Question

N, N'-Dimethylformamide (DMF) is a commonly-used polar solvent. Its normal boiling point is 426K and is has ΔH°_vap = 47.6 kJ/mol. Suppose a laboratory vacuum system is able to maintain a flask at total pressure of 5.0 Torr. Estimate the temperature at which DMF will boil in this flask.

Please show all work.

Answer 1

We use the clausius-clapeyron equation,

ln ( P2 / P1 ) = - ( H / R ) ( 1 /T1 - 1 / T2 )

Where, P2 = Normal pressure = 760 torr T1 = Normal boiling point = 426 K

P1 = Reduced pressure = 5 torr T2 = BP at reduced pressure = ( to be calculated )

H = 47.6 kJ / mol R = Gas constant = 8.314

Putting this values in above equation,

  ln ( 5 / 760 ) = - ( 47.6 / 8.314 ) ( 1 / 426 - 1 / T2 )

ln 0.00657 = - ( 5.725 ) ( 0.00234 - 1/T2 )

2.303 log 0.00657 = - ( 5.725 ) ( 0.00234 - 1/T2 )

2.303 x ( -2.182 ) = - ( 5.725 ) ( 0.00234 - 1/T2 )

- 5.026 =  - ( 5.725 ) ( 0.00234 - 1/T2 )

5.026 = ( 5.725 ) ( 0.00234 - 1/T2 )-----------------------Cancelling -ve sing from both the sides.

5.026 = ( 5.725 x 0.00234 ) - ( 5.725 x 1 / T2 )

5.026 = 0.01339 - 5.725 / T2

5.026 - 0.01339 = - 5.725 /T2

5.012 = - 5.725 / T2

T2 = 5.725 / 5.012

= 1.142 K

At 5 torr N, N'-Dimethylformamide boils at 1.142 K.