Question

A solution that contains nitromethane (1) in acetonitrile (2) is heated at a constant pressure of 1 bar until the first bubble appears. If the temperature of the solution at this point is 85^◦C, what is the composition of the original solution?

You may assume that the solution is ideal. The saturation pressures for the pure components (in kPa) for T in ^◦C are given by

ln(p₁^sat) = 14.2742 – 2945.47/(224 + T)

ln(p₂^sat) = 14.2043 – 2972.64/(209 + T)

Answer 1

Apply Raoults law:

x1*P°1 = y1*PT

x2*P°2 = y2*PT

and

ln(P°1) = 14.2742 – 2945.47/(224 + T)

ln(P2°) = 14.2043 – 2972.64/(209 + T)

x2 = 1-x1

y2 = 1-y1

then..

if P = 1 bar --> 100 kPa

T = 85°C

substitute

ln(P°1) = 14.2742 – 2945.47/(224 + 85) = 4.74193 kPa

ln(P2°) = 14.2043 – 2972.64/(209 + 85) = 4.09327 kPa

x1*P°1 = y1*PT

x2*P°2 = y2*PT

Pt = 100 kPa

x1*4.74193 = y1*100

x2*4.09327 = y2*100

subs

x1*4.74193 = y1*100

(1-x1)*4.09327 = (1-y1)*100

x1 = 100/4.74193*y1 = 21.088*y1

(1- 21.088*y1)*4.09327 = (1-y1)*100

4.09327 - 21.088*4.09327 y1 = 100 - 100y1

y1(21.088*4.09327 +100) = 100-4.09327

y1 = 95.9067/186.318 = 0.51474

y2 = 1-0.51474 = 0.48526