Question

Chromium has many positive oxidation states. waht is "x" in the formula CrClx if a solution that has 5.00 g of this compound dissolved in 100ml of water, has a freezing point of -2.46C? assume an ideal value for i, kf for water =1.86C/m and 1.00 g/ml for the density of water

Answer 1

atomic mass of Cr = 52.00 u

atomic mass of Cl = 35.45 u

Therefore, molar mass of CrCl_x = [52.00 + x(35.45)]g/mol

no. of moles of compound in 5.00 g of it = 5.00/(52.00 + 35.45x)

density of water is 1.00 g/mL. Hence, mass of 100 mL water = 100g = 0.1 kg

Therefore, molality of the solution = [5.00/(52.00 + 35.45x)]/(0.1 kg)

depression in freezing point is given by:

where,

T_f = T_f(solvent) - T_f(solution) = 0 - (-2.46) = 2.46 ⁰C

k_f = 1.86 C/m

i = x + 1

Therefore,

or, 1.32(0.1)(52.00+35.45x) = 5(x+1)

or, 6.88 + 4.679x = 5x + 5

or, x = 6 (rounding off to nearest integer)

Hence, the formula is CrCl₆