GATE CY 2016 Question Paper (31-Jan-2016) (Shift 2)

The Larmor frequency of ${}^{1}H$ at 1 Tesla (T) is 42.57 MHz. If the magnetogyric ratios for ${}^{1}H$ and ${}^{13}C$ are $26.75\times 10^7\text{ rad }{T}^{-1}{s}^{-1}$ and $6.72\times 10^7\text{ rad }{T}^{-1}{s}^{-1}$, respectively, the Larmor frequency of ${}^{13}C$, in MHz, at 1 Tesla will be ________

At 1 bar and 298 K, for the process $A(s)\to A(l)$, the $\Delta G$ is $200{\text{ J mol}}^{-1}$ and the $\Delta V_m$ is $-2\times 10^{-6}{\text{ m}}^3{\text{ mol}}^{-1}$. The minimum pressure, in bar, at which the process becomes spontaneous at 298 K is ________ (1 bar = $10^5\text{ Pa}$)

The reaction, $A\rightleftharpoons B$, is first order in both the directions. The forward and reverse rate constants are $4.2\times 10^{-4}{s}^{-1}$ and $1.04\times 10^{-3}{s}^{-1}$, respectively. The relaxation time for this reaction, in seconds, in a temperature jump experiment is ________

Adsorption of CO on charcoal at 273 K follows Langmuir isotherm. A plot of $P\text{ (kPa) }/V{\text{ (cm}}^3)$ versus $P\text{ (kPa)}$ is linear with a slope of 0.01 and y-intercept of 0.5. The equilibrium constant, $K{\text{ (kPa}}^{-1})$, for the adsorption is ________

For the following reaction,

$A+B\underset{k_{-1}=10^4{s}^{-1}}{\overset{k_1=10^5{\text{ L mol}}^{-1}{s}^{-1}}{\rightleftharpoons }}I\stackrel{k_2=10s^{-1}}{\to }P$

if steady state approximation can be applied on $[I]$, the observed rate constant of product formation, in $L{\text{ mol}}^{-1}{s}^{-1}$, will be ________