\text {reversible }}\right|$ for compression in infinite stage. (d) $\left|w_{\text {irreversible }}\right|$ for compression in single stage. Choose the correct answer from the options given below:

Consider the equilibrium $\mathrm{CO}(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_4(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{~g})$ If the pressure applied over the system increases by two fold at constant temperature then (A) Concentration of reactants and products increases. (B) Equilibrium will shift in forward direction. (C) Equilibrium constant increases since concentration of products increases. (D) Equilibrium constant remains unchanged as concentration of reactants and products remain same. Choose the correct answer from the options given below :

The bond dissociation enthalpy of $\mathrm{X}_2 \Delta \mathrm{H}_{\text {bond }}$ calculated from the given data is $\qquad$ $\mathrm{kJ} \mathrm{mol}^{-1}$. (Nearest integer) $\begin{aligned} & \mathrm{M}^{+} \mathrm{X}^{-}(\mathrm{s}) \rightarrow \mathrm{M}^{+}(\mathrm{g})+\mathrm{X}^{-}(\mathrm{g}) \Delta \mathrm{H}_{\text {lattice }}^*=800 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ & \mathrm{M}(\mathrm{~s}) \rightarrow \mathrm{M}(\mathrm{~g}) \Delta \mathrm{H}_{\text {sub }}^{\circ}=100 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned}$ $\mathrm{M}(\mathrm{~g}) \rightarrow \mathrm{M}^{+}(\mathrm{g})+\mathrm{e}^{-}(\mathrm{g}) \Delta \mathrm{H}_{\mathrm{i}}=500 \mathrm{~kJ} \mathrm{~mol}^{-1}$ $\mathrm{X}(\mathrm{~g})+\mathrm{e}^{-}(\mathrm{g}) \rightarrow \mathrm{X}^{-}(\mathrm{g}) \Delta \mathrm{H}_{\mathrm{eg}}^*=-300 \mathrm{~kJ} \mathrm{~mol}^{-1}$ $\mathrm{M}(\mathrm{~s})+\frac{1}{2} \mathrm{X}_2(\mathrm{~g}) \rightarrow \mathrm{M}^{+} \mathrm{X}^{-}(\mathrm{s}) \Delta \mathrm{H}_f^{\circ}=-400 \mathrm{~kJ} \mathrm{~mol}^{-1}$ [Given : $\mathrm{M}^{+} \mathrm{X}^{-}$is a pure ionic compound and X forms a diatomic molecule $\mathrm{X}_2$ in gaseous state]

Given below are two statements about X-ray spectra of elements : Statement (I) : A plot of $\sqrt{v}$ ( $v=$ frequency of $X$-rays emitted) vs atomic mass is a straight line. Statement (II) : A plot of $v(v=$ frequency of $X$-rays emitted) vs atomic number is a straight line. In the light of the above statements, choose the correct answer from the options given below :

If \(\mathrm{a}_0\) is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength \((\lambda)\) of the electron present in the second orbit of hydrogen atom? [n : any integer]

Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K . If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from following

For hydrogen atom, the orbital/s with lowest energy is/are : (A) 4 s (B) $3 \mathrm{p}_x$ (C) $3 \mathrm{~d}_{x^2-y^2}$ (D) $3 \mathrm{~d}_{z^2}$ (E) $4 \mathrm{p}_z$ Choose the correct answer from the options given below :

The calculated spin-only magnetic moments of $\mathrm{K}_3\left[\mathrm{Fe}(\mathrm{OH})_6\right]$ and $\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{OH})_6\right]$ respectively are :

0.1 M solution of KI reacts with excess of $\mathrm{H}_2 \mathrm{SO}_4$ and $\mathrm{KIO}_3$ solutions. According to equation $5 \mathrm{I}^{-}+\mathrm{IO}_3^{-}+6 \mathrm{H}^{+} \rightarrow 3 \mathrm{I}_2+3 \mathrm{H}_2 \mathrm{O}$ Identify the correct statements : (A) 200 mL of KI solution reacts with 0.004 mol of $\mathrm{KIO}_3$ (B) 200 mL of KI solution reacts with 0.006 mol of $\mathrm{H}_2 \mathrm{SO}_4$ (C) 0.5 L of KI solution produced 0.005 mol of $\mathrm{I}_2$ (D) Equivalent weight of $\mathrm{KIO}_3$ is equal to ( $\frac{\text { Molecular weight }}{5}$ ) Choose the correct answer from the options given below :

Consider the following cases of standard enthalpy of reaction $\left(\Delta \mathrm{H}_{\mathrm{r}}^{\circ}\right.$ in $\left.\mathrm{kJ} \mathrm{mol}{ }^{-1}\right)$ $\begin{aligned} & \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})+\frac{7}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \Delta \mathrm{H}_1^{\circ}=-1550 \\ & \mathrm{C} \text { (graphite) }+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g}) \quad \Delta \mathrm{H}_2^{\circ}=-393.5 \\ & \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \quad \Delta \mathrm{H}_3^{\circ}=-286 \end{aligned}$ The magnitude of $\Delta \mathrm{H}_{f \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})}^{\circ}$ is _______ $\mathrm{kJ} \mathrm{mol}{ }^{-1}$ (Nearest integer).

Consider the following half cell reaction $\mathrm{Cr}_2 \mathrm{O}_7^{2-}(\mathrm{aq})+6 \mathrm{e}^{-}+14 \mathrm{H}^{+}(\mathrm{aq})$ $\rightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_2 \mathrm{O}(\mathrm{l})$ The reaction was conducted with the ratio of $\frac{\left[\mathrm{Cr}^{3+}\right]^2}{\left[\mathrm{Cr}_2 \mathrm{O}_7^{2-}\right]}=10^{-6}$. The pH value at which the EMF of the half cell will become zero is ________. (nearest integer value) [Given : standard half cell reduction potential $\left.\mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-}, \mathrm{H}^{+} / \mathrm{Cr}^{3+}}^{\mathrm{o}}=1.33 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V}\right]$

The molar conductance of an infinitely dilute solution of ammonium chloride was found to be $185 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and the ionic conductance of hydroxyl and chloride ions are 170 and $70 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-}$ ${ }^1$, respectively. If molar conductance of 0.02 M solution of ammonium hydroxide is $85.5 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$, its degree of dissociation is given by $\mathrm{x} \times 10^{-1}$. The value of $x$ is ________ (Nearest integer)

Which of the following graphs most appropriately represents a zero order reaction ?