Physical Chemistry PYQ

If shortest wavelength of hydrogen atom in Lyman series is $x$, then longest wavelength in Balmer series of $\text{He}^+$ is:

If $3.365$ g of ethanol $(l)$ is burnt completely in a bomb calorimeter at $298.15$ K, the heat produced is $99.472$ kJ. The $|\Delta H_f°|$ of ethanol at $298.15$ K is ______ $\times 10^2$ kJ mol$^{-1}$. (Nearest integer) Given: Standard enthalpy for combustion of graphite $=-393.5$ kJ mol$^{-1}$ Standard enthalpy of formation of water $(l)=-285.8$ kJ mol$^{-1}$ Molar mass in g mol$^{-1}$ of C, H, O are $12$, $1$ and $16$ respectively

Correct statements regarding Arrhenius equation among the following are : A. Factor $e^{-E a / R T}$ corresponds to fraction of molecules having kinetic energy less than Ea. B. At a given temperature, lower the Ea, faster is the reaction. C. Increase in temperature by about $10^{\circ} \mathrm{C}$ doubles the rate of reaction. D. Plot of $\log \mathrm{k}$ vs $\frac{1}{\mathrm{~T}}$ gives a straight line with slope $=-\frac{E a}{R}$. Choose the correct answer from the options given below :

Consider the given graph showing variation of reactant concentration with time. Three different reactions were started with identical initial concentration of reactants. Which of the following statement is correct? 

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)

The osmotic pressure of a living cell is 12 atm at 300 K. The strength of sodium chloride solution that is isotonic with the living cell at this temperature is $\_\_\_\_$ $\mathrm{g} \mathrm{L}^{-1}$. (Nearest integer) Given : $\mathrm{R}=0.08 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ Assume complete dissociation of NaCl (Given : Molar mass of Na and Cl are 23 and $35.5 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively.)

Dissociation of a gas $\mathrm{A}_{2}$ takes place according to the following chemical reaction. At equilibrium, the total pressure is 1 bar at 300 K. $\mathrm{A}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{~A}(\mathrm{~g})$ The standard Gibbs energy of formation of the involved substances has been provided below: \(\begin{array}{|c|c|} \hline \text { Substance } & \Delta \mathrm{G}_{\mathrm{f}}^{\circ} / \mathrm{kJ} \mathrm{~mol}^{-1} \\ \hline \mathrm{~A}_2 & -100.00 \\ \hline \mathrm{~A} & -50.832 \\ \hline \end{array}\) The degree of dissociation of $\mathrm{A}_{2}(\mathrm{~g})$ is given by $\left(x \times 10^{-2}\right)^{1 / 2}$ where $x=$ $\_\_\_\_$. (Nearest integer). [Given: $\mathrm{R}=8 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, \log 2=0.3010, \log 3=0.48$ ] Assume degree of dissociation is not negligible.

14.0 g of calcium metal is allowed to react with excess HCl at 1.0 atm pressure and 273 K. Which of the following statements is incorrect? [Given : Molar mass in $\mathrm{g} \mathrm{mol}^{-1}$ of $\mathrm{Ca}-40, \mathrm{Cl}-35.5, \mathrm{H}-1$]

Consider the general reaction given below at 400 K $x \mathrm{~A}(\mathrm{~g}) \rightleftharpoons y \mathrm{~B}(\mathrm{~g})$ The values of $\mathrm{K}_{\mathrm{p}}$ and $\mathrm{K}_{\mathrm{c}}$ are studied under the same condition of temperature but variation in $x$ and $y$. (i) $\mathrm{K}_{\mathrm{p}}=85.87$ and $\mathrm{K}_{\mathrm{c}}=2.586$ appropriate units (ii) $\mathrm{K}_{\mathrm{p}}=0.862$ and $\mathrm{K}_{\mathrm{c}}=28.62$ appropriate units. The values of $x$ and $y$ in (i) and (ii) respectively are:

Observe the following reactions at $\mathrm{T}(\mathrm{K})$. I. $\mathrm{A} \rightarrow$ products. II. $5 \mathrm{Br}^{-}(\mathrm{aq})+\mathrm{BrO}_{3}{ }^{-}(\mathrm{aq})+6 \mathrm{H}^{+}(\mathrm{aq}) \rightarrow 3 \mathrm{Br}_{2}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$ Both the reactions are started at 10.00 am. The rates of these reactions at 10.10 am are same. The value of $-\frac{\Delta\left[\mathrm{Br}^{-}\right]}{\Delta \mathrm{t}}$ at 10.10 am is $2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}$. The concentration of A at 10.10 am is $10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}$. What is the first order rate constant (in $\mathrm{min}^{-1}$) of reaction $I$ ?

Consider the following electrochemical cell : $\mathrm{Pt}\left|\mathrm{O}_{2}(\mathrm{~g})(1 \mathrm{bar})\right| \mathrm{HCl}(\mathrm{aq}) \| \mathrm{M}^{2+}(\mathrm{aq}, 1.0 \mathrm{M}) \mid \mathrm{M}(\mathrm{~s})$ The pH above which, oxygen gas would start to evolve at anode is $\_\_\_\_$ (nearest integer). $\left[\begin{array}{ll}\text { Given: } & \mathrm{E}^{\mathrm{o}}{ }_{\mathrm{M}^{2+} / \mathrm{M}}=0.994 \mathrm{~V} \\ & \mathrm{E}^{\mathrm{o}}{ }_{\mathrm{O}_{2} / \mathrm{H}_{2} \mathrm{O}}=1.23 \mathrm{~V}\end{array}\right\}$ standard reduction potential $]$

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)

A cup of water at $5^{\circ} \mathrm{C}$ (system) is placed in a microwave oven and the oven is turned on for one minute during which the water begins to boil. Which of the following option is true ?

Consider the following reduction processes : $\mathrm{Al}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}(\mathrm{s}), \mathrm{E}^{0}=-1.66 \mathrm{~V}$ $\mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+}, \mathrm{E}^{0}=+0.77 \mathrm{~V}$ $\mathrm{Co}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Co}^{2+}, \mathrm{E}^{0}=+1.81 \mathrm{~V}$ $\mathrm{Cr}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Cr}(\mathrm{s}), \mathrm{E}^{\circ}=-0.74 \mathrm{~V}$ The tendency to act as reducing agent decreases in the order :

X and Y are the number of electrons involved, respectively during the oxidation of $\mathrm{I}^{-}$to $\mathrm{I}_{2}$ and $\mathrm{S}^{2-}$ to S by acidified $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$. The value of $\mathrm{X}+\mathrm{Y}$ is $\_\_\_\_$.

80 mL of a hydrocarbon on mixing with 264 mL of oxygen in a closed U-tube undergoes complete combustion. The residual gases after cooling to 273 K occupy 224 mL. When the system is treated with KOH solution, the volume decreases to 64 mL. The formula of the hydrocarbon is :

What is the energy (in J atom$^{-1}$) required for the following process? $Li^{2+}(g) \rightarrow Li^{3+}(g) + e^-$ (Take the ionization energy for the H atom in the ground state as $2.18 \times 10^{-18}$ J atom$^{-1}$)

Identify the correct statements from the following: A. Heisenberg uncertainty principle is applicable to electrons. B. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital. C. The energy of $2s$ orbital of H atom is equal to the energy of $2s$ orbital of Li. D. The electronic configuration of Cr is $[\text{Ar}] 3d^5 4s^1$ Choose the correct answer from the options given below:

$M_3 A_2$ is a sparingly soluble salt of molar mass $y$ g mol$^{-1}$ and solubility $x$ g L$^{-1}$. The ratio of the molar concentration of the anion ($A^{3-}$) to the solubility product of the salt is

Solid carbon, CaO and CaCO$_3$ are mixed and allowed to attain equilibrium at T K. $\text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \quad K_{p_1} = 0.08$ atm $\text{C}(s) + \text{CO}_2(g) \rightleftharpoons 2\text{CO}(g) \quad K_{p_2} = 2$ atm The partial pressure of CO is ________ $\times 10^{-1}$ atm

One mole each of He and $A(g)$ are taken in a $10$ L closed flask and heated to $400$ K to establish the following equilibrium. $A(g) \rightleftharpoons B(g)$. $K_c$ for this reaction at $400$ K is $4.0$. The partial pressures (in atm) of He and $B(g)$ are respectively (at equilibrium) (Assume He, $A(g)$ and $B(g)$ behave as ideal gases) (Given: $R = 0.082$ L atm K$^{-1}$ mol$^{-1}$)

Consider two radiations of wavelengths 1. $\lambda_1 = 2000$ Å 2. $\lambda_2 = 6000$ Å The ratio of the energies of these two radiations $\left(\dfrac{E_1}{E_2}\right)$ is ________ (Nearest integer).