0.636 g of acetic acid (molar mass = 60 g/mol) is dissolved in 1 kg of water, the solution freezes at -0.0205^ C. Calculate van't Hoff factor of acetic acid ( K _f water = 1.86 K-kg/mol)

Step-by-step solution

Given: Mass of acetic acid, w = 0.636 g Molar mass of acetic acid, M = 60 g/mol Mass of solvent (water), W = 1 kg Depression in freezing point, T_f = 0 - (-0.0205) = 0.0205 K Cryoscopic constant, K_f = 1.86 K kg/mol The molality ( m ) of the solution is calculated as: m = w M W = 0.636 60 1 = 0.0106 mol/kg Using the formula for depression in freezing point: T_f = i K_f m Substituting the given values: 0.0205 = i 1.86 0.0106 0.0205 = i 0.019716 i = 0.0205 0.019716 1.041 Answer: 1.041