JEE Main Chemistry — Physical Chemistry previous year questions with solutions.
Which one of the following about an electron occupying the 1 s orbital in a hydrogen atom is incorrect ? (Bohr's radius is represented by a $a_0$)
Some $\mathrm{CO}_2$ gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of $\mathrm{CO}_2$ gas was later passed through an aqueous solution of $\mathrm{Ca}(\mathrm{OH})_2$. The excess unreacted $\mathrm{Ca}(\mathrm{OH})_2$ was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of $\mathrm{CO}_2$ was $x$, then $x$ is ________ $\mathrm{cm}^3$ (nearest integer). [Given : The entire amount of $\mathrm{CO}_2(\mathrm{~g})$ reacted with exactly half the initial amount of $\mathrm{Ca}(\mathrm{OH})_2$ present in the aqueous solution.]
The calculated spin-only magnetic moments of $\mathrm{K}_3\left[\mathrm{Fe}(\mathrm{OH})_6\right]$ and $\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{OH})_6\right]$ respectively are :
$0.2 \%(\mathrm{w} / \mathrm{v})$ solution of NaOH is measured to have resistivity $870.0 \mathrm{~m} \Omega \mathrm{~m}$. The molar conductivity of the solution will be ______ $\times 10^2 \mathrm{mS} \mathrm{dm}{ }^2 \mathrm{~mol}^{-1}$. (Nearest integer)
${ }^1$ The standard enthalpy and standard entropy of decomposition of $\mathrm{N}_2 \mathrm{O}_4$ to $\mathrm{NO}_2$ are $55.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $175.0 \mathrm{~J} / \mathrm{K} / \mathrm{mol}$ respectively. The standard free energy change for this reaction at $25^{\circ} \mathrm{C}$ in J $\mathrm{mol}^{-1}$ is ______ (Nearest integer)
At temperature T, compound \(\mathrm{AB}_{2(\mathrm{~g})}\) dissociates as \(\mathrm{AB}_{2(\mathrm{~g})} \rightleftharpoons \mathrm{AB}_{(\mathrm{g})}+\frac{1}{2} \mathrm{~B}_{2(\mathrm{~g})}\) having degree of dissociation \(x\) (small compared to unity). The correct expression for \(x\) in terms of \(\mathrm{K}_{\mathrm{p}}\) and p is
The equilibrium constant for decomposition of $\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ $\mathrm{H}_2 \mathrm{O}(\mathrm{~g}) \rightleftharpoons \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g})\left(\Delta \mathrm{G}^{\circ}=92.34 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)$ is $8.0 \times 10^{-3}$ at 2300 K and total pressure at equilibrium is 1 bar. Under this condition, the degree of dissociation $(\alpha)$ of water is ________ $\times 10^{-2}$ (nearest integer value). [Assume $\alpha$ is negligible with respect to 1 ]
x mg of $\mathrm{Mg}(\mathrm{OH})_2($ molar mass $=58)$ is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ________ mg. (Nearest integer) (Given : $\mathrm{Mg}(\mathrm{OH})_2$ is assumed to dissociate completely in $\mathrm{H}_2 \mathrm{O}$)
The pH of a 0.01 M weak acid $\mathrm{HX}\left(\mathrm{K}_{\mathrm{a}}=4 \times 10^{-10}\right)$ is found to be 5. Now the acid solution is diluted with excess of water so that the pH of the solution changes to 6. The new concentration of the diluted weak acid is given as $x \times 10^{-4} \mathrm{M}$. The value of x is ________ (nearest integer)
pH of water is 7 at $25^{\circ} \mathrm{C}$. If water is heated to $80^{\circ} \mathrm{C}$., it's pH will :
$\begin{aligned} & \mathrm{S}(\mathrm{~g})+\frac{3}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{SO}_3(\mathrm{~g})+2 x \mathrm{kcal} \\ & \mathrm{SO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{SO}_3(\mathrm{~g})+y \mathrm{kcal} \end{aligned}$ The heat of formation of $\mathrm{SO}_2(\mathrm{~g})$ is given by :
The species which does not undergo disproportionation reaction is :
Consider the following plots of log of rate constant $\mathrm{k}(\log \mathrm{k})$ vs $\frac{1}{\mathrm{~T}}$ for three different reactions. The correct order of activation energies of these reactions is 
$\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ is a first order reaction. $\begin{array}{|l|l|l|}\hline \text{Time} & T & \infty \\\hline \mathbf{P}_{\text {system }} & \mathrm{P}_{\mathrm{t}} & \mathrm{P}_{\infty} \\\hline\end{array}$ The reaction was started with reactant A only. Which of the following expression is correct for rate constant k ?
Consider the following statements related to temperature dependence of rate constants. Identify the correct statements, A. The Arrhenius equation holds true only for an elementary homogenous reaction. B. The unit of A is same as that of k in Arrhenius equation. C. At a given temperature, a low activation energy means a fast reaction. D. A and Ea as used in Arrhenius equation depend on temperature. E. When $\mathrm{Ea} \gg \mathrm{RT}$. A and Ea become interdependent. Choose the correct answer from the options given below :
Reactant A converts to product D through the given mechanism (with the net evolution of heat) : $\mathrm{A} \rightarrow \mathrm{B} \quad$ slow $; \Delta \mathrm{H}=+\mathrm{ve}$ $\mathrm{B} \rightarrow \mathrm{C}$ fast; $\Delta \mathrm{H}=-\mathrm{ve}$ $\mathrm{C} \rightarrow \mathrm{D} \quad$ fast ; $\Delta \mathrm{H}=-\mathrm{ve}$ Which of the following represents the above reaction mechanism?
In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $t_1$ and $t_2(s)$, respectively. The ratio $t_1 / t_2$ will :
 For a given reaction $\mathrm{R} \rightarrow \mathrm{P}, \mathrm{t}_{1 / 2}$ is related to $[\mathrm{A}]_0$ as given in table. Given: $\log 2=0.30$ Which of the following is true? A. The order of the reaction is $1 / 2$. B. If $[\mathrm{A}]_0$ is 1 M , then $\mathrm{t}_{1 / 2}$ is $200 \sqrt{10} \mathrm{~min}$ C. The order of the reaction changes to 1 if the concentration of reactant changes from 0.100 M to 0.500 M . D. $\mathrm{t}_{1 / 2}$ is 800 min for $[\mathrm{A}]_0=1.6 \mathrm{M}$ Choose the correct answer from the options given below: Options
$\mathrm{A} \rightarrow \mathrm{~B}$ The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K . If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and the frequency factor is $10^{20}$, the time required for $50 \%$ molecules of A to become $B$ is _________ picoseconds (nearest integer). $\left[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$
For the thermal decomposition of $\mathrm{N}_2 \mathrm{O}_5(\mathrm{~g})$ at constant volume, the following table can be formed, for the reaction mentioned below. $2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \rightarrow 2 \mathrm{~N}_2 \mathrm{O}_4(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g})$  $\mathrm{x}=\ldots \times 10^{-3} \mathrm{~atm} \text { [nearest integer] }$ Given : Rate constant for the reaction is $4.606 \times 10^{-2} \mathrm{~s}^{-1}$.
Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom? (A)$1 \mathrm{~s} \lt 2 \mathrm{p} \lt 3 \mathrm{~d} \lt 4 \mathrm{~s}$ (B) $1 \mathrm{~s} \lt 2 \mathrm{~s}=2 \mathrm{p} \lt 3 \mathrm{~s}=3 \mathrm{p}$ (C) $1 \mathrm{~s} \lt 2 \mathrm{~s} \lt 2 \mathrm{p} \lt 3 \mathrm{~s} \lt 3 \mathrm{p}$ (D) $1 \mathrm{~s} \lt 2 \mathrm{~s} \lt 4 \mathrm{~s} \lt 3 \mathrm{~d}$ Choose the correct answer from the options given below :
500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm. The final temperature and the change in internal energy respectively are: Given : \(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\)
Match the LIST-I with LIST-II  Choose the correct answer from the options given below: