The variation of equilibrium constant with temperature is given below  Temperature \(\quad\) Equilibrium constant \(\begin{array}{ll} T _{1}=25^{\circ} C & K _{1}=100 \\ T _{2}=100^{\circ} C & K _{2}=100\end{array}\) The values of \(\Delta H ^{\circ}, \Delta G ^{\circ}\) at \(T _{1}\) and \(\Delta G ^{\circ}\) at \(T _{2}\) (in \(kJ\, mol ^{-1}\) ) respectively, are close to \(\left[\right.\) Use \(\left. R =8.314\, JK ^{-1} mol ^{-1}\right]\)

The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process shown below \({O_3}(g)\, + \,C{l^ * }(g)\, \to \,{O_2}(g) + Cl{O^ * }(g)\) ..... \((i)\)               \([{K_i} = 5.2 \times {10^9}\,\,L\,mo{l^{ - 1}}\,{s^{ - 1}}]\) \(Cl{O^ * }(g) + {O^ * }(g)\, \to \,{O_2}(g) + \,C{l^ * }(g)\) ..... \((ii)\)                \([{K_{ii}} = 2.6 \times {10^{10}}\,\,L\,mo{l^{ - 1}}\,{s^{ - 1}}]\) The closest rate constant for the overall reaction  \({O_3}(g){\mkern 1mu}  + {\mkern 1mu} {O^*}(g){\mkern 1mu}  \to {\mkern 1mu} 2{O_2}(g)\) is  ........... \(L\,\,mo{l^{ - 1}}\,{s^{ - 1}}\)

Outermost electronic configurations of four elements \(A, B, C, D\) are given below. \(3 s^{2}\); \(3 s^{2} 3 p^{1}\); \(3 s ^{2} 3 p ^{3}\); \(3 s^{2} 3 p^{4}\) The correct order of first ionization enthalpy for them is.

The solubility product of \(BaSO _4\) is \(1 \times 10^{-10}\) at \(298\,K\). The solubility of \(BaSO _4\) in \(0.1\,M\,K _2 SO _4( aq )\) solution is \(.........\times 10^{-9}\,g\,L ^{-1}\) (nearest integer). Given : Molar mass of \(BaSO _4\) is \(233\,g\,mol ^{-1}\)

What is the standard reduction potential \((E^o)\) for \(Fe^{3+} \to Fe\) ?  ............... \(\mathrm{V}\) Given that : \(F{e^{2 + }} + 2{e^ - } \to Fe;\)      \({E^o}_{F{e^{2 + }}/Fe} =  - 0.47\,V\) \(F{e^{3 + }} + {e^ - } \to F{e^{2 + }};\)   \({E^o}_{F{e^{3 + }}/F{e^{2 + }}} =  + 0.77\,V\)

Conversion of benzene diazonium chloride to chlorobenzene is an example of which of the following reactions?

\(\dot{ Cl }+ CH _{4} \rightarrow A + B\) \(A\) and \(B\) in the above atmospheric reaction step are.

In a Young’s double slit experiment with slit separation \(0.1\, mm\), one observes a bright fringe at angle \(\frac{1}{{40}}\, rad\) by using light of wavelength \({\lambda _1}\). When the light of wavelength \(\lambda _2\) is used a bright fringe is seen at the same angle in the same set up. Given that \({\lambda _1}\) and \({\lambda _2}\) are in visible range (\(380\, nm\) to \(740\, nm\)), their values are

Using column chromatography, mixture of two compounds ' \(A\) ' and ' \(B\) ' was separated. '\(A\)' eluted first, this indicates ' \(B\) ' has

For the function \(f(x) = e^{\sin|x|} - |x|\), \(x \in \mathbb{R}\), consider the following statements:
Statement I: \(f\) is differentiable for all \(x \in \mathbb{R}\).
Statement II: \(f\) is increasing in \(\left(-\pi, -\dfrac{\pi}{2}\right)\).
In the light of the above statements, choose the correct answer from the options given below:

The pH and conductance of a weak acid (HX) was found to be 5 and \( 4 \times 10^{-5} \) S, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of \( 1 \, cm^{2} \) were at a distance of 15 cm apart. The value of the limiting molar conductivity is ......... \( S \, m^{2} \, mol^{-1} \). (nearest integer) (Given: degree of dissociation of the weak acid (a) \(\ll 1\) )

An ether \((A)\), \(C_5H_{12}O\), when heated with excess of hot concentrated \(HI\) produced two alkyl halides which when treated with \(NaOH\) yielded compounds \((B)\) and \((C)\). Oxidation of \((B)\) and \((C)\) gave a propanone and an ethanoic acid respectively. The \(IUPAC\) name of the ether \((A)\) is 

If \({\Delta _r} = \left| {\begin{array}{*{20}{c}}
  r&{2r - 1}&{3r - 2} \\ 
  {\frac{n}{2}}&{n - 1}&a \\ 
  {\frac{1}{2}n\left( {n - 1} \right)}&{{{\left( {n - 1} \right)}^2}}&{\frac{1}{2}\left( {n - 1} \right)\left( {3n - 4} \right)} 
\end{array}} \right|\) then the value of \(\sum\limits_{r = 1}^{n - 1} {{\Delta _r}} \)