4.[4 points] A liquid-vapor equilibrium mixture is confined in a closed system w

Question

4.[4 points] A liquid-vapor equilibrium mixture is confined in a closed system with a total volume of 1 m3 The temperature of the mixture is 350 K and the pressure is 150 kPa. The liquid has a molar volume of 8 x 10 m mol and the vapor can be modeled as an ideal gas. If there are 100 total moles, what is the number of moles in the liquid phase? A. 51.3 mol B. 48.7 mol C. -51.3 mol D. 0.414 mol E. Only 1 degree of freedom exists in the system, but two properties are specified (T and P), so the problem is invalid/void/impossible.

Explanation / Answer

Calculate the moles of vapor using ideal gas equation.

Total mole of liquid and vapor = 100 moles

n1 + n2 = 100 ...... (1)

v1 + v2 = 1 m3   ...... (2)

PV = nRT

V 1= n1RT/P

= n1 * 8.314 * 350 K / 150000

V 1= 0.02 n1

V2 / n2 = 8x 10-5 m3 /mol

n1 + n2 = 100 ...... (1)

0.02 n1 + 8x 10-5  n2= 1 ...... (2)

n1 =49.70 mol

n2 =51.30 mol

thus, the moles of liquid = 51.3 mol

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