In thermodynamics and chemical engineering, the vapor–liquid equilibrium (VLE) describes the distribution of a chemical species between the vapor phase and a liquid phase.
The concentration of a vapor in contact with its liquid, especially at equilibrium, is often expressed in terms of vapor pressure, which will be a partial pressure (a part of the total gas pressure) if any other gas(es) are present with the vapor. The equilibrium vapor pressure of a liquid is in general strongly dependent on temperature. At vapor–liquid equilibrium, a liquid with individual components in certain concentrations will have an equilibrium vapor in which the concentrations or partial pressures of the vapor components have certain values depending on all of the liquid component concentrations and the temperature. The converse is also true: if a vapor with components at certain concentrations or partial pressures is in vapor–liquid equilibrium with its liquid, then the component concentrations in the liquid will be determined dependent on the vapor concentrations and on the temperature. The equilibrium concentration of each component in the liquid phase is often different from its concentration (or vapor pressure) in the vapor phase, but there is a relationship. The VLE concentration data can be determined experimentally, approximated with the help of theories such as Raoult's law, Dalton's law, and Henry's law.
Such vapor–liquid equilibrium information is useful in designing columns for distillation, especially fractional distillation, which is a particular specialty of chemical engineers. Distillation is a process used to separate or partially separate components in a mixture by boiling (vaporization) followed by condensation. Distillation takes advantage of differences in concentrations of components in the liquid and vapor phases.
In mixtures containing two or more components, the concentrations of each component are often expressed as mole fractions. The mole fraction of a given component of a mixture in a particular phase (either the vapor or the liquid phase) is the number of moles of that component in that phase divided by the total number of moles of all components in that phase.
Binary mixtures are those having two components. Three-component mixtures are called ternary mixtures. There can be VLE data for mixtures with even more components, but such data is often hard to show graphically. VLE data is a function of the total pressure, such as 1 atm or at the pressure the process is conducted at.
When a temperature is reached such that the sum of the equilibrium vapor pressures of the liquid components becomes equal to the total pressure of the system (it is otherwise smaller), then vapor bubbles generated from the liquid begin to displace the gas that was maintaining the overall pressure, and the mixture is said to boil. This temperature is called the boiling point of the liquid mixture at the given pressure. (It is assumed that the total pressure is held steady by adjusting the total volume of the system to accommodate the specific volume changes that accompany boiling.) The boiling point at an overall pressure of 1 atm is called the normal boiling point of the liquid mixture.
we assume that we have an exergonic reaction , a substrate going to a product , is the negative ΔG′° the principal reason that the equilibrium favors the product (there is more product than substrate at equilibrium )?, or it is not and that depends on other factors? , thanks .
So basically, I got close to a zero for my solution to this problem. I'm guessing based on the posted solutions that I wasn't able to get partial credit
due to the fact that my coordinate axis was aligned with the slender bar and not in its usual perpendicular position.
This resulted in...
I am struggling to understand Callen's explanation for stability, I understand that the concavity of S(U) must be negative because otherwise we can show that this means that the temperature increases as the internal energy decreases (dT/dU<0) but I cannot understand equation (8.1) which...
It is desired to remove the molecular hydrogen present in a flask. What will be better to introduce, ##Cl_2## or ##Br_2##? Why?
##2 HCl <-> H_2 + Cl_2## (1)
##k = 3,2.10^{-14}##
##H_2 + Br_2 <->2 HBr## (2)
##k = 2.10^9##
I thought about turning equation (1) to make the...
According to the book "Principles of Statistical Mechanics" by Amnon Katz, page 123, ##\alpha## must be such that ##\exp ( -\alpha N ) ## can be expanded in powers of ##\alpha## with only the first order term kept. Is this the necessary and sufficient condition for small deviations from...
i am having a problem in understanding the question , what will be the volume of hcl ? and how is the reaction going to take place ? please help me i am stuck on this problem for quite a long time.
I've written out the half reaction
8e- + 9H+ + SO42- = HS- + 4H2O
and I know the logK = 4.25 (that's the constant mentioned in the prompt)
I've written out the equilibrium statement of 10^4.25 = ([x^1/8]*[H2O^1/2])/([10x^1/8]*[e-]*[(10^-8.2)^9/8]
However, from there, it seems like I have two...
For finding the pH of the acid, I made use of the equilibrium law (or the law of mass action) to arrive at the degree of dissociation which I later used to get the [H+] concentration.
I am stuck in finding the pH of the salt solution.
##CH2ClOO^- + H2O <---> CHClOOH + OH^-##
Could you please...
I was thinking that we can equate the electrostatic potential energy and the spring energy (as the force is similar to that of a spring so energy will also be 1/2kx^2 ) but i am not getting the correct ans but by equating the net force on one charge to kr i am getting the correct ans can...
I isolated the member ABC and drew the free body diagram:
α is then calculated using inverse tan: Tan-1=(6.25+15)/50=23.03
Then force of member BD on the joint can be found by sum of all moments around point A.
Then Ax is calculated which is equal to BD×Cos(α)=235.2×Cos(23.03) Ax=216.48...
Homework Statement
Homework Equations
Formula of Kp and Kc
The Attempt at a Solution
You will easily be able to identify that the reaction will proceed in the forward direction when some inert gas is introduced.
So,my question is that why won't the amount of chlorine formed increase in...
Homework Statement
A car is lifted vertically by a jack placed at the car's rear end 40cm off the central axis, so that the weight of the car is supported by the jack and the two front wheels. The distance between the front wheels is 1.60m, the distance from the axis connecting the two wheels...
Homework Statement
For silicon at T=300K with donor density ND=2×109cm−3, acceptor density NA=0 and ni=8.2×109cm−3, calculate the equilibrium electron and hole concentration
Homework Equations
n_0=\frac{N_D-N_A}{2}+\sqrt{\frac{N_D-N_A}{2}^2+n_i^2}
p_o=\frac{n_i^2}{n_0}
The Attempt at a...
Homework Statement
I had to answer which of the pulley arrangements illustrated (see picture) is in equilibrium (the drawing went a bit difficult, please see all outer boxes as equal in size and the middle ones as well) I managed to answer that it is arrangement C, by finding out that...
Homework Statement
See this question.
Homework Equations
Pressure=Height*Density*Gravity
The Attempt at a Solution
I think P_atm=P_gas.
I think so because for the two liquids(oil and Hg) to be in equilibrium the net force on them should be zero.
And,since they are not getting displaced...
Hello,
Let us imagine a rod resting on a frictionless horizontal surface such that the rod is made up of 2 identical molecules. Let these molecules be named A and B from left to right. If we pull A to the left and B to the right with forces of equal magnitude, the rod must remain at equilibrium...
Consider chain of two radioactive decays ##A \to B\to C##. The equation that regulates ##N_B## is
$${\frac {\mathrm {d} N_{B}}{\mathrm {d} t}}=-\lambda _{B}N_{B}+\lambda _{A}N_{A}$$
I can't understand why the activity of ##B## is get as ##\lambda_B N_B##, for example at page 20 here...
Homework Statement
A thin stiff uniform rectangular plate with width L (L =AB) is lying on two inclined surface as shown in Fig. 3-1. The angle between the horizontal surface and the left inclined surface is α, and that between the horizontal surface and the right inclined surface is β. It is...
Homework Statement
Homework Equations
The Attempt at a Solution
I've resolved all the relevant forces (tension, weight, normal force), but upon looking at the mark scheme, there is no normal force to be resolved.
Forgive me if I'm missing out on something obvious, but shouldn't there be a...
Homework Statement
if a beam fixed at two points is on an angle say 45 degrees from the x or y-axis instead of running parallel to x-axis in most questions does this effect calculations? The force acting upon it would be a load directly downwards
Homework Equations
N/A
The Attempt at a...
Homework Statement
A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in _______ equilibrium with respect to rotation about the edge and in _________ equilibrium with respect to rotation about a horizontal axis that is...
I was reading the *Statistical Physics An Introductory Course* by Daniel J.Amit and need some help to understand a certain passage:
In an isolated composite system of two paramagnetic system:
System a with ##N_a## spins and a magnetic field ##H_a ##
System b with ##N_b## spins and a...
Homework Statement
Problem image: https://prnt.sc/gvhjso
In this case I have to find the reaction forces at the point E (the Fx, Fy, and the Moment at point E) by using the given data. The 20kN forces at the load AC are concentrated, and are 1.8m far from each other. The tension of the cable is...
Hey
So I am still a beginner in Physics and work asked me today to calculate if a 63mm Bore Pneumatic Ram will do the required job. Anyway, so I know how to calculate the weight capacity the ram can handle if it is at a 90 deg angle however if the ram is on an angle then I am stuck. I need to...
Homework Statement
I'm trying to solve for this problem below.How would you be able to get the force in member ID and GC? Find the reaction forces in member AFGH
Homework Equations
∑M = 0
∑[F][/y] = 0
∑[F][/x] = 0[/B]
The Attempt at a Solution
I dismembered all of its parts but no matter...
Homework Statement
The board shown below is being held in equilibrium in the vertical plane by three smooth rods at A, B, and C
Determine the magnitudes of forces at A, B, and C in terms of the weight of the body, W.
Homework Equations
Moment = f*r
Here's a diagram
The Attempt at a...
here is the question (part I):
For part I, I need some assistance, I cannot figure out how to do the question. I know eventually what to do, it's just working out the equilibrium constants I'm having trouble with. So to start, I want to work out the K values at 600K and 800K, I do this by...
Homework Statement
A 1.0kg of ice at 0◦C, 3.0kg of water at 0◦C, and 5.0kg of iron at temperature T are placed in a sealed and insulated container. cFe =400J/ kg◦C ,cWater=4200J/ kg◦C , cIce= 2000 J/ kg◦C
latent heat for ice is 3.3×105 J .
The equilibrium temperature is 20◦C.
Homework...
Homework Statement
A human holds a ball of mass 8kg at his hand, so that the forearm is perpendicular to the upperarm.
The distance between the elbow and the center of mass of the forearm is 0.15 meters, the distance between the elbow and the muscle is 0.05 meters and the mass of the forearm...
Hello members,
I wish to produce and "store" "Methane" gas. I wish to accomplish this task by conducting out a reaction between carbon-dioxide an water. I have my own source of energy and I completely understand that the reaction is endothermic.
The reaction is: CO2 + 2H2O + energy = CH4 + 2O2...
Homework Statement
A rigid wire frame is formed in a right triangle, and set in a vertical plane as shown. Two beads, of weight W1 = 1.5 N and W2 = 2.5 N, slide without friction on the wires, and are connected by a cord. When the system is in static equilibrium, what is the tension in the...
Homework Statement
I feel so stuck.
Given the Logistic Equation:
$$\frac{dP}{dt}=kP(1-\frac{P}{A})$$
a.). Find the equilibrium solutions by setting $$\frac{dP}{dt}=0$$ and solving for P.
b.). The equation is separable. Separate it and write the separated form of the equation.
c.). Use partial...
I understand that the change in Gibbs Free Energy at equillibrium is 0 and this leads to the equation -deltaH=TdeltaS. My questions here is that if a reaction is at equillibrium, how can there be any change in enthalpy or entropy at all? Why wouldn't these terms be 0?
What is the pH of a solution made from 34.6 ml if 3.45*10^-4 M of H2SO4 added to 41.7 ml of 4.56*10^-4 M of Al(OH)3?
I know how to find H+ and OH- and pH I also know how to use x mol / L, but I cannot get them to click together. Everyone keeps telling me to use RICE but my professor never...
Homework Statement
U = Ax2 - Bx3
Homework Equations
du/dx = 2Ax - 3Bx2
The Attempt at a Solution
If I was given a potential energy function U = Ax2 - Bx3 and am asked to find:
1) The expression for the force as a function of x.
2) The equilibrium points and determine if are they stable or...
A ball of mass 15.47kg rests on a table of height 0.73m. The tabletop is rectangular with a mass of 12.11kg, supported by 4 thin legs. The width of it is 134.0cm and length of 63.7cm. If the ball touches the tabletop at point (67.0cm, 16.4cm) relative to corner 1, what is the force the tabletop...
Homework Statement
Find the displacement from the equilibrium position of the particle that is in the distance x=£/12 from the wave source, for the moment t=T/4. The amplitude of the wave is A=0.2 m
Homework Equations
x=A*cos(wt)=A*cos2*pi/T* t
The Attempt at a Solution
x=£/12...
Homework Statement
see attachment ***indicates correct answer
Homework Equations
F=ks
The Attempt at a Solution
I do not understand how this works, and I haven't been able to find any examples of this.
Homework Statement
This is a more than one part question that depends on answers from the previous parts, which I have so I will not rewrite those questions. I will write the question I am facing difficulty with:
Answers from previous parts:
Length = 1.95 m (From top of chains to center, its...
Homework Statement
A mass M hangs in equilibrium on a spring. M is made to oscillate about the equilibrium position by pulling it down 10 cm and releasing it. The time for M to travel back to the equilibrium position for the first time is 0.5s. Which line, A to D, is correct for these...
Homework Statement
If m=5.0kg, φ=30◦ and μs =0.87, what is the minimum force needed to make the box slide down the slope?
[/B]
Homework Equations
force of status friction is less than or equal to the normal force multiplied by the coefficient of static friction
F,normal=mgcosφ
The image...
The question asks:
Recall that you observed very little corrosion occurring on the iron nail immersed in NaOH(aq) solution. This observation is difficult to explain from an electrochemistry perspective since electrochemistry principles predict a spontaneous reaction that should cause...