JEE Main 2009 — Physical Chemistry

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

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, $e_m=9.1 \times 10^{-31} \mathrm{~kg}$ )

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:

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 $\left.\mathrm{Ba} \mathrm{CO}_3=5.1 \times 10^{-9}\right)$.

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 $(\log 2=0.301)$ :

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 :