Physical Chemistry PYQ — Page 61

What is the standard reduction potential $({E}^{o})$ for ${\mathrm{Fe}}^{3+}\rightarrow \mathrm{Fe}?$ Given that: ${\mathrm{Fe}}^{2+}+2{e}^{-}\rightarrow \mathrm{Fe};{E}_{{\mathrm{Fe}}^{2+}/\mathrm{Fe}}^{o}=-0.47V$ ${\mathrm{Fe}}^{3+}+{e}^{-}\rightarrow {\mathrm{Fe}}^{2+};{E}_{{\mathrm{Fe}}^{3+}/{\mathrm{Fe}}^{2+}}^{o}=+0.77V$

Two reactions ${A}_{1}$ and ${A}_{2}$ have identical pre-exponential factors. The activation energy of ${A}_{1}$ is more than ${A}_{2}$ by $10\mathrm{kJ}{\mathrm{mol}}^{-1}$ . If ${k}_{1}$ and ${k}_{2}$ are the rate constants for reactions ${A}_{1}$ and ${A}_{2}$, respectively at $300K$, then $\mathrm{ln}⁡(\frac{{k}_{2}}{{k}_{1}})$ is equal to $(R=8.314 J {\mathrm{mol}}^{-1}{K}^{-1})$

$50 \mathrm{mL}$ of $0.2M$ ammonia solution is treated with $25\mathrm{mL}\mathrm{of}0.2M\mathrm{HCl}$. If ${\mathrm{pK}}_{b}$ of ammonia solution is $4.75$, the $\mathrm{pH}$ of the mixture will be:

What quantity (in $\mathrm{mL}$) of a $45%$ acid solution of a mono-protic strong acid must be mixed with a $20%$ solution of the same acid to produce $800\mathrm{mL}$ of a $29.875%$ acid solution?

The freezing point of benzene decreases by ${0.45}^{^{\circ}}C$ on adding $0.2 g$ of acetic acid to $20g$ of benzene. If acetic acid associates to form a dimer in benzene, then what is the percentage association of acetic acid in benzene? $({K}_{f}\mathrm{for} \mathrm{benzene}=5.12 K \mathrm{kg} {\mathrm{mol}}^{-1} )$

The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal: $\text{F}{\text{e}}_{2}{\text{O}}_{3}(\text{s})+3\text{C}\text{O}(\text{g}) \rightleftharpoons 2\text{F}\text{e} (\text{l})+3\text{C}{\text{O}}_{2}(\text{g})$ Using the Le Chatelier's principle, predict which one of the following will not disturb the equilibrium?

Excess of $\mathrm{NaOH}(\mathrm{aq})$ was added to $100\mathrm{mL}$ of ${\mathrm{FeCl}}_{3} (\mathrm{aq})$ resulting into $2.14g$ of $\mathrm{Fe}{(\mathrm{OH})}_{3}$. The molarity of ${\mathrm{FeCl}}_{3}(\mathrm{aq})$ is: (Given the molar mass of$\mathrm{Fe}=56g$${\mathrm{mol}}^{-1}$ and molar mass of $\mathrm{Cl}=35.5 g {\mathrm{mol}}^{-1}$)

$1$ gram of a carbonate $({M}_{2}{\mathrm{CO}}_{3})$ on treatment with excess $\mathrm{HCl}$ produces $0.01186$ moles of ${\mathrm{CO}}_{2}$ . The molar mass of ${M}_{2}{\mathrm{CO}}_{3}$ in ${\mathrm{gmol}}^{-1}$ is:

To find the standard potential of ${M}^{3+}/M$ electrode, the following cell is constituted: $\mathrm{Pt}/M/{M}^{3+} (0.001 \mathrm{mol} {L}^{-1})/{\mathrm{Ag}}^{+} (0.01 \mathrm{mol} {L}^{-1})/\mathrm{Ag}$ The emf of the cell is found to be $0.421\mathrm{volt}$ at $298K$. The standard potential of half-reaction ${M}^{3+}+3{e}^{-}\rightarrow M$ at $298K$ will be: (Given: ${E}_{\frac{{\mathrm{Ag}}^{+}}{\mathrm{Ag}}}^{\circleddash }$ at $298K=0.80\mathrm{volt}$)

The rate of a reaction quadruples when the temperature changes from $300$ to $310K$ . The activation energy of this reaction is: (Assume Activation energy and pre-exponential factor are independent of temperature; $\mathrm{ln}(2)=0.693;R=8.314J{\mathrm{mol}}^{-1}{K}^{-1}$)

The radius of the second Bohr orbit for hydrogen atom is (Planck's constant, $(h)=6.6262\times {10}^{-34}\mathrm{Js};$ mass of electron $=9.1091\times {10}^{-31}\mathrm{kg};$ charge of electron $=1.60210\times {10}^{-19}C;$ permittivity of vacuum, $({\in }_{0})=8.854185\times {10}^{-12}{\mathrm{kg}}^{-1}{m}^{-3}{A}^{2}$)

The rate of a reaction A doubles on increasing the temperature from$300\mathrm{to}310K$. By how much, the temperature of reaction B should be increased from $300K$ so that rate doubles if activation energy of the reaction B is twice to that of reaction A.

A solution is prepared by mixing $8.5$ g of ${\mathrm{CH}}_{2}{\mathrm{Cl}}_{2}$ and $11.95 \text{g}$ of ${\mathrm{CHCl}}_{3}$ . If vapour pressure of ${\mathrm{CH}}_{2}{\mathrm{Cl}}_{2}$ and ${\mathrm{CHCl}}_{3}$ at $298$K are $415$ and $200$ mm Hg respectively, the mole fraction of ${\mathrm{CHCl}}_{3}$ in vapour form is: $(\text{M}\text{o}\text{l}\text{a}\text{r} \text{m}\text{a}\text{s}\text{s} \text{o}\text{f} \mathrm{Cl}=35.5 \text{g} \text{m}\text{o}{\text{l}}^{-1})$

The solubility of ${N}_{2}$ in water at $\text{300} \text{K}$ and $\text{500} \text{torr}$ partial pressure is $0.01g{L}^{-1}.$ The solubility (in ${ \text{g L}}^{ -\text{1}}$ ) at $\text{750} \text{torr}$ partial pressure is:

A reaction at 1 bar is non-spontaneous at low temperature but becomes spontaneous at high temperature. Identify the correct statement about the reaction among the following:

What will happen when a block of copper metal is dropped into a beaker containing a solution of $1 \text{M}$ $ZnS{O}_{4}$?

$18g$ glucose $({C}_{6}{H}_{12}{O}_{6})$ is added to $178.2g$ water. The vapour pressure of water (in torr) for this aqueous solution is:

If$100\mathrm{mole}$ of ${H}_{2}{O}_{2}$ decompose at $1\mathrm{bar}$ and $300K$, the work is done ($\mathrm{kJ}$) by one mole of ${O}_{2}(g)$ as it expands against $1\mathrm{bar}$ pressure is: $2{H}_{2}{O}_{2}(l)\rightleftharpoons 2{H}_{2}O(l)+{O}_{2}(g)$ $(R=8.3 J {K}^{-1} {\mathrm{mol}}^{-1})$

A solid $\mathrm{XY}$kept in an evacuated sealed container undergoes decomposition to form a mixture of gases $X\mathrm{and}Y$ at temperature $T$. The equilibrium pressure is $10\mathrm{bar}$ in this vessel. ${K}_{p}$ for this reaction is?

At $300K$ and $1\mathrm{atm}$, $15\mathrm{mL}$ of a gaseous hydrocarbon requires $375\mathrm{mL}$ air containing $20%{O}_{2}$ by volume, for complete combustion. After combustion, the gases occupy $345\mathrm{mL}$. Assuming that the water formed is in liquid form and the volumes were measured at the same temperature and pressure, the formula of the hydrocarbon is: (Assume complete combustion of reactant)

The total number of orbitals associated with the principal quantum number $5$ is:

For the reaction, $A(g)+B(g)\rightarrow C(g)+D(g), \Delta {H}^{o}$ and $\Delta {S}^{o}$ are, respectively, $-29.8 kJ mo{l}^{-1}$ and $-0.100 kJ {K}^{-1} mo{l}^{-1}$ at 298 K. The equilibrium constant for the reaction at 298 k is:

Decomposition of ${H}_{2}{O}_{2}$ follows a first order reaction. In fifty minutes the concentration of ${\text{H}}_{2} {\text{O}}_{2}$ decreases from $0.5$ to $0.125 M$ in one such decomposition. When the concentration of ${H}_{2}{O}_{2}$ reaches $0.05 M$ , the rate of formation of ${O}_{2}$ will be:

The heats of combustion of carbon and carbon monoxide are $-393.5 and-283.5 kJ mo{l}^{-1},$ respectively. The heat of formation $(\mathrm{in}\mathrm{kJ})$ of carbon monoxide per mole is: