The spin only magnetic moment value (in Bohr magneton units) of \(\mathrm{Cr}(\mathrm{CO})_6\) is

Consider the kinetic data given in the following table for the reaction $\mathrm{A}+\mathrm{B}+\mathrm{C}\to$ Product.

Ex peri ment No.	\([\text A]\) \((\text{mol}\) \(\text{dm} ^{-3})\)	\([\text B]\) \((\text{mol}\) \(\text{dm} ^{-3})\)	\([\text C]\) \((\text{mol}\) \(\text{dm} ^{-3})\)	Rate of reaction \((\text{mol}\) \(\text{dm} ^{-3}\) \(\text s^{-1})\)
1	0.2	0.1	0.1	\(6.0 \times\) \(10^{-5}\)
2	0.2	0.2	0.1	\(6.0 \times \) \(10^{-5}\)
3	0.2	0.1	0.2	\(1.2 \times \) \(10^{-4}\)
4	0.3	0.1	0.1	\(9.0 \times \) \(10^{-5}\)

The rate of the reaction for $\left[\mathrm{A}\right]=0.15\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3},\mathrm{ }\left[\mathrm{B}\right]=0.25\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3}$ and $\left[\mathrm{C}\right]=0.15\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3}$ is found to be $\mathrm{Y}\times {10}^{-5}\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}.$ The value of $\mathrm{Y}$ is __________

For the reaction, \(\mathbf{X}(s) \rightleftharpoons \mathbf{Y}(s)+\mathbf{Z}(g)\), the plot of \(\ln \frac{p_{\mathbf{Z}}}{p^{\theta}}\) versus \(\frac{10^{4}}{T}\) is given below (in solid line), where \(p_{\mathbf{Z}}\) is the pressure (in bar) of the gas \(\mathbf{Z}\) at temperature \(T\) and \(p^{\theta}=1\) bar.

(Given, \(\frac{\mathrm{d}(\ln K)}{\mathrm{d}\left(\frac{1}{T}\right)}=-\frac{\Delta H^{\theta}}{R}\), where the equilibrium constant, \(K=\frac{p_{z}}{p^{\theta}}\) and the gas constant, \(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) )
The value of standard enthalpy, $∆{\mathrm{H}}^{\mathrm{o}}$ (in $\mathrm{kJ} {\mathrm{mol}}^{-1}$) for the given reaction is ___.

To form a complete monolayer of acetic acid on \(1 \mathrm{~g}\) of charcoal, \(100 \mathrm{~mL}\) of \(0.5 \mathrm{M}\) acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 \(\mathrm{mL}\) of \(1 \mathrm{M} \mathrm{NaOH}\) solution was required. If each molecule of acetic acid occupies \(\mathbf{P} \times 10^{-23} \mathrm{~m}^2\) surface area on charcoal, the value of \(\mathbf{P}\) is _______ [Use given data: Surface area of charcoal \(=1.5 \times 10^2 \mathrm{~m}^2 \mathrm{~g}^{-1} ;\) Avogadro's number \(\left(\mathrm{N}_{\mathrm{A}}\right)=6.0 \times 10^{23}\) \(\left.\mathrm{mol}^{-1}\right]\)

A solution of $0.1\mathrm{M}$ weak base $\left(\mathrm{B}\right)$ is titrated with $0.1\mathrm{M}$ of a strong acid $\left(\mathrm{HA}\right)$. The variation of $\mathrm{pH}$ of the solution with the volume of $\mathrm{HA}$ added is shown in the figure below. What is the ${\mathrm{pK}}_{\mathrm{b}}$ of the base? The neutralization reaction is given by$\mathrm{B}+\mathrm{HA}\to {\mathrm{BH}}^{+}+{\mathrm{A}}^{-}$.

The species having bond order different from that in \(\mathrm{CO}\) is

The surface of copper gets tarnished by the formation of copper oxide. $N_2$ gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the $N_2$ gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below:

$2Cu\left(s\right)+ H_{2}O\left(g\right)\to C{u}_{2}O\left(s\right) + H_2\left(g\right)$

$P_{H_2}$ Is the minimum partial pressure of $H_2$ (in bar) needed to prevent the oxidation at 1250 K. The value of $\ln \left(p{H}_2\right)$ is ____.

(Given: total pressure \(=1\) bar, R (universal gas constant) \(=8 J K ^{-1} mol^{-1}, \ln (10) =2.3 \cdot Cu (s)\) and \(Cu _2 O (s)\) are mutually immiscible.

At \(1250 K: 2 Cu ( s )+\frac{1}{2} O _2(g) \rightarrow Cu _2 O ( s ) ;\) \(\Delta G^{\ominus}=-78,000 J mol ^{-1}\)

\(H _2(g)+\frac{1}{2} O _2(g) \rightarrow H _2 O ( g ) ; \quad \Delta^{\ominus}=\)\(-1,78,000 J mol ^{-1} ; G\) is the Gibbs energy)/mi> \(\Theta=\) \(-78,000 J mol -1\)

\(H _2(g)+\frac{1}{2} O _2(g) \rightarrow H _2 O ( g ) ; \quad\)\(\Delta^{\ominus}=-1,78,000 J mol ^{-1} ; G\) is the Gibbs energy)

A transparent thin film of uniform thickness and refractive index ${\mathrm{n}}_1=1.4$ is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index ${\mathrm{n}}_2=1.5$ , as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f₁ from the film, while rays of light traversing from glass to air get focused at distance f₂ from the film. Then

The correct stability order of the following resonance structure is

The area of the region
$\left\{(x,y):0\le x\le \frac{9}{4}, 0\le y\le 1, x\ge 3y, x+y\ge 2\right\}$ is

Two beads, each with charge \(q\) and mass \(m\), are on a horizontal, frictionless, non-conducting, circular hoop of radius \(R\). One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by
[ \(\varepsilon_0\) is the permittivity of free space.]

The correct statements about the oxoacids, ${\mathrm{HClO}}_4\mathrm{ }\mathrm{and}\mathrm{ }\mathrm{HClO}$ are,

Let $S$ be the set of all complex numbers $z$ satisfying $\left|z-2+i\right|\ge \sqrt{5}.$ If the complex number $z_0$ is such that $\frac{1}{\left|z_0-1\right|}$ is the maximum of the set $\left\{\frac{1}{\left|z-1\right|}:z\in S\right\},$ then the principal argument of $\frac{4-z_0-{\overline{z}}_0}{z_0-{\overline{z}}_0+2i}$ is