The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a solution of a weak acid HY (0.10 M). If ${\mathrm{\lambda }}_{{\mathrm{X}}^{-}}^0\approx {\mathrm{\lambda }}_{{\mathrm{Y}}^{-}}^0$ , the difference in their $\mathrm{p}{\mathrm{K}}_{\mathrm{a}}$ values, $\mathrm{p}{\mathrm{K}}_{\mathrm{a}}\left(\mathrm{H}\mathrm{X}\right)-\mathrm{p}{\mathrm{K}}_{\mathrm{a}}\left(\mathrm{H}\mathrm{Y}\right)$ , is (Consider degree of ionization of both acids to << 1)

The given graph represent the variations of compressibility factor \((Z)=\frac{P V}{n R T}\) versus \(P\), for three real gases \(A, B\) and \(C\). Identify the only incorrect statement

Identify the binary mixture(s) that can be separated into individual compounds, by differential extraction as shown in the given scheme.

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The reactions of \(\mathrm{Cl}_{2}\) gas with cold-dilute and hot-concentrated \(\mathrm{NaOH}\) in water give sodium salts of two (different) oxoacids of chlorine, \(\boldsymbol{P}\) and \(\boldsymbol{Q}\), respectively. The \(\mathrm{Cl}_{2}\) gas reacts with \(\mathrm{SO}_{2}\) gas, in presence of charcoal, to give a product \(\boldsymbol{R}\). \(\boldsymbol{R}\) reacts with white phosphorus to give a compound \(\boldsymbol{S}\). On hydrolysis, \(\boldsymbol{S}\) gives an oxoacid of phosphorus, \(\boldsymbol{T}\).
Question:
\(P\) and \(Q\), respectively, are the sodium salts of

In the reaction,
\(
2 \mathrm{X}+\mathrm{B}_2 \mathrm{H}_6 \longrightarrow\left[\mathrm{BH}_2(\mathrm{X})_2\right]^{+}\left[\mathrm{BH}_4\right]^{-}
\)
The amine (s) \(X\), is (are)

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Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately \(6.023 \times 10^{23}\) ) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.
A \(4.0\) molar aqueous solution of \(\mathrm{NaCl}\) is prepared and \(500 \mathrm{~mL}\) of this solution is electrolysed. This leads to the evolution of chlorine gas at one of electrodes (atomic mass: \(\mathrm{Na}=23, \mathrm{Hg}=200 ; 1\) faraday \(=96500\) coulombs).
Question:
If the cathode is a Hg electrode, the maximum weight \((g)\) of amalgam formed from this solution is

The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II.
(given, order of migratory aptitude: aryl > alkyl hydrogen)

	LIST-I		LIST -II
A)		P)	${\mathrm{I}}_2,\mathrm{NaOH}$
B)		Q)	$\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\mathrm{OH}\right]$
C)		R)	Fehling solution
D)		S)	$\mathrm{H}\mathrm{C}\mathrm{H}\mathrm{O},\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}$
		T)	$\mathrm{NaOBr}$

In the complex acetylbromidodicarbonylbis(triethylphosphine)iron (II), the number of $\mathrm{F}\mathrm{e}-\mathrm{C}$ bond (s) is

Consider the following reactions (unbalanced)
$\mathrm{Z}\mathrm{n}+H\mathrm{o}\mathrm{t}\mathrm{ }\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}.\mathrm{ }{\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4\to \mathrm{G}+\mathrm{R}+\mathrm{X}$
$\mathrm{Z}\mathrm{n}+\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}.\mathrm{ }\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\to \mathrm{T}+\mathrm{Q}$
\(\text G +\text H _2\text S+ \text{NH} _4 \text{OH} \rightarrow\text Z ~(\)a precipitate\()+\text X +\text Y\)
Choose the correct option(s).

In the $\text{xy - plane}$, the region $y>0$ has a uniform magnetic field $B_1\widehat{k}$ and the region $y<0$ has another uniform magnetic field $B_2\widehat{k}$. A positively charged particle is projected from the origin along the positive $\text{y}-\text{axis}$ with speed $v_0=\pi \mathrm{m}{s}^{-1}$ at $t=0$, as shown in the figure. Neglect gravity in this problem. Let $t=T$ be the time when the particle crosses the $\text{x}-\text{axis}$ from below for the first time. If $B_2=4B_1$, the average speed of the particle, in $\mathrm{m}{\mathrm{s}}^{-1}$, along the $\text{x}-\text{axis}$ in the time interval $T$ is ________.

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K ) at which the reduction of cassiterite by coke would take place.

\(298 K: \Delta_{ f } H ^0\left( SnO _2(s)\right)=-581.0 kJ mol ^{-1}\), \(\Delta_{ f } H ^0\left( CO _2(g)\right)=-394.0 kJ mol ^{-1}\)

\(S ^0\left( SnO _2(s)\right)=56.0 JK ^{-1} mol^{-1}, S^0( Sn ( s ))\) \(=52.0 JK ^{-1} mol^{-1}\)

\(S ^0( C ( s ))=6.0 JK ^{-1} mol^{-1}, S^0\left( CO _2(g)\right)\) \(=210.0 JK ^{-1} mol^{-1}\)

Assume that the enthalpies and the entropies are temperature independent.

Solubility product constant \(\left(K_{\mathrm{sp}}\right)\) of salts of types \(M X, M X_2\) and \(M_3 X\) at temperature ' \(T\) ' are \(4.0 \times 10^{-8}, 3.2 \times 10^{-14}\) and \(2.7 \times 10^{-15}\), respectively. Solubilities \(\left(\mathrm{mol} \mathrm{dm}^{-3}\right)\) of the salts at temperature ' \(T\) ' are in the order

Let \(P(3,2,6)\) be a point in space and \(Q\) be a point on the line \(\mathbf{r}=(\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}})+\mu(-3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+5 \hat{\mathbf{k}})\).
Then, the value of \(\mu\) for which the vector \(\mathbf{P Q}\) is parallel to the plane \(x-4 y+3 z=1\) is