Concentration and solubility

At 300 K, an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (h) of the solution (density $= 1.00\ \mathrm{g\,cm^{-3}}$) where h is equal to 2.00 cm. If the concentration of the dilute solution of the macromolecule is $2.00\ \mathrm{g\,dm^{-3}}$, the molar mass of the macromolecule is calculated to be $\boldsymbol{X}\times10^4\ \mathrm{g\,mol^{-1}}$. The value of $\boldsymbol{X}$ is _____.

Use: Universal gas constant (R) $= 8.3\ \mathrm{J\,K^{-1}\,mol^{-1}}$ and acceleration due to gravity ($g$) $= 10\ \mathrm{m\,s^{-2}}$

50 mL of 0.2 molal urea solution (density $= 1.012\ \mathrm{g\,mL^{-1}}$ at 300 K) is mixed with 250 mL of a solution containing 0.06 g of urea. Both the solutions were prepared in the same solvent. The osmotic pressure (in Torr) of the resulting solution at 300 K is _____.

[Use: Molar mass of urea $= 60\ \mathrm{g\,mol^{-1}}$; gas constant, $R = 62\ \mathrm{L\,Torr\,K^{-1}\,mol^{-1}}$; Assume, $\Delta_\mathrm{mix}H = 0$, $\Delta_\mathrm{mix}V = 0$]

A company dissolves 'x' amount of $\mathrm{CO_2}$ at 298 K in 1 litre of water to prepare soda water. X = ______ $\times10^{-3}$ g. (nearest integer)

(Given: partial pressure of $\mathrm{CO_2}$ at 298 K = 0.835 bar.

Henry's law constant for $\mathrm{CO_2}$ at 298 K = 1.67 kbar.

Atomic mass of H, C and O is 1, 12, and 6 g mol$^{-1}$, respectively)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : At 10°C, the density of a 5 M solution of KCl [atomic masses of K & Cl are 39 & 35.5 g mol$^{-1}$ respectively], is '$x$' g ml$^{-1}$. The solution is cooled to $-21$°C. The molality of the solution will remain unchanged.

Reason (R) : The molality of a solution does not change with temperature as mass remains unaffected with temperature.

In the light of the above statements, choose the correct answer from the options given below.

For a solution of the gases A, B, C and D in water at 298 K, the values of Henry's law constant ($K_H$) are 30.40, 2.34, $1.56\times10^{-5}$ and 0.513 k bar respectively. In the given graph, the lines marked as 'p' and 's' correspond respectively to :

If O$_2$ gas is bubbled through water at 303 K, the number of millimoles of O$_2$ gas that dissolve in 1 litre of water is _______. (Nearest Integer)

(Given : Henry's Law constant for O$_2$ at 303 K is 46.82 k bar and partial pressure of O$_2$ = 0.920 bar)

(Assume solubility of O$_2$ in water is too small, nearly negligible)

The mole fraction of urea in an aqueous urea solution containing 900 g of water is 0.05. If the density of the solution is 1.2 g cm⁻³, the molarity of urea solution is ______

(Given data: Molar masses of urea and water are 60 g mol⁻¹ and 18 g mol⁻¹, respectively)

The Henry's law constant for the solubility of $\ce{N2}$ gas in water at 298 K is $1.0\times10^5$ atm. The mole fraction of $\ce{N2}$ in air is 0.8. The number of moles of $\ce{N2}$ from air dissolved in 10 moles of water at 298 K and 5 atm pressure is