$50 \mathrm{mL}$ of $0.2$ molal urea solution (density $=1.012 \mathrm{g} {\mathrm{mL}}^{-1}$ at $300 \mathrm{K}$ ) is mixed with $250 \mathrm{mL}$ of a solution containing $0.06 \mathrm{g}$ of urea. Both the solutions were prepared in the same solvent. The osmotic pressure (in torr) of the resulting at $300 \mathrm{K}$ is
[Use : Molar mass of urea $=60 \mathrm{g} {\mathrm{mol}}^{-1}$; gas constant, $\mathrm{R}=62 \mathrm{L}-\mathrm{torr} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$;
Assume, $\left.{\mathrm{\Delta }}_{mix}\mathrm{H}=0,{\mathrm{\Delta }}_{\text{mix }}\mathrm{V}=0\right]$

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Redox reaction play a pivotal role in chemistry and biology. The values of standard redox potential \(\left(E^{\circ}\right)\) of two half-cell reactions decide which way the reaction is expected to proceed. A simple example is a Daniel cell in which zinc goes into solution and copper gets deposited. Given below are a set of half-cell reactions (acidic medium) along with their \(E^{\circ}(V\) with respect to normal hydrogen electrode) values. Using this data obtain the correct explanations to Questions 14-19.
\(\mathrm{I}_2+2 e^{-} \longrightarrow 2 \mathrm{I}^{-} E^{\circ}=0.54 \)
\( \mathrm{Cl}_2+2 e^{-} \longrightarrow 2 \mathrm{Cl}^{-} E^{\circ}=1.36 \)
\( \mathrm{Mn}^{3+}+e^{-} \longrightarrow \mathrm{Mn}^{2+} E^{\circ}=1.50 \)
\( \mathrm{Fe}^{3+}+e^{-} \longrightarrow \mathrm{Fe}^{2+} E^{\circ}=0.77 \)
\( \mathrm{O}_2+4 \mathrm{H}^{+}+4 e^{-} \longrightarrow 2 \mathrm{H}_2 \mathrm{O} E^{\circ}=1.23\)
Question:
While \(\mathrm{Fe}^{3+}\) is stable, \(\mathrm{Mn}^{3+}\) is not stable in acid solution because

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at $1$ bar pressure is given. ${\mathrm{S}}_{\mathrm{T}}$ and ${\mathrm{S}}_0$ are entropies of the phases at temperatures $\mathrm{T}$ and $0 \mathrm{K}$, respectively. The transition temperature for $\alpha$ to $\beta$ phase change is $600 \mathrm{K}$ and ${\mathrm{C}}_{\mathrm{p},\mathrm{\beta }}-{\mathrm{C}}_{\mathrm{p},\mathrm{\alpha }}=1 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$. Assume $\left({\mathrm{C}}_{\mathrm{p},\mathrm{\beta }}-{\mathrm{C}}_{\mathrm{p},\mathrm{\alpha }}\right)$ is independent of temperature in the range of $200$ to $700 \mathrm{K}.{\mathrm{C}}_{\mathrm{p},\mathrm{\alpha }}$ and ${\mathrm{C}}_{\mathrm{p},\mathrm{\beta }}$ are heat capacities of $\alpha$ and $\beta$ phases, respectively. The value of enthalpy change, ${\mathrm{H}}_{\beta }-{\mathrm{H}}_{\alpha }$ (in ${\mathrm{Jmol}}^{-1}$ ), at $300 \mathrm{K}$ is

LIST-I contains compounds and LIST-II contains reactions

List - I	List - II
(I) \(H _2 O _2\)	(P) \(Mg \left( HCO _3\right)_2+ Ca\) \((OH)_2 \rightarrow\)
(II) \(Mg ( OH )_2\)	(Q) \(BaO _2+ H _2 SO _4 \rightarrow\)
(III) \(BaCl _2\)	(R) \(Ca \left( OH _2\right) 2\) \(+ MgCl _2 \rightarrow\)
(IV) \(CaCO _3\)	(S) \(BaO _2+ HCl \rightarrow\)
	(T) \(Ca \left( HCO _3\right)_2\) \(+ Ca ( OH )_2\)

Match each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the correct option

In an electrochemicalcell, dichromate ions in aqueous acidic medium are reduced to \(\mathrm{Cr}^{3+}\). The current (in amperes) that flows through the cell for 48.25 minutes to produce 1 mole of \(\mathrm{Cr}^{3+}\) is _____ .
Use: 1 Faraday \(=96500 \mathrm{C} \mathrm{mol}^{-1}\)

The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are)

Vessel-1 contains \(\mathbf{w}_2 \mathrm{~g}\) of a non-volatile solute \(\mathbf{X}\) dissolved in \(\mathbf{w}_1 \mathrm{~g}\) of water. Vessel- 2 contains \(\mathbf{w}_2 \mathrm{~g}\) of another non-volatile solute \(\mathbf{Y}\) dissolved in \(\mathbf{w}_1 \mathrm{~g}\) of water. Both the vessels are at the same temperature and pressure. The molar mass of \(\mathbf{X}\) is \(80 \%\) of that of \(\mathbf{Y}\). The van't Hoff factor for \(\mathbf{X}\) is 1.2 times of that of \(\mathbf{Y}\) for their respective concentrations.
The elevation of boiling point for solution in Vessel-1 is ________. \(\%\) of the solution in Vessel-2.

Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter \(D\) of a tube. The measured value of \(D\) is:

An aqueous solution is prepared by dissolving $0.1$ mole of an ionic salt in $1.8 \mathrm{kg}$ of water at $35°\mathrm{C}$. The salt remains $90\%$ dissociated in the solution. The vapour pressure of the solution is $59.724 \mathrm{mm}$ of $\mathrm{Hg}$. Vapor pressure of water at $35°\mathrm{C}$ is $60.000 \mathrm{mm}$ of $\mathrm{Hg}$. The number of ions present per formula unit of the ionic salt is _____.

Consider the following reversible reaction:
$\mathrm{A} \left(\mathrm{g}\right)+\mathrm{B}\mathrm{ }\left(\mathrm{g}\right)\rightleftharpoons \mathrm{AB} \left(\mathrm{g}\right)$
The activation energy of the backward reaction exceeds that of the forward reaction by $2\mathrm{RT}$ (in $\mathrm{ }{\mathrm{mol}}^{-1}$). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction, the absolute value of $∆{\mathrm{G}}^{⊝} \left(\mathrm{in}\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}\right)$ for the reaction at $300 \mathrm{K}$ is ____.
(Given; $\ln \left(2\right)=\mathrm{ }0.7, =\mathrm{ }2500\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}\mathrm{ }\mathrm{at}\mathrm{ }300\mathrm{ }\mathrm{K}$ and $\mathrm{G}$ is the Gibbs energy)

The line passing through the extremity \(A\) of the major axis and extremity \(B\) of the minor axis of the ellipse \(x^2+9 y^2=9\) meets its auxiliary circle at the point \(M\). Then, the area of the triangle with vertices at \(A, M\) and the origin \(O\) is

The difference in the oxidation numbers of the two types of sulphur atoms in \(\mathrm{Na}_2 \mathrm{~S}_4 \mathrm{O}_6\) is

Let \(\mathbb{R}^3\) denote the three-dimensional space. Take two points \(P=(1,2,3)\) and \(Q=(4,2,7)\). Let \(\operatorname{dist}(X, Y)\) denote the distance between two points \(X\) and \(Y\) in \(\mathbb{R}^3\). Let
\(\begin{gathered}S=\left\{X \in \mathbb{R}^3:(\operatorname{dist}(X, P))^2-(\operatorname{dist}(X, Q))^2=50\right\} \text { and } \\T=\left\{Y \in \mathbb{R}^3:(\operatorname{dist}(Y, Q))^2-(\operatorname{dist}(Y, P))^2=50\right\} .\end{gathered}\)
Then which of the following statements is (are) TRUE?