Read the passage carefully and answer the Questions.

A homogeneous mixture of two or more than two components has uniform composition and properties. The binary solutions have two components, which may be solid, liquid or gas. The resultant solution has a larger amount of solvent and a smaller amount of solute. The amount of solute in a given amount of solvent decides the concentration of the resulting solution. The concentration can be expressed in various ways, like molarity, molality, normality and mole fraction.

The molality of a 1 liter aqueous solution of 93% $H_2SO_4$ (mass/volume) is:

(Given: density of the solution = $1.84\, g\, mL^{-1}$, molar mass of $H_2SO_4 = 98\, g\, mol^{-1}$)

$10.43\, mol\, kg^{-1}$

The correct answer is Option (1) → $10.43\, mol\, kg^{-1}$

Given:

Volume of solution = $\text{1 L = 1000 mL}$

Density of solution = $\text{1.84 g mL}^{-1}$

Mass % (m/v) of $H_2SO_4$ = 93%

Molar mass of $H_2SO_4 = 98\, g\, mol^{-1}$

Step 1: Mass of 1 L solution

Mass = density × volume

Mass = 1.84 × 1000 = 1840 g

Step 2: Mass of $H_2SO_4$ in solution

93% means 93 g $H_2SO_4$ per 100 g solution.

So in 1840 g solution:

Mass of $H_2SO_4 = (93/100) × 1840= 1711.2\, g$

Step 3: Moles of $H_2SO_4$

Moles = mass / molar mass

Moles = 1711.2/98 = 17.46 mol

Step 4: Mass of solvent (water)

Mass of solvent = total mass - mass of solute

= 1840 - 1711.2 = 128.8 g = 0.1288 kg

Step 5: Molality

Molality = moles of solute / kg of solvent

= 17.46/0.1288

$≈ 10.43\, mol\, kg^{-1}$

Hence, the correct option is $10.43\, mol\, kg^{-1}$.