Class 11th

6. Steam distillation is a special type of separation technique for temperature sensitive materials such as natural organic compounds. Few organic compounds tend to decompose at higher temperatures and normal distillation does not fit for this purpose. So, water is added to the apparatus and the temperature of the compounds is depressed, evaporating them at lower temperature. Once the distillation is accomplished, the vapours are condensed and  there occurs,   the separation of the constituents at ease.

4. Liquids which have different boiling points vaporize at different temperatures. The vapours are cooled and then liquids so formed are collected separately. Liquid A can be separated from B and C due to the large difference in boiling points. Liquid B and Liquid C have boiling points very close to each other and cannot be separated by simple distillation and are separated by fractional distillation. Liquid B distilled first since the order of boiling points of A, B and C is as follows: B < C < A.

3. When the difference in boiling points of two liquids is not much then simple distillation cannot be used to separate them. Vapours of such liquids are formed within the same temperature range and are condensed simultaneously. The technique of fractional distillation is used in such cases. In this technique, vapours of a liquid mixture are passed through a fractionating column before condensation. The fractionating column is fitted over the mouth of the round bottom flask. The liquid (A) with low boiling point will distill first.

2.  Benzoic acid can be purified by hot water because of following characteristics.
(i) Benzoic acid is more soluble in hot water and less soluble in cold water.
(ii) Impurities present in benzoic acid are either insoluble in water or more soluble in water to such an extent that they remain in solution as the mother liquor upon crystallisation.

1. The atomic orbitals combine to give rise to a new set of equivalent orbitals called hybrid orbitals and are used in bond formation. This phenomenon is known as hybridization which can be defined as the process of intermixing of the orbitals of slightly different energies so as to redistribute their energies, resulting in the formation of new sets of orbitals having equivalent energies and shape. In H₂C=C=CH₂ (allene) carbon atom l and 3 are sp² hybridized as each one has 3σ bonds while carbon atom 2 has 2σ bonds so it is sp hybridized while the allene molecule as a whole is found to be non-planar. 

15. ${\left[3x^2-2ax+3a^2\right]}^3$

= ${\left[3x^2+a\left(-2x+3a\right)\right]}^3$

We know that by binomial theorem,

${(a+b)}^3$ = $a^3+b^3+3ab\left(a+b\right)$

= $a^3+b^3+3a^{2}b+3a{b}^2$

Then,

${\left[3x^2+a\left(-2x+3a\right)\right]}^3$

= (3x²)³ + ${\left[a\left(-2x+3a\right)\right]}^3$ + $\left[3(3x^2){}^2 a\left(-2x+3a\right)\right]$ + $\left[ 3(3x^2){\left\{a\left(-2x+3a\right)\right\}}^2\right]$

= 27x⁶ + $\left[a^3{\left(-2x+3a\right)}^3\right]$ + $\left[3(9x^4)\left(-2ax+3a^2\right)\right]$ + $\left[3(3x^2)\left\{a^2{\left(3a-2x\right)}^2\right\}\right]$

= 27x⁶ + $\left[a^3\left\{-8x^3+27a^3+3\left(4x^2\right)\left(3a\right)+3\left(-2x\right)\left(9a^2\right)\right\}\right]$ + $\left[-54a{x}^5+81a^2{x}^4\right]$ + [ $\left(9a^2{x}^2\right)$ $\left(9a^2+4x^2-12ax\right)$ ]

= 27x⁶ + [ $-8a^3{x}^3+27a^6+36a^4{x}^2-54a^{5}x$ ] + [ $-54a{x}^5+81a^2{x}^4$ ] + [ $(81a^4{x}^2+36a^2{x}^4-108a^3{x}^3$ ]

= 27x⁶ $- 8a^3{x}^3+27a^6+36a^4{x}^2-54a^{5}x$ $- 54a{x}^5+81a^2{x}^4$ + $81a^4{x}^2+36a^2{x}^4-108a^3{x}^3$

= 27x⁶– 54ax⁵ $+ 117a^2{x}^4$ $- 116a^3{x}^3$ + $117a^4{x}^2$ $- 54a^{5}x$ $+ 27a^6$

13. The general term of the expansion ${\left(3+ax\right)}^9$ is

T_r+1 = ⁹C_r $3^{\left(9-r\right)}$ ${\left(ax\right)}^r$

= ⁹C_r $3^{\left(9-r\right)}{a}^r{x}^r$

At r = 2,

T₂₊₁ = ⁹C₂ $3^{\left(9-2\right)}{a}^2{x}^2$

= $\frac{9!}{2!\left(9-2\right)!}$ 3⁷a²x²

= $\mathrm{9\prime }$$\mathrm{8\prime }$$7!$/$\mathrm{2\prime }$$\mathrm{1\prime }$$7!\mathrm{}$ 3⁷a²x²

= 36 *3⁷a²x²

At r = 3,

T₃₊₁ = ⁹C₃ $3^{\left(9-3\right)}{a}^3{x}^3$

= $\frac{9!}{3!\left(9-3\right)!}$ 3⁶a³x³

= 9'8'7'6!/3'2'1'6! 3⁶a³x³

= 84 *3⁶a³x³

Given that,

Co-efficient of $x^2$ = co-efficient of $x^3$

=> 36 * $3^7{a}^2$ = 84 * $3^6{a}^3$

=> $\frac{a^3}{a^2}$ = 36' 3^{7  /84'}3⁶

=> $a$ = $\mathrm{3\prime 3/7}$

= $\frac{9}{7}$