Question

6. The melting points and heats of fusion of o-, p-dinitrobenzene are 390.1 and 446.7 K, and 16.33 and 14.00 kJ/mol, respectively. Assuming ideal solubility behavior, calculate the melting point for a solution of 10 mol% o-dinitrobenzene in 90 mol% p- dinitrobenzene.

The melting points and heats of fusion of o-, p-dinitrobenzene are 390.1 and 446.7K, and 16.33 and 14.00 kJ/mol, respectively. Assuming ideal solubility behavior, calculate the melting point for a solution of 10 mol% o-dinitrobenzene in 90 mol% p-dinitrobenzene.

Answer 1

The mole fractions are given as

o-dinitirobenzene = 0.1

p-dinitirobenzene = 0.9

we know that

lnXA = -(∆H°fus_A/R)(1/T - 1/T_A°)

Where

A = one solid in mixture of two solids

we know that ,∆H°fus_ortho = 16.33 KJ /mole R = gas constant = 8.314 X 10^-3 KJ / K mole ; T_ortho° = 390.1 K

T = ? [melting point of solution]

ln (0.1) = -(16.33 / 8.314 X 10^-3 ) (1/T - 1/390.1)

-2.303 = -1964.16 (1/T - 0.00256)

0.00117 = (1/T - 0.00256)

1/T = 0.00373

T = 268.09 Kelvin