Werner’s coordination theory in 1893 was the first attempt to explain the bonding in coordination complexes. It must be remembered that this theory was put forward before the electron had been discovered by J.J. Thomson in 1897, and before the electronic theory of valency. Werner did not have any of the modern instrumental techniques and all his studies were made using simple experimental techniques. Werner was able to explain the nature of bonding in complexes and he concluded that in complexes, the metal shows two different sorts of valency: primary and secondary. Primary valences are normally ionisable whereas secondary valences are non-ionisable.
The Lineweaver-Burk plot for an enzyme obeying the Michaelis-Menten mechanism is given below.
The slope of the line is \(0.36 \times 10^2\) s, and the y-intercept is \(1.20\) mol\(^{-1}\) L s. The value of the Michaelis constant (\(K_M\)) is ________ \( \times 10^{-3} \) mol L\(^{-1}\) (in integer). [Note: \(v\) is the initial rate, and \([S]_0\) is the substrate concentration]
Consider a Carnot engine with a hot source kept at 500 K. From the hot source, 100 J of energy (heat) is withdrawn at 500 K. The cold sink is kept at 300 K. The efficiency of the Carnot engine is ___________ (rounded off to one decimal place).
For the cell reaction, \[ Hg_2Cl_2 (s) + H_2 (1 \, {atm}) \rightarrow 2Hg (l) + 2H^+ (a=1) + 2Cl^- (a=1) \] The standard cell potential is \( \mathcal{E}^0 = 0.2676 \) V, and \( \left(\frac{\partial \mathcal{E}^0}{\partial T}\right)_P = -3.19 \times 10^{-4} \) V K\(^{-1}\). The standard enthalpy change of the reaction (\( \Delta_r H^0 \)) at 298 K is \( -x \) kJ mol\(^{-1}\). The value of \( x \) is ___________ (rounded off to two decimal places). [Given: Faraday constant \( F = 96500 \) C mol\(^{-1}\)]
The mean energy of a molecule having two available energy states at \( \epsilon = 0 \) J and \( \epsilon = 4.14 \times 10^{-21} \) J at 300 K is ___________ \( \times 10^{-21} \) J (rounded off to two decimal places). [Given: Boltzmann constant \( k_B = 1.38 \times 10^{-23} \) J K\(^{-1}\)]
The kinetic energies of an electron (\(e\)) and a proton (\(p\)) are \(E\) and \(3E\), respectively. Given that the mass of a proton is 1836 times that of an electron, the ratio of their de Broglie wavelengths (\(\lambda_e / \lambda_p\)) is ___________ (rounded off to two decimal places).