The decomposition of formic acid on gold surface follows first order kinetics. If the rate constant at \(300\, K\) is \(1.0 \times 10^{-3} s ^{-1}\) and the activation energy \(E _{ a }=11.488\, kJ\, mol ^{-1},\) the rate constant at \(200\, K\) is ............  \(\quad \times 10^{-5} s ^{-1} .\) (Round of to the Nearest Integer). (Given : \(\left. R =8.314\, J\, mol ^{-1} K ^{-1}\right)\)

Consider the reaction \(X \rightleftharpoons Y\) at \(300\) K. If \(\Delta H^{\theta}\) and \(K\) are \(28.40\) kJ mol\(^{-1}\) and \(1.8 \times 10^{-7}\) at the same temperature, then the magnitude of \(\Delta S^{\theta}\) for the reaction in J K\(^{-1}\) mol\(^{-1}\) is _______. (Nearest integer) (Given: \(R = 8.3\) J K\(^{-1}\) mol\(^{-1}\), \(\ln 10 = 2.3\), \(\log 3 = 0.48\), \(\log 2 = 0.30\))

The standard enthalpy of formation \((\Delta _f\,H^o_{298})\) for methane, \(CH_4\) is \(-74.9\,kJ\,mol^{-1}\) . In order to calculate the average energy given out in the formation of a \(C - H\) bond from this it is necessary to know which one of the following?

The wavelength of an electron and a neutron will become equal when the velocity of the electron is \(x\) times the velocity of neutron. The value of \(x\) is (Nearest Integer)(Mass of electron is \(9.1 \times 10^{-31} kg\) and mass of neutron is \(1.6 \times 10^{-27}\,kg\) )

For the following reactions \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br}+\mathrm{Z}^{-}\)\(\xrightarrow[{{\text{Sublimation}}}]{{{k_s}}} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Z}+\mathrm{Br}^{-}\) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br}+\mathrm{Z}^{-}\)\(\xrightarrow[{{\text{elimination}}}]{{{k_e}}}\mathrm{CH}_{3} \mathrm{CH}= \mathrm{CH}_{2} +\mathrm{HZ}+\mathrm{Br}^{-}\) where  \(\mathrm{Z}^{-}=\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{O}^{-}(\mathrm{A})\) or \(\begin{array}{*{20}{c}}
  {\,C{H_3}} \\ 
  {|\,\,\,\,\,} \\ 
  {C{H_3} - C - {O^ - }(B)} \\ 
  {|\,\,\,\,} \\ 
  {\,\,C{H_3}} 
\end{array}\) \(\mathrm{k}_{\mathrm{s}}\) and \(\mathrm{k}_{\mathrm{e}},\) are \(,\) respectively, the rate constants for the substitution and elimination, and \(\mu=\frac{\mathrm{k}_{\mathrm{s}}}{\mathrm{k}_{\mathrm{e}}},\) the correct options is

Boiling point of a \(2 \%\) aqueous solution of a nonvolatile solute \(A\) is equal to the boiling point of \(8 \%\) aqueous solution of a non-volatile solute \(B\). The relation between molecular weights of \(A\) and \(B\) is.

Sum of bond order of \(\mathrm{CO}\) and \(\mathrm{NO}^{+}\)is____________.

A mixture of \(2\, moles\) of helium gas (atomic mass \(= 4\, u\)), and \(1\, mole\) of argon gas (atomic mass \(= 40\, u\)) is kept at \(300\, K\) in a container. The ratio of their rms speeds \(\left[ {\frac{{{V_{rms}}{\rm{(helium)}}}}{{{V_{rms}}{\rm{(argon)}}}}} \right]\), is close to

Let \(\vec{a}, \vec{b}, \vec{c}\) be three vectors mutually perpendicular to each other and have same magnitude. If a vector \(\overrightarrow{\mathrm{r}}\) satisfies. \(\overrightarrow{\mathrm{a}} \times\{(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{a}}\}+\overrightarrow{\mathrm{b}} \times\{(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{c}}) \times \overrightarrow{\mathrm{b}}\}+\overrightarrow{\mathrm{c}} \times\{(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{a}}) \times \overrightarrow{\mathrm{c}}\}=\overrightarrow{0}\) then \(\overrightarrow{\mathrm{r}}\) is equal to:

Let \(\mathrm{T}_{\mathrm{r}}\) be the \(\mathrm{r}^{\text {th }}\) term of an A.P. If for some \(\mathrm{m}, \mathrm{T}_{\mathrm{m}}=\frac{1}{25}, \mathrm{~T}_{25}=\frac{1}{20}\), and \(20 \sum_{\mathrm{r}=1}^{25} \mathrm{~T}_{\mathrm{r}}=13\), then \(5 \mathrm{~m} \sum_{\mathrm{r}=\mathrm{m}}^{2 \mathrm{~m}} \mathrm{~T}_{\mathrm{r}}\) is equal to

The position of a particle as a function of time \(t\), is given by \(x\left( t \right) = at+ b{t^2} - c{t^3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be

Let \(f(x)=\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x\) . If \(f(3)=\frac{1}{2}\left(\log _e 5-\log _e 6\right)\), then \(f(4)\) is equal to

A rod of linear mass density ' \(\lambda\) ' and length ' \(L\) ' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :