List of top Chemistry Questions asked in GATE CY

The major product formed in the given reaction is: \[ \text{TiCl}_3(\text{DME})_2 \text{Zn-Cu} \text{DME, r.t.} \longrightarrow 1,2-\text{Dimethoxyethane}. \]

For the non-dissociative adsorption of a gas on solid,
(i) the Freundlich isotherm is given by $\theta = k\,p^{1/n}$ (where $\theta$ is surface coverage, $p$ pressure, $k,n$ empirical constants); and
(ii) the BET isotherm is given by $\displaystyle \frac{p}{p^{\ast}-p}=\frac{\theta}{c}+\theta(c-1)\left(\frac{p}{p^{\ast}}\right)$
(where $p^{\ast}$ and $c$ are empirical constants, and $p<p^{\ast}$).
The correct statement(s) is(are)

The enthalpy change for the exothermic reaction between BeI$_2$ and HgF$_2$ is _____ kJ mol$^{-1}$ (rounded off to the nearest integer).
(Given bond dissociation energies in kJ mol$^{-1}$: Be–F = 632, Be–I = 289, Hg–F = 268, Hg–I = 145)

Two different enzyme catalysis reactions I and II have identical Y-intercepts for the Lineweaver–Burke plots. The slope for reaction I is twice that of reaction II. If the initial concentrations of enzymes in I and II are same, the correct statement(s) is(are)
\[ \frac{1}{v}=\frac{1}{v_{\max}}+\frac{K_M}{v_{\max}}\frac{1}{[S]} \]

The intrinsic viscosity of a sample of polystyrene in toluene is $84\ \text{cm}^3\ \text{g}^{-1}$ at $30\^{\circ}\text{C}$. It follows the Mark–Houwink equation with empirical constants $K = 1.05\times 10^{-2}\ \text{cm}^3\ \text{g}^{-1}$ and $a = 0.75$. The molecular weight of the polymer is ______$\times10^{3}\ \text{g mol}^{-1}$ (rounded off to the nearest integer).

A solution is prepared by dissolving 128 g of naphthalene (C10H8) in 780 g of benzene (C6H6). The vapor pressure of pure benzene is 12.6 kPa at 25$^\circ$C. Assuming that naphthalene in benzene is an ideal solution, the partial vapor pressure of benzene is _____ kPa (rounded off to two decimal places).

For the galvanic cell: H$_2$(g) | HCl(aq) | Cl$_2$(g), the standard electromotive force is \[ E^0 = 1.73 - (1.25\times10^{-3})T + (1.00\times10^{-6})T^2 \quad (\text{V, with }T\text{ in K}). \] Find the standard enthalpy change $\Delta_r H^0$ at $300\ \text{K}$ (kJ mol$^{-1}$). Assume the cell reaction is written per mole of HCl, i.e., $\tfrac12\mathrm{H_2} + \tfrac12\mathrm{Cl_2} \rightarrow \mathrm{HCl(aq)$ so that $n=1$. (Given $F=96500\ \text{C mol}^{-1}$).}

A solution of three non-interacting compounds P, Q, and R is taken in a cuvette of 1 cm path length. Their concentrations are [P] = $1\times10^{-6}$ M, [Q] = $2\times10^{-6}$ M, [R] = $3\times10^{-6}$ M and the molar extinction coefficients at 300 nm are $\varepsilon_P = 1\times10^{5}\ \mathrm{M^{-1}\,cm^{-1}}$, $\varepsilon_Q = 2\times10^{5}\ \mathrm{M^{-1}\,cm^{-1}}$ and $\varepsilon_R = 3\times10^{5}\ \mathrm{M^{-1}\,cm^{-1}}$. The % transmittance at 300 nm is ___________ (rounded off to two decimal places)

Two-component solid–liquid system of naphthalene–benzene forms a simple eutectic mixture. Assuming an ideal solution, the mole fraction of naphthalene in benzene at $300~\text{K}$ and $1~\text{bar}$ is _____ (rounded off to two decimal places).
(Given: freezing point $T_{\mathrm{fp}}$ and enthalpy of fusion $\Delta H_{\mathrm{fus}}$ of naphthalene are $353~\text{K}$ and $19.28~\text{kJ mol}^{-1}$, respectively; $R=8.31~\text{J K}^{-1}\text{mol}^{-1}$)

According to Debye–Hückel limiting law, the mean molal activity coefficient for 0.87 g K$_2$SO$_4$ (molar mass = 174 g mol$^{-1}$) in 1 kg of water at 25 °C is ____ (rounded off to two decimal places).

Number of carbon atoms connected to the metal center in [W(C$_{60}$)(CO)$_5$] is ____ (rounded off to the nearest integer).
(Given: atomic number of W = 74)

The major product obtained by the treatment of $(\eta^{5}\text{-}\mathrm{C_5H_5})_2\mathrm{Ni}$ with Na/Hg in ethanol is

The number of shared corners of the constituent SiO4 units in orthosilicate, pyrosilicate, cyclic silicate and sheet silicate, respectively, are

The wavefunction for Be$^{3+}$ in a certain state is given by $\psi = N e^{-\left(\tfrac{4}{a_0}\right)r}$, where $N$ is the normalization constant, $r$ is the distance of electron from the nucleus and $a_0$ is the Bohr radius. The most probable distance of the electron from the nucleus in this state is

Column I	Column II
(P) Associated Legendre polynomials	(III) Angular part of H atom ($Y_\ell^m(\theta,\phi)$)
(Q) Hermite polynomials	(I) Harmonic oscillator ($\psi_n(x)\propto e^{-x^2/2}H_n(x)$)
(R) Associated Laguerre polynomials	(IV) Radial part of H atom ($R_{n\ell}(r)\propto e^{-r/na_0}L_{n-\ell-1}^{2\ell+1}\!\left(\tfrac{2r}{na_0}\right)$)
(S) Trigonometric functions	(II) Particle in a box model ($\psi_n(x)=\sin\!\left(\tfrac{n\pi x}{L}\right)$)

In the scheme $ \mathrm{P_2} \xrightleftharpoons[\;k_1\;]{\;I_a\;} 2\mathrm{Q} \xrightarrow{k_2} \mathrm{R} $, $I_a$ represents the intensity of light absorbed. Assuming the quantum yield of the first step is one, the steady-state concentration of $\mathrm{Q}$ is given by

The correct statement(s) for XeF$_2$ is(are)

The correct statement(s) regarding Co$_2$(CO)$_8$ is(are)

The compound(s) having [Xe]4f$^1$ configuration is(are)
(Given the atomic numbers Ce:58, Lu:71, Pr:59 and Nd:60)