GATE CY 2012 Question Paper (12-Feb-2012) (Shift-2)

From a carboxymethyl-cellulose column at pH 6.0, arginine, valine and glutamic acid will elute in the order

Symmetry operations of the four $C_2$ axes perpendicular to the principal axis belong to the same class in the point group(s)

At 298 K, the EMF of the cell
$Pt|H_2(1\text{ bar})|H^{+}(solution)||C{l}^{-}|H{g}_{2}C{l}_2|Hg$
is 0.7530 V. The standard potential of the calomel electrode is 0.2802 V. If the liquid junction potential is zero, the pH of the solution is

The wavefunction of a 1-D harmonic oscillator between $x=+\infty$ and $x=-\infty$ is given by $\psi (x)=N(2x^2-1)e^{-x^2/2}$. The value of $N$ that normalizes the function $\psi (x)$ is
(Given: ${\int }_{-\infty }^{+\infty }{x}^{2n}{e}^{-x^2}dx=\frac{1\cdot 3\cdot 5\dots (2n-1)}{2^n}\sqrt{\pi }$)

Consider the reaction
$H_2+C_2{H}_4\to C_2{H}_6$
The molecular diameters of $H_2$ and $C_2{H}_4$ are 1.8 Å and 3.6 Å respectively. The pre-exponential factor in the rate constant calculated using collision theory in $m^3(mole{)}^{-1}{s}^{-1}$ is approximately
(For this reaction at 300 K, $(\frac{8k_{B}T}{\pi \mu }{)}^{\frac{1}{2}}{N}_A=1.11\times 10^{27}m(mole{)}^{-1}{s}^{-1}$, where the symbols have their usual meanings)