JEE Main 2013 — Physical Chemistry

A radioactive isotope having a half - life period of $3$ days was received after $12$ days. If $3 \mathrm{~g}$ of the isotope is left in the container, what would be the initial mass of the isotope ?

Which one of the following arrangements represents the correct order of the proton affinity of the given species :

A molecule $M$ associates in a given solvent according to the equation $\mathrm{M} \rightleftharpoons(\mathrm{M})_n$. For a certain concentration of M, the van't Hoff factor was found to be $0.9$ and the fraction of associated molecules was $0.2$. The value of $n$ is:

How many grams of methyl alcohol should be added to $10$ litre tank of water to prevent its freezing at $268 \mathrm{~K}$ ? ( $\mathrm{K}_{\mathrm{f}}$ for water is $1.86 \mathrm{~K} \mathrm{~kg}$ $\left.\mathrm{mol}^{-1}\right)$

The wave number of the first emission line in the Balmer series of $\mathrm{H}$-Spectrum is : $(\mathrm{R}=$ Rydberg constant $)$ :

Experimentally it was found that a metal oxide has formula ${M}_{0.98}O$. Metal M, is present as ${M}^{2+}$ and ${M}^{3+}$ in its oxide. Fraction of the metal which exists as ${M}^{3+}$ would be:

Which one of the following arrangements represents the correct order of solubilities of sparingly soluble salts $\mathrm{Hg}_2 \mathrm{Cl}_2, \mathrm{Cr}_2\left(\mathrm{SO}_4\right)_3$, $\mathrm{BaSO}_4$ and $\mathrm{CrCl}_3$ respectively?

Number of atoms in the following samples of substances is largest in:

Given : $\mathrm{XNa}_2 \mathrm{HAsO}_3+\mathrm{YNaBrO}_3+\mathrm{ZHCl} \rightarrow \mathrm{NaBr}+\mathrm{H}_3 \mathrm{AsO}_4+\mathrm{NaCl}$ The values of $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ in the above redox reaction are respectively :

$10 \mathrm{~mL}$ of $2(\mathrm{M}) \mathrm{~NaOH}$ solution is added to $200 \mathrm{~mL}$ of $0.5$ $\mathrm{(M)}$ of $\mathrm{NaOH}$ solution. What is the final concentration ?

The Gibbs energy for the decomposition of $\mathrm{Al}_2 \mathrm{O}_3$ at $500 \mathrm{~C}$ is as follows : $\frac{2}{3} \mathrm{Al}_2 \mathrm{O}_3 \rightarrow \frac{4}{3} \mathrm{Al}+\mathrm{O}_2, \Delta_r G=+940 \mathrm{~kJ} \mathrm{~mol}^{-1}$ The potential difference needed for the electrolytic reduction of aluminium oxide at $500^{\circ} \mathrm{C}$ should be at least :

A solution of copper sulphate $\left(\mathrm{CuSO}_4\right)$ is electrolysed for $10$ minutes with a current of $1.5$ amperes. The mass of copper deposited at the cathode (at. mass of $\mathrm{Cu}=63 \mathrm{u}$ ) is :

Four successive members of the first row of transition elements are listed below with atomic numbers. Which one of them is expected to have the highest ${\text{E}}_{{\text{M}}^{3+}/{\text{M}}^{2+}}^{o}$ value?

The de Broglie wavelength of a car of mass 1000 $\mathrm{kg}$ and velocity $36 \mathrm{~km} / \mathrm{hr}$ is :

The molarity of a solution obtained by mixing $750\mathrm{mL}$ of $0.5(M)\mathrm{HCl}$ with $250\mathrm{mL}$ of $2(M)\mathrm{HCl}$ will be

Given that: (i) $\Delta_{\mathrm{f}} \mathrm{H}^{\circ}$ of $\mathrm{N}_2 \mathrm{O}$ is $82 \mathrm{~kJ} \mathrm{~mol}^{-1}$ (ii) Bond energies of $\mathrm{N} \equiv \mathrm{N}, \mathrm{N}=\mathrm{N}, \mathrm{O}=\mathrm{O}$ and $\mathrm{N}=\mathrm{O}$ are $946,418,498$ and $607 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively, The resonance energy of $\mathrm{N}_2 \mathrm{O}$ is :

Given Reaction Energy Change $\begin{array}{ll} & \text { (in kJ) } \\ \mathrm{Li}(\mathrm{s}) \rightarrow \mathrm{Li}(\mathrm{g}) & 161 \\ \mathrm{Li}(\mathrm{g}) \rightarrow \mathrm{Li}^{+}(\mathrm{g}) & 520 \\ \frac{1}{2} \mathrm{~F}_2(\mathrm{~g}) \rightarrow \mathrm{F}(\mathrm{g}) & 77 \\ \mathrm{~F}(\mathrm{~g})+\mathrm{e}^{-} \rightarrow \mathrm{F}^{-}(\mathrm{g}) & \begin{array}{l}\text { (Electron gain } \\ \text { enthalpy) }\end{array} \\ \mathrm{Li}^{+}(\mathrm{g})+\mathrm{F}^{-}(\mathrm{g}) \rightarrow \mathrm{LiF}(\mathrm{s}) & -1047 \\ \mathrm{Li}(\mathrm{s})+\frac{1}{2} \mathrm{~F}_2(\mathrm{~g}) \rightarrow \mathrm{LiF}(\mathrm{s}) & -617\end{array}$ Based on data provided, the value of electron gain enthalpy of fluorine would be :

Given : $$ \begin{gathered} \mathrm{E}_{\frac{1}{2} \mathrm{Cl}_2 / \mathrm{Cl}^{-}}^{\mathrm{o}}=1.36 \mathrm{~V}, \mathrm{E}_{\mathrm{Cr}^{3+} / \mathrm{Cr}}^{\mathrm{o}}=-0.74 \mathrm{~V} \\ \mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-} / \mathrm{Cr}^{3+}}^{\mathrm{o}}=1.33 \mathrm{~V}, \mathrm{E}_{\mathrm{MnO}_4^{-} / \mathrm{Mn}^{2+}}^{\mathrm{o}}=1.51 \mathrm{~V} \end{gathered} $$ The correct order of reducing power of the species $\left(\mathrm{Cr}, \mathrm{Cr}^{3+}, \mathrm{Mn}^{2+}\right.$ and $\left.\mathrm{Cl}^{-}\right)$will be:

The rate of a reaction doubles when its temperature changes from $300K\mathrm{to}310K$. Activation energy of such a reaction will be: $(\text{R}={\text{8.314 JK}}^{-1}{mol}^{-1}\mathrm{and}log 2=\text{0.301})$

$\mathrm{NaOH}$ is a strong base. What will be $\mathrm{pH}$ of $5.0 \times 10^{-2} \mathrm{M} \mathrm{NaOH}$ solution ? $(\log 2=0.3)$

What would be the $\mathrm{pH}$ of a solution obtained by mixing $5 \mathrm{~g}$ of acetic acid and $7.5 \mathrm{~g}$ of sodium acetate and making the volume equal to $500 \mathrm{~mL}$ ? $\left(\mathrm{K}_{\mathrm{a}}=1.75 \times 10^{-5}, \mathrm{pK}_{\mathrm{a}}=4.76\right)$

A gaseous hydrocarbon on combustion gives $0.72g$ of water and $3.08g$ ${\mathrm{CO}}_{2}$. What is the empirical formula of the hydrocarbon?

$6$ litres of an alkene require $27$ litres of oxygen at constant temperature and pressure for complete combustion. The alkene is :

What is the $\mathrm{pH}$ of a $10^{-4} \mathrm{M} \mathrm{OH}^{-}$solution at $330 \mathrm{~K}$, if $\mathrm{K}_{\mathrm{w}}$ at $330 \mathrm{~K}$ is $10^{-13.6}$ ?

Consider the following reaction: $x {\mathrm{MnO}}_{4}^{-}+y {C}_{2}{O}_{4}^{2-}+{\mathrm{zH}}^{+}\longrightarrow x {\mathrm{Mn}}^{2+}+2y {\mathrm{CO}}_{2}+\frac{z}{2}{H}_{2}O$ The values of x, y and z in the reaction are, respectively:

$12 \mathrm{~g}$ of a nonvolatile solute dissolved in $108 \mathrm{~g}$ of water produces the relative lowering of vapour pressure of $0.1$. The molecular mass of the solute is :

Electrode potentials $\left(\mathrm{E}^{\circ}\right)$ are given below : $\begin{aligned} & \mathrm{Cu}^{+} / \mathrm{Cu}=+0.52 \mathrm{~V} ,\\ & \mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}=+0.77 \mathrm{~V}, \\ & \frac{1}{2} \mathrm{I}_2(\mathrm{~s}) / \mathrm{I}^{-}=+0.54 \mathrm{~V}, \\ & \mathrm{Ag}^{+} / \mathrm{Ag}=+0.88 \mathrm{~V}. \end{aligned}$ Based on the above potentials, strongest oxidizing agent will be :

Given (A) $\mathrm{n}=5, \mathrm{~m}_{\ell}=+1$ (B) $\mathrm{n}=2, \ell=1, \mathrm{~m}_{\ell}=-1, \mathrm{~m}_{\mathrm{s}}=-\mathrm{l} / 2$ The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) are respectively:

The ratio $\frac{K_p}{K_c}$ for the reaction $\mathrm{CO}(g)+\frac{1}{2} O_2(g) \rightleftharpoons C O_2(g)$ is:

The reaction $\mathrm{X} \rightarrow \mathrm{Y}$ is an exothermic reaction. Activation energy of the reaction for $\mathrm{X}$ into $\mathrm{Y}$ is $150 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Enthalpy of reaction is $135 \mathrm{~kJ}$ $\mathrm{mol}^{-1}$. The activation energy for the reverse reaction, $\mathrm{Y} \rightarrow \mathrm{X}$ will be :

A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of $3 7 . {0}^{\circ } \text{C}$. As it does so, it absorbs 208 J of heat. The values of q and w for the process will be (R = 8.314 J/mol K) (ln7.5 = 2.01)

The instantaneous rate of disappearance of $\mathrm{MnO}_4^{-}$ion in the following reaction is $4.56 \times 10^{-3} \mathrm{Ms}^{-1}$ $2 \mathrm{MnO}_4^{-}+10 \mathrm{I}^{-}+16 \mathrm{H}^{+} \rightarrow 2 \mathrm{Mn}^{2+}+5 \mathrm{I}_2+8 \mathrm{H}_2 \mathrm{O}$ The rate of appearance $\mathrm{I}_2$ is :

Vapour pressure of pure benzene is 119 torr and that of toluene is $37.0$ torr at the same temperature. Mole fraction of toluene in vapour phase which is in equilibrium with a solution of benzene and toluene having a mole fraction of toluene $0.50$, will be :

Which of the following statements/relationships is not correct in thermodynamic changes ?

In which of the following exothermic reactions, the heat liberated per mole is the highest ?

The rate constant of a zero order reaction is $2.0 \times$ $10^{-2} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$. If the concentration of the reactant after 25 seconds is $0.5 \mathrm{M}$. What is the initial concentration?

Values of dissociation constant, $K_a$ are given as follows : $\begin{array}{lc}\text { Acid } & \boldsymbol{K}_{\boldsymbol{a}} \\ \mathrm{HCN} & 6.2 \times 10^{-10} \\ \mathrm{HF} & 7.2 \times 10^{-4} \\ \mathrm{HNO}_2 & 4.0 \times 10^{-4}\end{array}$ Correct order of increasing base strength of the base $\mathrm{CN}^{-}, \mathrm{F}^{-}$and $\mathrm{NO}_2^{-}$will be :

(1) $\mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{~g}), \mathrm{K}_1$ (2) $\mathrm{N}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}), \mathrm{K}_2$ (3) $\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightleftharpoons \mathrm{H}_2 \mathrm{O}(\mathrm{g}), \mathrm{K}_3$ The equation for the equilibrium constant of the reaction $$ 2 \mathrm{NH}_3(\mathrm{~g})+\frac{5}{2} \mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) \text {, } $$ $\left(K_4\right)$ in terms of $\mathrm{K}_1, \mathrm{~K}_2$ and $\mathrm{K}_3$ is :

The density of $3 \mathrm{M}$ solution of sodium chloride is $1.252 \mathrm{~g} \mathrm{~mL}^{-1}$. The molality of the solution will be : $\left(\right.$ molar mass, $\left.\mathrm{NaCl}=585 \mathrm{~g} \mathrm{~mol}^{-1}\right)$

Given: $\mathrm{(I)}$ $\begin{aligned} & \mathrm{H}_2(\mathrm{g})+\frac{1}{2} \mathrm{O}_2(\mathrm{g}) \rightarrow \mathrm{H}_2 \mathrm{O}(l) ; \\ & \Delta \mathrm{H}^{\circ}{ }_{298 \mathrm{~K}}=-285.9 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned}$ $\mathrm{(II)}$ $\begin{aligned} & \mathrm{H}_2(\mathrm{g})+\frac{1}{2} \mathrm{O}_2(\mathrm{g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g}); \\ & \Delta \mathrm{H}^{\circ}{ }_{298 \mathrm{~K}}=-241.8 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned}$ The molar enthalpy of vapourisation of water will be :

Energy of an electron is given by $\text{E}=-2\text{.}178\times 1{0}^{-18}(\frac{{\text{Z}}^{2}}{{\text{n}}^{2}})\text{ J}$. Wavelength of light required to excite an electron in a hydrogen atom from level n=1 to n=2 will be : $(\text{h}=6.62\times {10}^{-34} \text{J} \text{s} \text{a}\text{n}\text{d} \text{c}=3.0\times {10}^{8} \text{m}{\text{s}}^{-1})$

How many litres of water must be added to $1$ litre of aqueous solution of $\mathrm{HCl}$ with a pH of $1$ to create an aqueous solution with pH of $2$?

In reaction $\mathrm{A}+2 \mathrm{~B} \rightleftharpoons 2 \mathrm{C}+\mathrm{D}$, initial concentration of $\mathrm{B}$ was $1.5$ times of $\mathrm{[A]}$, but at equilibrium the concentrations of $\mathrm{A}$ and $\mathrm{B}$ became equal. The equilibrium constant for the reaction is :

In an atom how many orbital(s) will have the quantum numbers; $n=3, l=2$ and $m_l=+2$ ?

Solid $\mathrm{Ba}\left(\mathrm{NO}_3\right)_2$ is gradually dissolved in a $1.0 \times 10^{-4} \mathrm{~M} \mathrm{~Na}_2 \mathrm{CO}_3$ solution. At which concentration of $\mathrm{Ba}^{2+}$, precipitate of $\mathrm{BaCO}_3$ begins to form ? $\left(K_{s p}\right.$ for $\left.\mathrm{BaCO}_3=5.1 \times 10^{-9}\right)$