Physical Chemistry PYQ — Page 13

Consider a complex reaction taking place in three steps with rate constants $k_1, k_2$ and $k_3$ respectively. The overall rate constant $k$ is given by the expression $k=\sqrt{\frac{k_1 k_3}{k_2}}$. If the activation energies of the three steps are 60,30 and $10 \mathrm{~kJ} \mathrm{~mol}{ }^{-1}$ respectively, then the overall energy of activation in $\mathrm{kJ} \mathrm{mol}^{-1}$ is $\ldots\ldots$ . (Nearest integer)

On charging the lead storage battery, the oxidation state of lead changes from $x_1$ to $y_1$ at the anode and from $x_2$ to $y_2$ at the cathode. The values of $x_1, y_1, x_2, y_2$ are respectively :

Arrange the following solutions in order of their increasing boiling points. (i) $10^{-4} \mathrm{M~} \mathrm{NaCl}$ (ii) $10^{-4} \mathrm{M~}$ Urea (iii) $10^{-3} \mathrm{M~} \mathrm{NaCl}$ (iv) $10^{-2} \mathrm{M~} \mathrm{NaCl}$

Consider the reaction $\mathrm{X}_2 \mathrm{Y}(\mathrm{~g})=\mathrm{X}_2(\mathrm{~g})+\frac{1}{2} \mathrm{Y}_2(\mathrm{~g})$ The equation representing correct relationship between the degree of dissociation (x) of $\mathrm{X}_2 \mathrm{Y}(\mathrm{g})$ with its equilibrium constant Kp is ______ . Assume $x$ to be very very small.

Consider the following chemical equilibrium of the gas phase reaction at a constant temperature : $\mathrm{A}(\mathrm{~g}) \rightleftharpoons \mathrm{B}(\mathrm{~g})+\mathrm{C}(\mathrm{~g})$ If $p$ being the total pressure, $K_p$ is the pressure equilibrium constant and $\alpha$ is the degree of dissociation, then which of the following is true at equilibrium?

2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is : (Given : Ebullioscopic constant of water $\left.=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$

The elemental composition of a compound is $54.2 \% \mathrm{C}, 9.2 \% \mathrm{H}$ and $36.6 \% \mathrm{O}$. If the molar mass of the compound is $132 \mathrm{~g} \mathrm{~mol}^{-1}$, the molecular formula of the compound is : [Given : The relative atomic mass of $\mathrm{C}: \mathrm{H}: \mathrm{O}=12: 1: 16$ ]

Consider an elementary reaction $\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g}) \rightarrow \mathrm{C}(\mathrm{g})+\mathrm{D}(\mathrm{g})$ If the volume of reaction mixture is suddenly reduced to $\frac{1}{3}$ of its initial volume, the reaction rate will become ' $x$ ' times of the original reaction rate. The value of $x$ is :

1.24 g of \(\mathrm{AX}_2\) (molar mass \(124 \mathrm{~g} \mathrm{~mol}^{-1}\) ) is dissolved in 1 kg of water to form a solution with boiling point of \(100.0156^{\circ} \mathrm{C}\), while \(25.4 \mathrm{~g}^{\circ}\) of \(\mathrm{AY}_2\) (molar mass \(250 \mathrm{~g} \mathrm{~mol}^{-1}\) ) in 2 kg of water constitutes a solution with a boiling point of \(100.0260^{\circ} \mathrm{C}\). \(\mathrm{K}_{\mathrm{b}}\left(\mathrm{H}_2 \mathrm{O}\right)=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) Which of the following is correct ?

For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth ? Where N - Number of Bacteria at any time, $\mathrm{N}_0$ - Initial number of Bacteria.

For $\mathrm{A}_2+\mathrm{B}_2 \rightleftharpoons 2 \mathrm{AB}$ $\mathrm{E}_{\mathrm{a}}$ for forward and backward reaction are 180 and $200 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively If catalyst lowers $\mathrm{E}_{\mathrm{a}}$ for both reaction by $100 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Which of the following statement is correct?

The energy of an electron in first Bohr orbit of H -atom is -13.6 eV. The magnitude of energy value of electron in the first excited state of $\mathrm{Be}^{3+}$ is ________ eV. (nearest integer value)

At the sea level, the dry air mass percentage composition is given as nitrogen gas : 70.0, oxygen gas : 27.0 and argon gas : 3.0. If total pressure is 1.15 atm , then calculate the ratio of followings respectively : (i) partial pressure of nitrogen gas to partial pressure of oxygen gas (ii) partial pressure of oxygen gas to partial pressure of argon gas (Given : Molar mass of $\mathrm{N}, \mathrm{O}$ and Ar are 14, 16, and $40 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively)

The molar conductivity of a weak electrolyte when plotted against the square root of its concentration, which of the following is expected to be observed ?

In the following system, $\mathrm{PCl}_5(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g})$ at equilibrium, upon addition of xenon gas at constant $\mathrm{T} \& \mathrm{p}$, the concentration of

Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12 . The current in Amperes used for the given electrolysis is ____. (Nearest integer).

Given below are two statements : Statement (I) : A spectral line will be observed for a $2 \mathrm{p}_x \rightarrow 2 \mathrm{p}_y$ transition. Statement (II) : $2 P_x$ and $2 p_y$ are degenerate orbitals. In the light of the above statements, choose the correct answer from the options given below :

One mole of an ideal gas expands isothermally and reversibly from $10 \mathrm{dm}^3$ to $20 \mathrm{dm}^3$ at $300 \mathrm{~K}. \Delta \mathrm{U}$, q and work done in the process respectively are : Given : $\mathrm{R}=8.3 \mathrm{JK}^{-1}$ and $\mathrm{mol}^{-1}$ $\begin{aligned}<br />& \text { In } 10=2.3 \\ & \log 2=0.30 \\ & \log 3=0.48<br />\end{aligned}$

20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is _______ $\times 10^{-2} \mathrm{M}$. (Nearest integer)

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?

$37.8 \mathrm{~g} \mathrm{~N}_2 \mathrm{O}_5$ was taken in a 1 L reaction vessel and allowed to undergo the following reaction at 500 K $2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightleftharpoons 2 \mathrm{~N}_2 \mathrm{O}_{4(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})}$ The total pressure at equilibrium was found to be 18.65 bar. Then, $\mathrm{Kp}=$ ______ $\times 10^{-2}$ [nearest integer] Assume $\mathrm{N}_2 \mathrm{O}_5$ to behave ideally under these conditions. Given: $\mathrm{R}=0.082$ bar $\mathrm{L} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$

$1$ Faraday electricity was passed through $\mathrm{Cu}^{2+}(1.5$ $\mathrm{M}, 1 \mathrm{~L}) / \mathrm{Cu}$ and $0.1$ Faraday was passed through $\mathrm{Ag}^{+}(0.2 \mathrm{M}, 1 \mathrm{~L}) / \mathrm{Ag}$ electrolytic cells. After this the two cells were connected as shown below to make an electrochemical cell. The emf of the cell thus formed at 298 K is-  Given: $\mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{\mathrm{o}}=0.34 \mathrm{~V}$ $\mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^0=0.8 \mathrm{~V}$ $\frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.06 \mathrm{~V}$

The reaction \(\mathrm{A}_2+\mathrm{B}_2 \rightarrow 2 \mathrm{AB}\) follows the mechanism  The overall order of the reaction is :

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).