GATE CY 2017 Question Paper (05-Feb-2017) (Shift 1)

The mobility of a univalent ion in aqueous solution is $6.00\times 10^{-8}{\text{ m}}^2{\text{ s}}^{-1}{\text{ V}}^{-1}$ at 300 K. Its diffusion coefficient at 300 K is $X\times 10^{-9}{\text{ m}}^2{\text{ s}}^{-1}$. The value of X is ________ (up to two decimal places)

For the following consecutive first order reactions

$X\stackrel{k_1=2.0{\text{ s}}^{-1}}{\to }Y\stackrel{k_2=0.1{\text{ s}}^{-1}}{\to }Z$

the time (in seconds) required for Y to reach its maximum concentration (assuming only X is present at time $t=0$) is ________ (up to two decimal places)

Under physiological conditions, the conversion of $C{O}_2$ to bicarbonate ion by carbonic anhydrase enzyme (MW = $30,000{\text{ g mol}}^{-1}$) has a turnover number of $4.00\times 10^5{\text{ s}}^{-1}$. The minimum amount of enzyme (in $\mu \text{g}$) required to convert 0.44 g of $C{O}_2$ to bicarbonate ions in 100 seconds is ________ (up to two decimal places)

Assume 1,3,5-hexatriene to be a linear molecule and model the $\pi$ electrons as particles in a one-dimensional box of length 0.70 nm. The wavelength (in nm) corresponding to the transition from the ground-state to the first excited-state is ________

The standard Gibbs free energy change of the reaction shown below is -2.7 kJ mol${}^{-1}$.

$Sn(s)+P{b}^{2+}=S{n}^{2+}+Pb(s)$

Given that $E^{\circ }(P{b}^{2+}/Pb)$ is -0.126 V, the value of $E^{\circ }(S{n}^{2+}/Sn)$ in V is ________ (up to two decimal places)