Calculate Molar Volume of Vapour-Liquid System with X=0.2

[mojo4king]

Ive been trying to figure this one out for too long,please help :s !

Molar volume of a saturated vapour-liquid system is given by V=Vf(1-X) + VgX,
where Vf=molar vol. of condensed phase
Vg=molar volume of vapour phase
X=quality
A given closed system contains only water in VLE at 25oC. Vapour pressure of water at this temp. is 3168 Pa.

Calculate the molar volume of the system if the quality is 0.2.

Any ideas??
Thanks

 

[Astronuc]

This seems like a homework problem.

Firstly, one must understand the definition of quality, x.

x=m_v/(m_v + m_l)

where m_v = mass of vapor and m_l = mass of liquid

So quality is defined on a mass basis, which can be related to moles.

Also the volume of either liquid or vapor is simply mass*specific volume and liquid and vapor have different specific volumes depending upon temperature and pressure. Specific volume is simply the reciprocal of density.

 

[Blueshift5]

for reaching out. To calculate the molar volume of a vapour-liquid system, we can use the equation V=Vf(1-X) + VgX, where Vf is the molar volume of the condensed phase and Vg is the molar volume of the vapour phase. In this case, we are given that the system only contains water in VLE at 25oC, with a vapour pressure of 3168 Pa. We also know that the quality is 0.2.

To solve for the molar volume, we need to first find the molar volume of the condensed phase and the molar volume of the vapour phase. For the condensed phase, we can use the ideal gas law, PV=nRT, where P is the vapour pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. At 25oC, R=8.314 J/mol·K. We can assume that the volume of the condensed phase is negligible compared to the volume of the vapour phase, so we can use the total volume of the system as the volume of the vapour phase.

Using the ideal gas law, we can solve for the number of moles of water in the system:
n = PV/RT = (3168 Pa)(V)/(8.314 J/mol·K)(298.15 K) = 0.127 moles

Next, we can use the molar mass of water (18.015 g/mol) to convert moles to mass:
m = nM = (0.127 moles)(18.015 g/mol) = 2.29 g

Now, using the density of liquid water at 25oC (0.997 g/cm3), we can solve for the volume of the condensed phase:
Vf = m/ρ = (2.29 g)/(0.997 g/cm3) = 2.30 cm3

Finally, we can plug in the values for Vf, Vg, and X into the equation V=Vf(1-X) + VgX:
V = (2.30 cm3)(1-0.2) + (Vg)(0.2)

Solving for Vg, we get:
Vg = (V - 1.84 cm3)/0.2

Therefore, the m