The sequence of reagents required to convert ethylbromide to propanal is

At \(\mathrm{T}(\mathrm{K}), \mathrm{K}_{\mathrm{c}}\) value of \(\mathrm{AO}_2(\mathrm{~g})+\mathrm{BO}_2(\mathrm{~g}) \rightleftharpoons \mathrm{AO}_3(\mathrm{~g})+\mathrm{BO}(\mathrm{g})\) is 16. In a closed 1 L flask, one mole each of \(\mathrm{AO}_2, \mathrm{BO}_2, \mathrm{AO}_3\) and BO are taken and heated to \(\mathrm{T}(\mathrm{K})\). Identify the correct statements about this equilibrium.
I) Total number of moles at equilibrium is 4
II) At equilibrium, the ratio of moles of \(\mathrm{AO}_2\) and \(\mathrm{AO}_3\) is \(1: 4\)
III) Total number of moles of \(\mathrm{AO}_2\) and \(\mathrm{BO}_2\) at equilibrium is 0.8

Using the data provided, find the value of equilibrium constant for the following reaction at $298 \mathrm{K}$ and $1$ atm pressure. ${\mathrm{NO}}_{\left(\mathrm{g}\right)}+\frac{1}{2}{\mathrm{O}}_2( \mathrm{g})\rightleftharpoons {\mathrm{NO}}_2( \mathrm{g})$
${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^0\left({\mathrm{NO}}_{\left(\mathrm{g}\right)}\right)=90.4\mathrm{kJ}.{\mathrm{mol}}^{-1}$ ${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^0\left({\mathrm{NO}}_2\left(\mathrm{g}\right)\right)=32.48\mathrm{kJ}\cdot {\mathrm{mol}}^{-1}$ ${\mathrm{\Delta S}}^{\circ }@298\mathrm{K}=-70.8\mathrm{J}\cdot {\mathrm{K}}^{-1}\cdot {\mathrm{mol}}^{-1}$ $\mathrm{antilog}(0.50)=3162$

Calculate the ratio of the effusion of \(\mathrm{CO}\) and \(\mathrm{N}_2\), when temperature and pressure gradients are held constant?

Assertion (A): Sodium acetate on Kolbe's electrolysis gives ethane. Reason (R): Methyl free radical is formed at cathode.

The ore which is concentrated by leaching

Among \(\mathrm{V}, \mathrm{Cr}, \mathrm{Zn}, \mathrm{Fe}\), the metal having lowest enthalpy of atomization is

\(\int e^x \frac{x^2+1}{(x+1)^2} d x\) is equal to

If \(2 \sin 2 \theta=\sqrt{3}\), then \(\theta=\)

The condition \(f(x)=x^3+p x^2+q x+r(x \in R)\) to have no extreme value, is

If \(x y \neq 0, x+y \neq 0\) and \(x^m y^n=(x+y)^{m+n}\), where \(m, n \notin N\), then \(\frac{d y}{d x}\) is equal to

The correct equation for one mole of a real gas is (a, b are constants)

A \(500 \mathrm{~g}\) ball is attached to one end of an aluminum wire of area of cross-section \(0.5 \mathrm{~mm}^2\) and an unstretched length of \(1.4 \mathrm{~m}\). The other end of the wire is fixed to the top of a vertical pole. The ball rotates about the pole in a horizontal plane such that the angle between the wire and the horizontal is \(30^{\circ}\). The increase in the length of the wire is ____ \(\mathrm{mm}\). (Young's modulus of aluminum \(=0.7 \times 10^{11} \mathrm{Nm}^{-2}\) and acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\))