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The elevation in the boiling point of a solution is defined as the difference between the boiling points of the solution and the pure solvents at a given pressure, e.g. If T₀ and T are the boiling points of a pure solvent and a solution, then the elevation in boiling point, ΔT_b = T – T₀. It is a colligative property.

Given :

Henry’s law constant = K 

= 4.27 × 10^-5 mm Hg mol dm^-3 

Pressure of the gas = P = 760 mm Hg

K_H = 4.27 × 10^-5 mm^-1 mol dm^-3

= 4.27 × 10^-5 × 760 atm^-1 mol dm^-3

= 3245 × 10^-5 atm^-1 mol dm^-3

P = 760 mm = \(\frac{760}{760}\) = 1 atm

By Henry’s law,

S = K_H x P = 3.245 x 10^-2atm^-1 mol dm^-3 x 1 atm

= 3.245 × 10^-2 mol dm^-3

∴ Solubility of methane = 3.245 × 10^-2 mol dm^-3

(a)
(i) Deep sea divers depend upon compressed air for breathing at high pressure under water. The compressed air contains  N₂ in addition to O₂, which are not very soluble in blood at normal pressure. However, at great depths when the diver breathes in compressed air from the supply tank, more N₂ dissolves in the blood and other body fluids because the pressure at that depth is far greater than the surface atmospheric pressure. When the diver comes towards the surface, the pressure decreases, N₂ comes out of the body quickly forming bubbles in the blood stream. These bubbles restrict blood flow, affect the transmission of nerve impulses. The bubbles can even burst the capillaries or block them and starve the tissues of O₂. This condition is called the bends, which are painful and life-threatening.
(ii) At high altitudes the partial pressure of O₂ is less than that at the ground level. This results in low concentration of oxygen in the blood and tissues of the people living at high altitudes or climbers. The low blood oxygen causes climbers to become weak and unable to think clearly known as anoxia.
(b) To increase the solubility of CO₂ in soft drinks, the soda water bottles are sealed under high pressure. When the bottle is opened at room temperature under normal atmosphere conditions, the pressure inside the bottle decreases to atmospheric pressure and excess CO₂ fizzes out.

A substance (solute) dissolves in a solvent if the intermolecular interactions are similar in both the components; for example, polar solutes dissolve in polar solvents and non polar solutes in non polar solvents thus we can say “like dissolves like”.

(ii) water will move from side (B) to side (A) if a pressure greater than osmotic pressure is applied on piston (B).

Molarity of a solution is defined as the number of moles of solute dissolved in one litre of solution. Since volume depends on temperature and undergoes a change with change in temperature, the molarity will also change with change in temperature. On the other hand, mass does not change with change in temperature, as a result other concentration terms given in the question remain unchanged by changing temperature. According to the definition of all these terms, mass of the solvent used for making the solution is related to the mass of solute.

At a given pressure the solubility of oxygen in water increases with decrease in temperature. Presence of more oxygen at lower temperature makes the aquatic species more comfortable in cold water.

Higher the value of Henry’s law constant K_H, the lower is the solubility of the gas in the liquid.

Strength of H₂O₂ = \(\frac{Weight\,of\,H_2O_2}{Volume\,of\,solution(L)}\)

= \(\frac{3.4g\times1000}{448L}\)

= 7.6 g/L
\(\underset{(2\times34g)}{2H_2O_2}\longrightarrow2H_2O+\underset{(22.4L)\,at\,NTP}{O_2}\) 

68 g of H₂O₂ produces 22.4 litres at oxygen gas at NTP.

Therefore, 

7.6g of H₂O₂ will produce

= 22.4/68 x 7.6

= 2.5 litre at oxygen.

Thus, volume strength of given H₂O₂ solution is 2.5

Hence, option(c) is Right answer.

∆ T_f = 273-272.07 =0.93

∆ T_f = (K_f x W_B )/(M_B x W_A) x1000

⇒ 0.93 = (1.86 x 18 )/ (M_B x 200)x1000

M_B =  180 g mol^-1

(d) 0.1 M Ba(NO₃)₂ and 0.1 M Na₂SO₄

0.1 x 3 ion [Ba² + 2NO₃^-], 0.1 x 3 ion [2Na⁺ , SO₄^-]

In 1880 van‘t Hoff introduced a factor i, known as the van‘t Hofffactor, to account for the extent of dissociation or association. This factor i is defined as the ratio of Normal molar mass to that of the Abnormal molar mass .It is also defined as i = Observed colligative property/Calculated colligative property.