2 g of benzoic acid (CHCOOH) dissolved in 25 g of benzene shows a depression in freezing point equal to 1.62 K. Molal depression constant for benzene is 4.9 K kg mol1. What is the percentage association of acid if it forms dimer in solution?

Question

Answer

Is it 100%

Answer

Given information:

Mass of benzoic acid = 2 g

Mass of benzene = 25 g

Depression in freezing point = 1.62 K

Molal depression constant of benzene = 4.9 K kg mol^-1

Calculating the molality of the solution:

Molality (m) = moles of solute / mass of solvent in kg

Molar mass of benzoic acid (C₆H₅COOH) = 122.12 g/mol

Number of moles of benzoic acid = 2 g / 122.12 g/mol = 0.01639 mol

Mass of benzene = 25 g = 0.025 kg

Molality (m) = 0.01639 mol / 0.025 kg = 0.6556 mol kg^-1

Calculating the degree of dissociation:

Assuming that benzoic acid associates to form a dimer in solution, the equation for depression in freezing point can be written as:

ΔT_f = iK_fm

where ΔT_f is the depression in freezing point, K_f is the molal depression constant of benzene, m is the molality of the solution, and i is the van't Hoff factor.

For a non-dissociating solute, i = 1. However, for a solute that associates to form a dimer, i = 2.

Substituting the given values in the equation:

1.62 K = (2)(4.9 K kg mol^-1)(0.6556 mol kg^-1)

Solving for i:

i = 2.081

The degree of dissociation (α) can be calculated using the equation:

α = 1 - 1/i

Substituting the value of i:

α = 1 - 1/2.081 = 0.5197 or 51.97%

Explanation:

Benzoic acid might associate to form a dimer in the given solution. The depression in freezing point of the solution is measured to determine the degree of association. The molality of the solution is calculated using the given mass of benzoic acid and benzene. Assuming that benzoic acid associates to form a dimer, the van't Hoff factor (i) is calculated using the equation for depression in freezing point. The degree of dissociation (α) is then calculated using the value of i. The calculated value of α is 51.97%, which means that approximately 52% of benzoic acid associates to form a dimer in the given solution.

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