Q55. Consider the dissociation of the weak acid HX as given below $\mathrm { HX } ( \mathrm { aq } ) \rightleftharpoons \mathrm { H } ^ { + } ( \mathrm { aq } ) + \mathrm { X } ^ { - } ( \mathrm { aq } ) , \mathrm { Ka } = 1.2 \times 10 ^ { - 5 } \left[ \mathrm {~K} _ { \mathrm { a } } : \right.$ dissociation constant $]$ The osmotic pressure of 0.03 M aqueous solution of HX at 300 K is $\_\_\_\_$ $\times 10 ^ { - 2 }$ bar (nearest integer). [Given : $\mathrm { R } = 0.083 \mathrm { Lbarmol } ^ { - 1 } \mathrm {~K} ^ { - 1 }$ ]

Q55. Consider the two different first order reactions given below $\mathrm { A } + \mathrm { B } \rightarrow \mathrm { C }$ (Reaction 1) $P \rightarrow Q$ (Reaction 2) The ratio of the half life of Reaction 1 : Reaction 2 is $5 : 2$. If $t _ { 1 }$ and $t _ { 2 }$ represent the time taken to complete $2 / 3 ^ { \text {rd } }$ and $45 ^ { \text {th } }$ of Reaction 1 and Reaction 2, respectively, then the value of the ratio $t _ { 1 } : t _ { 2 }$ is $\_\_\_\_$ $\times 10 ^ { - 1 }$ (nearest integer). [Given : $\log _ { 10 } ( 3 ) = 0.477$ and $\log _ { 10 } ( 5 ) = 0.699$ ]

Q55. A solution containing 10 g of an electrolyte $\mathrm { AB } _ { 2 }$ in 100 g of water boils at $100.52 ^ { \circ } \mathrm { C }$. The degree of ionization of the electrolyte $( \alpha )$ is $\_\_\_\_$ $\times 10 ^ { - 1 }$. (nearest integer) [Given : Molar mass of $\mathrm { AB } _ { 2 } = 200 \mathrm {~g} \mathrm {~mol} ^ { - 1 } , \mathrm {~K} _ { \mathrm { b } }$ (molal boiling point elevation const. of water) $= 0.52 \mathrm {~K} \mathrm {~kg} \mathrm {~mol} ^ { - 1 }$, boiling point of water $= 100 ^ { \circ } \mathrm { C } ; \mathrm { AB } _ { 2 }$ ionises as $\left. \mathrm { AB } _ { 2 } \rightarrow \mathrm {~A} ^ { 2 + } + 2 \mathrm {~B} ^ { - } \right]$

Q55. Total number of aromatic compounds among the following compounds is $\_\_\_\_$ . [Figure] [Figure] [Figure] [Figure] [Figure] [Figure]

Q55. How many compounds among the following compounds show inductive, mesomeric as well as [Figure] hyperconjugation effects? [Figure]

Q55. Number of compounds from the following which cannot undergo Friedel-Crafts reactions is: $\_\_\_\_$。 toluene, nitrobenzene, xylene, cumene, aniline, chlorobenzene, $m$-nitroaniline, $m$-dinitrobenzene

Q56. 2.5 g of a non-volatile, non-electrolyte is dissolved in 100 g of water at $25 ^ { \circ } \mathrm { C }$. The solution showed a boiling point elevation by $2 ^ { \circ } \mathrm { C }$. Assuming the solute concentration is negligible with respect to the solvent concentration, the vapor pressure of the resulting aqueous solution is $\quad \mathrm { mm }$ of Hg (nearest integer) [Given : Molal boiling point elevation constant of water $\left( \mathrm { K } _ { \mathrm { b } } \right) = 0.52 \mathrm {~K} . \mathrm { kgmol } ^ { - 1 } , 1 \mathrm {~atm}$ pressure $= 760 \mathrm {~mm}$ of Hg , molar mass of water $= 18 \mathrm {~g} \mathrm {~mol} ^ { - 1 }$ ]

Q56. Consider the following reaction, the rate expression of which is given below
$$\begin{aligned} & \mathrm { A } + \mathrm { B } \rightarrow \mathrm { C } \\ & \text { rate } = \mathrm { k } [ \mathrm {~A} ] ^ { 1 / 2 } [ \mathrm {~B} ] ^ { 1 / 2 } \end{aligned}$$
The reaction is initiated by taking 1 M concentration of A and B each. If the rate constant ( k ) is $4.6 \times 10 ^ { - 2 } \mathrm {~s} ^ { - 1 }$ , then the time taken for A to become 0.1 M is $\_\_\_\_$ sec. (nearest integer)

Q56. During Kinetic study of reaction $2 A + B \rightarrow C + D$, the following results were obtained :

	$\mathrm { A } [ \mathrm { M } ]$	$\mathrm { B } [ \mathrm { M } ]$	initial rate o
I	0.1	0.1	$6.0 \times 10 ^ { - 3 }$
II	0.3	0.2	$7.20 \times 10 ^ { - 2 }$
III	0.3	0.4	$2.88 \times 10 ^ { - 1 }$
IV	0.4	0.1	$2.40 \times 10 ^ { - 2 }$

Q56. Consider the following single step reaction in gas phase at constant temperature. $2 \mathrm {~A} _ { ( \mathrm { g } ) } + \mathrm { B } _ { ( \mathrm { g } ) } \rightarrow \mathrm { C } _ { ( \mathrm { g } ) }$ The initial rate of the reaction is recorded as $r _ { 1 }$ when the reaction starts with 1.5 atm pressure of $A$ and 0.7 atm pressure of B . After some time, the rate $\mathrm { r } _ { 2 }$ is recorded when the pressure of C becomes 0.5 atm . The ratio $\mathrm { r } _ { 1 } : \mathrm { r } _ { 2 }$ is $\_\_\_\_$ $\times 10 ^ { - 1 }$. (Nearest integer)

Q56. Time required for $99.9 \%$ completion of a first order reaction is $\_\_\_\_$ times the time required for completion of $90 \%$ reaction.(nearest integer)

Q56. Among $\mathrm { VO } _ { 2 } ^ { + } , \mathrm { MnO } _ { 4 } ^ { - }$and $\mathrm { Cr } _ { 2 } \mathrm { O } _ { 7 } ^ { 2 - }$, the spin-only magnetic moment value of the species with least oxidising ability is $\_\_\_\_$ BM (Nearest integer). (Given atomic member $\mathrm { V } = 23 , \mathrm { Mn } = 25 , \mathrm { Cr } = 24$ )

Q56. Consider the following reaction
$$\mathrm { A } + \mathrm { B } \rightarrow \mathrm { C }$$
The time taken for A to become $1 / 4 ^ { \text {th } }$ of its initial concentration is twice the time taken to become $1 / 2$ of the same. Also, when the change of concentration of $B$ is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis. The overall order of the reaction is

Q56. A solution is prepared by adding 1 mole ethyl alcohol in 9 mole water. The mass percent of solute in the solution is $\_\_\_\_$ (Integer answer) (Given : Molar mass in $\mathrm { gmol } ^ { - 1 }$ Ethyl alcohol : 46 water: 18)

Q56. The standard reduction potentials at 298 K for the following half cells are given below : $\mathrm { Cr } _ { 2 } \mathrm { O } _ { 7 } ^ { 2 - } + 14 \mathrm { H } ^ { + } + 6 \mathrm { e } ^ { - } \rightarrow 2 \mathrm { Cr } ^ { 3 + } + 7 \mathrm { H } _ { 2 } \mathrm { O } , \mathrm { E } ^ { \circ } = 1.33 \mathrm {~V}$ $\mathrm { Fe } ^ { 3 + } ( \mathrm { aq } ) + 3 \mathrm { e } ^ { - } \rightarrow \mathrm { Fe } \quad \mathrm { E } ^ { \circ } = - 0.04 \mathrm {~V}$ $\mathrm { Ni } ^ { 2 + } ( \mathrm { aq } ) + 2 \mathrm { e } ^ { - } \rightarrow \mathrm { Ni } \quad \mathrm { E } ^ { \circ } = - 0.25 \mathrm {~V}$ Consider the given electrochemical reactions, The $\mathrm { Ag } ^ { + } ( \mathrm { aq } ) + \mathrm { e } ^ { - } \rightarrow \mathrm { Ag } \quad \mathrm { E } ^ { \circ } = 0.80 \mathrm {~V}$ $\mathrm { Au } ^ { 3 + } ( \mathrm { aq } ) + 3 \mathrm { e } ^ { - } \rightarrow \mathrm { Au } \quad \mathrm { E } ^ { \circ } = 1.40 \mathrm {~V}$ number of metal(s) which will be oxidized be $\mathrm { Cr } _ { 2 } \mathrm { O } _ { 7 } ^ { 2 - }$, in aqueous solution is $\_\_\_\_$

Q56. The vapour pressure of pure benzene and methyl benzene at $27 ^ { \circ } \mathrm { C }$ is given as 80 Torr and 24 Torr , respectively. The mole fraction of methyl benzene in vapour phase, in equilibrium with an equimolar mixture of those two liquids (ideal solution) at the same temperature is $\_\_\_\_$ $\times 10 ^ { - 2 }$ (nearest integer)

Q57. Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below. $A + B$ Step $1 C \xrightarrow { \text { Step } 2 } P$ Some details of the above reactions are listed below. Step Rate constant ( $\mathbf { s e c } ^ { - \mathbf { 1 } }$ ) Activation energy ( $\mathbf { k J } \mathbf { ~ m o l } ^ { - \mathbf { 1 } }$ )

1	$\mathrm { k } _ { 1 }$	300
2	$\mathrm { k } _ { 2 }$	200
3	$\mathrm { k } _ { 3 }$	$\mathrm { Ea } _ { 3 }$

If the overall rate constant of the above transformation $( k )$ is given as $k = \frac { k _ { 1 } k _ { 2 } } { k _ { 3 } }$ and the overall activation energy $\left( \mathrm { E } _ { \mathrm { a } } \right)$ is $400 \mathrm {~kJ} \mathrm {~mol} ^ { - 1 }$, then the value of $\mathrm { Ea } _ { 3 }$ is $\mathrm { kJmol } ^ { - 1 }$ (nearest integer)

Q57. A first row transition metal with highest enthalpy of atomisation, upon reaction with oxygen at high temperature forms oxides of formula $\mathrm { M } _ { 2 } \mathrm { O } _ { \mathrm { n } }$ (where $\mathrm { n } = 3,4,5$ ). The 'spin-only' magnetic moment value of the amphoteric oxide from the above oxides is $\_\_\_\_$ BM (near integer) (Given atomic number: $\mathrm { Sc } : 21 , \mathrm { Ti } : 22 , \mathrm {~V} : 23 , \mathrm { Cr } : 24 , \mathrm { Mn } : 25 , \mathrm { Fe } : 26 , \mathrm { Co } : 27 , \mathrm { Ni } : 28 , \mathrm { Cu } : 29 , \mathrm { Zn } : 30$ )

Q57. The spin-only magnetic moment value of the ion among $\mathrm { Ti } ^ { 2 + } , \mathrm { V } ^ { 2 + } , \mathrm { Co } ^ { 3 + }$ and $\mathrm { Cr } ^ { 2 + }$, that acts as strong oxidising agent in aqueous solution is $\_\_\_\_$ BM (Near integer). (Given atomic numbers : $\mathrm { Ti } : 22 , \mathrm {~V} : 23 , \mathrm { Cr } : 24 , \mathrm { Co } : 27$ )

Q57. The fusion of chromite ore with sodium carbonate in the presence of air leads to the formation of products A and B along with the evolution of $\mathrm { CO } _ { 2 }$. The sum of spin-only magnetic moment values of $A$ and $B$ is $\_\_\_\_$ B.M. (Nearest integer) [Given atomic number : $\mathrm { C } : 6 , \mathrm { Na } : 11 , \mathrm { O } : 8 , \mathrm { Fe } : 26 , \mathrm { Cr } : 24$ ]

Q57. Among $\mathrm { CrO } , \mathrm { Cr } _ { 2 } \mathrm { O } _ { 3 }$ and $\mathrm { CrO } _ { 3 }$, the sum of spin-only magnetic moment values of basic and amphoteric oxides is $\_\_\_\_$ $10 ^ { - 2 } \mathrm { BM }$ (nearest integer). (Given atomic number of Cr is 24 )

Q57. Number of carbocations from the following that are not stabilized by hyperconjugation is $\_\_\_\_$ [Figure]

Q57. The 'spin only' magnetic moment value of $\mathrm { MO } _ { 4 } { } ^ { 2 - }$ is $\_\_\_\_$ BM. (Where M is a metal having least metallic radii. among $\mathrm { Sc } , \mathrm { Ti } , \mathrm { V } , \mathrm { Cr } , \mathrm { Mn }$ and Zn ). (Given atomic number: $\mathrm { Sc } = 21 , \mathrm { Ti } = 22 , \mathrm {~V} = 23 , \mathrm { Cr } = 24 , \mathrm { Mn } = 25$ and $\mathrm { Zn } = 30$ )

Q57. Molality of an aqueous solution of urea is 4.44 m . Mole fraction of urea in solution is $x \times 10 ^ { - 3 }$. Value of $x$ is - (Integer answer)

Q57. Given below are two statements : Statement I : The rate law for the reaction $A + B \rightarrow C$ is rate $( r ) = k [ A ] ^ { 2 } [ B ]$ . When the concentration of both A and B is doubled, the reaction rate is increased " $x$ " times. Statement II : [Figure]
The figure is showing "the variation in concentration against time plot" for a " $y$ " order reaction. The Value of $x + y$ is $\_\_\_\_$