\({ \triangle G }^{ o }={ -nE }^{ o }F,-{ \triangle G }^{ o }={ W }_{ max' }\) decrease in free energy is measure of maximum work obtainable from the cell.

\(-\frac{d\left[N_2\right]}{d t}=\frac{1}{3} \frac{d\left[N_2\right]}{d t}=+\frac{1}{2} \frac{d\left[N H_3\right]}{d t}\)

Melting points first increase because the number of unpaired electrons increases and hence strength of metallic bond increases. After reaching the maximum, the melting points decrease because the pairing of electrons starts in the d-subshell and number of unpaired electrons decreases and so the strength of metallic bond decreases. The dip in the middle is due to exactly half-filled configuration of d-subshell which has higher stability. Hence, electrons are held tightly by the nucleus. As a result, metallic bond is weaker.

Carboxylic acids react with hydrazoic acid (N₃H) in presence of conc.H₂SO₄ to form 1^∘ amines containing one carbon atom less than the carboxylic acid.

\(K_4\left[\mathrm{Fe}\left(C N_6\right)\right] \longrightarrow 4 K^{+}\left[\mathrm{Fe}\left(C N_6\right)\right]^{4-}\)

(i) DDT: It is used as insecticide to control flies, mosquitoes, etc. Iodoform: Iodoform is used as an antiseptic.
(ii) 1-Bromopentane, as it is a primary alkyl halide. and
(b) 1-Bromo-2-methyl butane, as it is a primary alkylhalide.

(i) Elastomers: The polymers in which polymer chains are held together by the weakest intermolecular forces.These weak forces permit the polymer to be stretched.A few 'cross-links' are introduced in between the chains which held the polymer to retract to its original position after the force is released, as in vulcanised rubber
(ii) Condensation polymers: It involves a series of condensation reaction generally involving two monomers.Each monomer normally contains two functional groups.The condensation reactions result in the loss of small molecules usually water and ammonia, e.g. nylon, terylene, bakelite are condensation polymers.This  process is Known as 'condensation polymerisation'
(iii) Addition polymers: The polymers which are formed by repeated addition of monomers to the polymer chain.The monomers are unsaturated compounds and commonly derivatives of ethene.the addition polymers have same empirical as their monomers, e.g

This process is 'addition polymerisation'.

357 pm

The reaction is thermodynamically favourable. Since in the given redox reaction, all the reactants and the products are solids at room temperature, therefore, it does not occur at room temperature. However, at high temperature when chromium melts, the reaction proceeds rapidly. Thus, heating is required for this reaction to start.

Depression in freezing point is related to the molality, therefore, the molality of the solution with respect to ethylene glycol \(=\frac{\text { moles of ethylene glycol }}{\text { mass of water in kilogram }}\)
\(\text {Moles of ethylene glycol }=\frac{45 \mathrm{~g}}{62 \mathrm{~g} \mathrm{~mol}^{-1}}=0.73 \mathrm{~mol}\)
\(\text {Mass of water in } \mathrm{kg}=\frac{600 \mathrm{~g}}{1000 \mathrm{~g} \mathrm{~kg}^{-1}}=0.6 \mathrm{~kg}\)
\(\text {Hence molality of ethylene glycol }=\frac{0.73 \mathrm{~mol}}{0.60 \mathrm{~kg}}=1.2 \mathrm{~mol} \mathrm{~kg}^{-1}\)
Therefore freezing point depression,
ÄT_f = 1.86 K kg mol^–1 x 1.2 mol kg^–1 = 2.2 K
Freezing point of the aqueous solution = 273.15 K – 2.2 K = 270.95 K

Step-I : Calculation for concentration of the solution.
According to Van't Hoff's equation
p = CRT or C = \(\frac { \pi }{ RT } \)
p = 8.8 atm, T = 40\(°\)C = 313 K
R = 0.0821 L atm K^-1 mol^-1
\(C=\frac { 8.8 }{ 0.0821\times 313 } \)=0.34 molL^-1(M)
Step-II: Calculation of freezing point of the solution depression in freezing point of solution
\(\Delta\)T_f = K_f \(\times\) m
m = 0.34 mol kg^-1
(same as molarity as given)
K_f = 1.86 K kg mol^-1
\(\Delta\)T_f = 1.86 \(\times\) 0.84 (\(\because\) \(\Delta\) T_f = K_f m)
 = 0.63 K = 0.63\(°\)C
Freezing point of the solution = 0 - 0.63 \(°\)C
= - 0.63\(°\) C

1.123

(i) As pressure of X is changing with time, it cannot be a zero order reaction. Let us now check it for 1st order.
At t = 100 min, \(k={2.303\over 100}log{P_0\over P_t}={2.303\over 100}log {800\over 400}=6.932\times 10^{-3}min^{-1}\)
At t = 200 min, \(k={2.303\over 200}log{800\over 200}={2.303\over 800}log4=6.932\times10^{-3}min^{-1}\)
As k comes out to be constant, hence it is a reaction of 1st order
(ii)\(t_{75./.}={2.303\over k}log{100\over 100-75}={2.303\over 6.932\times10-3min}log4=200min\)
(iii) 2x (g)⟶ 3 y (g) + 2z (g)
Initial Pressure             800mm      0             0
Pressure after time t     800 - 2p    3 p           2 p
When pressure of X is 700 mm, 800 - 2 p = 700 or p = 50 mm
Total pressure = (800 - 2 p) + 3 p + 2 p = 800 + 3 p = 800 + 3 x 50 = 950 mm.

(i) HOCI in presence of an acid generates the reactive electrophile, chloronium ion «r, which attacks benzene to give chlorobenzene (A).
(ii) Chlorobenzene (A) on treatment with NaNH2/liq. NH₃ undergaes-dehydrohalogenation via benzyne to afford aniline (B).
(iii) Aniline (B) on treatment with HBF4 forms the corresponding salt anilinium tetrafluoroborate (C) which on heating with NaNO₂ undergoes Balz-Schiemann reaction through the intermedium formation of benzenediazonium tetrafluoroborate to afford fluorobenzene (D).

(a) (i) The ratio of number of moles of one component to the total number of moles of solution is known as mole fraction.
(ii) The solution which follows Raoult's law over entire range of concentrations at specific temperature is called ideal solution.
(b) W_B = 15 g, W_A = 450 g, \(\Delta\)T_f = 0.34 K, M_B = ?
\({ M }_{ B }=\frac { 1000\times { K }_{ f }\times { W }_{ B } }{ \Delta { T }_{ f }\times { W }_{ A } } \)
\(=\frac { 1000\times 1.86 \ K \ kg \ { mol }^{ -1 }\times 15 \ g }{ 0.34K\times 450 \ g } \)
= 182.35 g/mol

(i) Aspartame, Saccharin (anyone).
(ii) No.

(ii) Alcohols have higher boiling point as compared to that of amines, because oxygen being more electronegative atom, forms strong hydrogen bond as compared to that of nitrogen. In tertiary amine, there is no hydrogen bond formation due to the absence of H-atoms and hence, has the lowest boiling point. Therefore, increasing order of boiling point (CH₃)₃N < C₂H₅NH₂ < C₂H₅OH .
(iii) (CH₃)₃NH and (CH₃)₃N are secondary and tertiary arnines respectively. These are distinguished by Hinsberg's reagent which gives sulphonamide with secondary amines and no reaction carried out with tertiary arnines. (CH₃)₃NH reacts with benzene sulphonyl chloride as follows:

(i) Soaps work due to the formation of micelles. But the formation of micelles takes place at a minimum temperature called 'Kraft temperature'. This temperature is reached in luke warm water.
(ii) Be humble to accept a scientific fact from a elder person.