Physical Chemistry PYQ — Page 4

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.

Consider a solution of $\mathrm{CO}_{2}(\mathrm{~g})$ dissolved in water in a closed container. Which one of the following plots correctly represents variation of log (partial pressure of $\mathrm{CO}_{2}$ in vapour phase above water) $[y$-axis] with $\log$ (mole fraction of $\mathrm{CO}_{2}$ in water) $[x$-axis $]$ at $25^{\circ} \mathrm{C}$ ?

The correct order of molar heat capacities measured at $298\text{ K}$ and $1\text{ bar}$ is :

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:

The reaction $A(g) \rightleftharpoons B(g) + C(g)$ was initiated with the amount '$a$' of $A(g)$. At equilibrium it is found that the amount of $A(g)$ remaining is $(a - x)$ at a total pressure of $p$. The equilibrium constant $K_p$ of the reaction can be calculated from the expression :

$\mathrm{X}_{2}(\mathrm{~g})+\mathrm{Y}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{Z}(\mathrm{g})$ $\mathrm{X}_{2}(\mathrm{~g})$ and $\mathrm{Y}_{2}(\mathrm{~g})$ are added to a 1 L flask and it is found that the system attains the above equilibrium at $\mathrm{T}(\mathrm{K})$ with the number of moles of $\mathrm{X}_{2}(\mathrm{~g}), \mathrm{Y}_{2}(\mathrm{~g})$ and $\mathrm{Z}(\mathrm{g})$ being 3,3 and 9 mol respectively (equilibrium moles). Under this condition of equilibrium, 10 mol of $\mathrm{Z}(\mathrm{g})$ is added to the flask and the temperature is maintained at $\mathrm{T}(\mathrm{K})$. Then the number of moles of $\mathrm{Z}(\mathrm{g})$ in the flask when the new equilibrium is established is $\_\_\_\_$. (Nearest integer)

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?

Arrange the following resultant mixtures in increasing order of their pH values A. $10$ mL $0.2$ M Ca(OH)$_2$ + $25$ mL $0.1$ M HCl B. $10$ mL $0.01$ M H$_2$SO$_4$ + $10$ mL $0.01$ M Ca(OH)$_2$ C. $10$ mL $0.1$ M H$_2$SO$_4$ + $10$ mL $0.1$ M KOH Choose the correct answer from the options given below:

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 :

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]

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)

$t_{100\%}$ 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?

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)

 Given above is the concentration vs time plot for a dissociation reaction : $\mathrm{A} \rightarrow \mathrm{nB}$. Based on the data of the initial phase of the reaction (initial 10 min), the value of n is $\_\_\_\_$.

The temperature at which the rate constants of the given below two gaseous reactions become equal is $\_\_\_\_$ K. (Nearest integer) $\mathrm{X} \longrightarrow \mathrm{Y} \quad \mathrm{k}_{1}=10^{6} e^{\frac{-30000}{\mathrm{~T}}}$ $\mathrm{P} \longrightarrow \mathrm{Q} \quad \mathrm{k}_{2}=10^{4} e^{\frac{-24000}{\mathrm{~T}}}$ Given: $\ln 10=2.303$

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 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)

MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K. $\mathrm{MX}(\mathrm{s}) \rightleftharpoons \mathrm{M}^{+}(\mathrm{aq})+\mathrm{X}^{-}(\mathrm{aq}) ; \mathrm{K}_{\mathrm{sp}}=10^{-10}$ If the standard reduction potential for $\mathrm{M}^{+}(\mathrm{aq}) \xrightarrow{+\mathrm{e}^{-}} \mathrm{M}(\mathrm{s})$ is $\left(\mathrm{E}_{\mathrm{M}^{+} / \mathrm{M}}^{\ominus}\right)=0.79 \mathrm{~V}$, then the value of the standard reduction potential for the metal/metal insoluble salt electrode $\mathrm{E}_{\mathrm{X}^{-} / \mathrm{MX}(\mathrm{s}) / \mathrm{M}}^{\ominus}$ is $\_\_\_\_$ mV. (nearest integer) [Given : $\frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{~V}$ ]

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: