Question

For the system of methanol (1) / methyl acetate (2) at P=101.33kPa, use Raoult’s law to find the pure boiling temperature of each component at P=101.33kPa

Extra Info (from previous calculations):
Bubble Point - If x₁ = 0.85, x₂ = 0.15, then T_guess = 63.55C and y₁ = 0.8123, y₂ = 0.1877
Dew Point - If y₁ = 0.45, y₂ = 0.55, then T_guess = 61C and x₁ = 0.4786, x₂ = 0.5214

**ANSWER IS SUPPOSED TO BE (T₁ *=64.7C T₁ *=56.9C)
Please show how this answer is found.

Answer 1

A phase at equilibrium is saturated with a chemical species if it holds as much of the species as it maximally can. For example, air at a given temperature and pressure will only hold so much water vapor. If more water vapor were somehow introduced into the air, condensation would occur and the extra water vapor would come out of the air as liquid water. When a gas that is saturated with a species A is in contact with a liquid of pure A, the rate at which molecules of A evaporate from the liquid into the gas equals the rate at which molecules of A from the gas condense into the liquid. On the other hand, if the amount of A in the gas is below saturation, the evaporation rate of A will be greater than its rate of condensation. This will continue unless the gas becomes saturated with A and equilibrium is established, at which point the two rates (evaporation and condensation) would become equal. Note that a liquid species that evaporates is referred to as being volatile, one that does not is nonvolatile. Gas-liquid systems with a single condensable component: These are systems in which a gas phase containing one or more chemical species is contacted with a liquid phase containing just one of those species. That is, only one component in the gas mixture can be induced to condense into liquid by a modest lowering of the temperature. Note that in this scenario the liquid phase consists of one, pure component. Raoult’s Law for a single condensable species: If i is the condensable component, then at equilibrium the partial pressure of i in the gas mixture must equal the vapor pressure of the pure i liquid. This is called Raoult’s Law. In equation form, Pi = yiP = p * i

For the system methanol (1)/methyl acetate (2), the following equations provide a reasonable correlation for the activity coefficients:

1=(2.771-0.00523T)x₂²

in 2=(2.771-0.00523T)x₁²

The anotone equation provides vapor pressures

in p1^sat/kpa =16.59158-364.31/T(K)-33.424

p2^sat/kpa =14.25326-2665.54/T(K)-53.424

a..for P = 101.33 kPa and x1 = 0.85

T₁^sat =337.71

T₂^sat =330.08

A iterative process is applied with T=(0.85)T₁^sat +(0.15)T₂^sat =336.57

subsutitute values 1 ,2

in p1^sat/kpa =16.59158-364.31/T(K)-33.424

converges at

T=331.20k

1=1.0236

2=2.1182

y1=0.670

y2=0.330

b.for P = 101.33 kPa and y1 = 0.40

T₁^sat =337.71

T₂^sat =330.08

A iterative process is applied with T=(0.40)T₁^sat +(0.60)T₂^sat =333.13

put 1=1,2=1 these values in

in p_i^sat and find p1sat and p2 sat

then we get x1 and x2 and 1,2 and repeat the process agian

in p1^sat/kpa =16.59158-364.31/T(K)-33.424

converges at

T=326.70k

1=1.3629

2=1.2523

x1=0.4602

x2=0.5398