Physical Chemistry PYQ — Page 70

The time for half life period of a certain reaction $A \rightarrow$ products is 1 hour. When the initial concentration of the reactant ' $A$ ', is $2.0 \mathrm{~mol} \mathrm{~L}^{-1}$, how much time does it take for its concentration to come from $0.50$ to $0.25 \mathrm{~mol} \mathrm{~L}^{-1}$ if it is a zero order reaction?

At $25^{\circ} \mathrm{C}$, the solubility product of $\mathrm{Mg}(\mathrm{OH})_2$ is $1.0 \times 10^{-11}$. At which $\mathrm{pH}$, will $\mathrm{Mg}^{2+}$ ions start precipitating in the form of $\mathrm{Mg}(\mathrm{OH})_2$ from a solution of $0.001 \mathrm{M} \mathrm{Mg}^{2+}$ ions ?

If $10^{-4} \mathrm{dm}^3$ of water is introduced into a $1.0 \mathrm{dm}^3$ flask to $300 \mathrm{~K}$, how many moles of water are in the vapour phase when equilibrium is established? (Given : Vapour pressure of $\mathrm{H}_2 \mathrm{O}$ at $300 \mathrm{~K}$ is $3170 \mathrm{~Pa} ; \mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ )

Two liquids $X$ and $Y$ form an ideal solution. At $300 \mathrm{~K}$, vapour pressure of the solution containing 1 mol of $X$ and $3 \mathrm{~mol}$ of $Y$ is $550 \mathrm{~mm} \mathrm{Hg}$. At the same temperature, if $1 \mathrm{~mol}$ of $Y$ is further added to this solution, vapour pressure of the solution increases by $10 \mathrm{~mm} \mathrm{Hg}$. Vapour pressure (in $\mathrm{mmHg}$ ) of $X$ and $Y$ in their pure states will be, respectively :

In an atom, an electron is moving with a speed of $600 \mathrm{~m} / \mathrm{s}$ with an accuracy of $0.005 \%$. Certainity with which the position of the electron can be located is $\left(h=6.6 \times 10^{-34} \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-1}\right.$, mass of electron, $e_m=9.1 \times 10^{-31} \mathrm{~kg}$ )

A binary liquid solution is prepared by mixing $n$-heptane and ethanol. Which one of the following statements is correct regarding the behaviour of the solution?

Calculate the wavelength (in nanometer) associated with a proton moving at $1.0 \times 10^3 \mathrm{~ms}^{-1}$ (Mass of proton $=1.67 \times 10^{-27} \mathrm{~kg}$ and $\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}$ ):

Solid Ba $\left(\mathrm{NO}_3\right)_2$ is gradually dissolved in a $1.0 \times 10^{-4} \mathrm{M} \mathrm{Na}_2 \mathrm{CO}_3$ solution. At what concentration of $\mathrm{Ba}^{2+}$ will a precipitate begin to form ? $\left(\mathrm{K}_{\mathrm{sp}}\right.$ for $\left.\mathrm{Ba} \mathrm{CO}_3=5.1 \times 10^{-9}\right)$.

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $\mathrm{CH}_3 \mathrm{OH}(\ell)+\frac{3}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\ell)$ At $298 \mathrm{~K}$ standard Gibb's energies of formation for $\mathrm{CH}_3 \mathrm{OH}(\ell), \mathrm{H}_2 \mathrm{O}(\ell)$ and $\mathrm{CO}_2(\mathrm{~g})$ are $-166.2,-237.2$ and $-394.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. If standard enthalpy of combustion of methanol is $-726 \mathrm{~kJ} \mathrm{~mol}^{-1}$, efficiency of the fuel cell will be

The half life period of a first order chemical reaction is $6.93$ minutes. The time required for the completion of $99 \%$ of the chemical reaction will be $(\log 2=0.301)$ :

Given : $\mathrm{E}_{\mathrm{Fe}^{3+} / \mathrm{Fe}}^{\circ}=-0.036 \mathrm{~V}, \quad \mathrm{E}_{\mathrm{Fe}^{2+} / \mathrm{Fe}}^{\circ}=-0.439 \mathrm{~V}$. The value of standard electrode potential for the change, $\mathrm{Fe}_{(\text {aq })}^{3+}+\mathrm{e}^{-} \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq})$ will be :

On the basis of the following thermochemical data: $\left(\Delta \mathrm{fG}^{\circ} \mathrm{H}_{\text {(aq) }}^{+}=0\right)$ $$ \begin{aligned} & \mathrm{H}_2 \mathrm{O}(\ell) \rightarrow \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) ; \Delta \mathrm{H}=57.32 \mathrm{~kJ} \\ & \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\ell) ; \Delta \mathrm{H}=-286.20 \mathrm{~kJ} \end{aligned} $$ The value of enthalpy of formation of $\mathrm{OH}^{-}$ion at $25^{\circ} \mathrm{C}$ is:

Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below: $$ \frac{1}{2} \mathrm{Cl}_2(\mathrm{~g}) \stackrel{\frac{1}{2} \Delta_{\mathrm{ass}} \mathrm{H}^{\ominus}}{\longrightarrow} \mathrm{Cl}(\mathrm{g}) \stackrel{\Delta_{\mathrm{eg} H^{\ominus}}}{\longrightarrow} \mathrm{Cl}^{-}(\mathrm{g}) \stackrel{\Delta_{\mathrm{m} \mathrm{on}^{H^{\ominus}}}^{\longrightarrow}}{\longrightarrow} \mathrm{Cl}^{-}(\mathrm{aq}) . $$ The energy involved in the conversion of $\frac{1}{2} \mathrm{Cl}_2(\mathrm{~g})$ to $\mathrm{Cl}^{-}(\mathrm{g})$ (using the data, $\left.\Delta_{\text {diss }} H_{\mathrm{Cl}_2}^{\ominus}=240 \mathrm{kJmol}^{-1}, \Delta_{\mathrm{eg}} H_{\mathrm{cl}}^{\ominus}=-349 \mathrm{kJmol}^{-1}, \Delta_{\mathrm{hyd}} \mathrm{H}_{\mathrm{Cl}}^{\ominus}=-381 \mathrm{kJmol}^{-1}\right)$ will be

For a reaction $\frac{1}{2} A \rightarrow 2 B$, rate of disappearance of ' $A$ ' is related to the rate of appearance of 'B' by the expression

The $\mathrm{pK}_{\mathrm{a}}$ of a weak acid, $\mathrm{HA}$, is $4.80$. The $\mathrm{pK}_{\mathrm{b}}$ of a weak base, $\mathrm{BOH}$, is $4.78$. The $\mathrm{pH}$ of an aqueous solution of the corresponding salt, BA, will be

At $80^{\circ} \mathrm{C}$, the vapour pressure of pure liquid ' $A$ ' is $520 \mathrm{~mm} \mathrm{Hg}$ and that of pure liquid ' $B$ ' is $1000 \mathrm{~mm}$ $\mathrm{Hg}$. If a mixture solution of ' $A$ ' and ' $B$ ' boils at $80^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ pressure, the amount of ' $A$ ' in the mixture is $(1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg})$

The equilibrium constants $K_{P_1}$ and $K_{P_2}$ for the reactions $X \rightleftharpoons 2 Y$ and $Z \rightleftharpoons P+Q$, respectively are in the ratio of $1: 9$. If the degree of dissociation of $X$ and $Z$ be equal then the ratio of total pressure at these equilibria is

The vapour pressure of water at $20^{\circ} \mathrm{C}$ is $17.5 \mathrm{~mm} \mathrm{Hg}$. If $18 \mathrm{~g}$ of glucose $\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6\right)$ is added to $178.2 \mathrm{~g}$ of water at $20^{\circ} \mathrm{C}$, the vapour pressure of the resulting solution will be

For the following three reactions $a, b$ and $c$, equilibrium constants are given: a. $\mathrm{CO}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) ; \quad \mathrm{K}_1$ b. $\mathrm{CH}_4(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_2(\mathrm{~g}) ; \quad \mathrm{K}_2$ c. $\mathrm{CH}_4(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_2(\mathrm{~g})+4 \mathrm{H}_2(\mathrm{~g}) ; \mathrm{K}_3$ Which of the following relations is correct?

Which one of the following constitutes a group of the isoelectronic species?

Standard entropy of $X_2, Y_2$ and $X Y_3$ are 60,40 and $50 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$, respectively. For the reaction, $\frac{1}{2} X_2+\frac{3}{2} Y_2 \rightarrow X Y_3, \Delta \mathrm{H}=-30 \mathrm{~kJ}$, to be at equilibrium, the temperature will be

Given $\mathrm{E}_{\mathrm{Cr}^3+/ \mathrm{Cr}}^{\circ}=-0.72 \mathrm{~V}, \mathrm{E}_{\mathrm{Fe}^{2+/ / \mathrm{Fe}}}^{\circ}=-0.42 \mathrm{~V}$. The potential for the cell $\mathrm{Cr}\left|\mathrm{Cr}^{3+}(0.1 \mathrm{M})\right|\left|\mathrm{Fe}^{2+}(0.01 \mathrm{M})\right| \mathrm{Fe}$ is

Four species are listed below i. $\mathrm{HCO}_3^{-}$ ii. $\mathrm{H}_3 \mathrm{O}^{+}$ iii. $\mathrm{HSO}_4^{-}$ iv. $\mathrm{HSO}_3 \mathrm{~F}$ Which one of the following is the correct sequence of their acid strength?

The ionization enthalpy of hydrogen atom is $1.312 \times 10^6 \mathrm{Jmol}^{-1}$. The energy required to excite the electron in the atom from $n=1$ to $n=2$ is