Equilibirium Definition and 65 Threads

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.

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  1. W

    Calculating the load required to tip a table?

    I would like to understand the topic discussed in this thread more. https://www.physicsforums.com/threads/tipping-over-a-table-how-much-overhang.1012197/post-6598527 As I understand it, I can find the load required to tip the table can be calculated by this formula. L<W a/x This is illustrated...
  2. samy4408

    Medical Question about reactions in biochemistry

    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 .
  3. Huzaifa

    How Do Acid-Base Equilibria Work?

    $$ \begin{array}{c} \mathrm{HA}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{A}^{-}+\mathrm{H}_{3} \mathrm{O}^{+} \\ \mathrm{K}=\dfrac{\left[\mathrm{A}^{-}\right]\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]}{\left.[\mathrm{HA}] \mathrm{H}_{2} \mathrm{O}\right]} \quad...
  4. rayjbryant

    Engineering Need help verifying symbolic calculations for an FBD statics problem

    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...
  5. E

    Stability and concavity of the entropy function

    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...
  6. S

    Chemistry Can anyone check my answers for these equilibrium problems?

    The following are my works for the problems: I put squares on my final answers! Thank you!
  7. il postino

    Chemistry Which Is Better to Remove H2: Cl2 or Br2?

    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...
  8. T

    Small deviations from equilibrium and Lagrange multipliers

    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...
  9. K

    Understanding rigid-body equilibrium problem

    So I have this problem The soultion to the problem gives me this drawing But I don't understand what ##F_h## and ##F_v## is
  10. Prabs3257

    Chemistry Solving Ionic Equilibrium Problem: Volume of HCl & Reaction Explained

    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.
  11. P

    Chemistry Solving for electron activity given pH and ratio of redox elements

    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...
  12. Kaushik

    Chemistry Finding the pH of this acid and its sodium salt solution

    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...
  13. Prabs3257

    Electrostatic force equilibrium

    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...
  14. bardia sepehrnia

    Calculating a force on a member (Statics)

    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...
  15. navneet9431

    Why doesn't the amount of Cl increase?

    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...
  16. P

    How to find the normal force of a car jack lifting a car

    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...
  17. B

    Calc Electron & Hole Concen in Silicon at 300K

    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...
  18. Physicsterian

    Defining equilibrium and movement in pulley arrangements

    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...
  19. navneet9431

    Is P_atm=P_gas? Solving the Homework Problem

    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...
  20. W

    B My Third Post: Change of Intermolecular Distance?

    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...
  21. C

    I Activity of daugther isotope in secular 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...
  22. thevinciz

    Equilibrium of a stiff plate on inclined planes

    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...
  23. SmamMir

    System of equilibrium, why won't the normal force apply?

    Homework Statement Homework EquationsThe 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...
  24. Jeviah

    Does the angle of a beam fixed at two points affect the method?

    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 downwardsHomework Equations N/A The Attempt at a Solution...
  25. E

    Cube balanced at equilibrium about two different axes

    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...
  26. WeiShan Ng

    I [Stat Phy] What does exhausting the states of a system mean?

    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...
  27. T

    Understanding Tension on a Pulley

    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...
  28. A

    I Can a 63mm Bore Pneumatic Ram handle the required weight at an angled position?

    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...
  29. C

    Finding forces in members of frames

    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...
  30. B

    Moment Equilibrium in terms of box weight

    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...
  31. T

    Effect of Temperature on Chemical Reaction Equilibrium

    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...
  32. heartshapedbox

    Latent heat and specific heat in insulated container

    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...
  33. P

    What is the equilibrium force exerted by the muscle in holding a ball?

    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...
  34. inund8

    Statics Homework: Solving for Weight with ΣFy = 0 and ΣFx = 0 Equations

    Homework Statement Homework Equations [/B] ΣFy = 0 ΣFx = 0 TanΘ = sinΘ/cosΘ...
  35. N

    How Can I Store Methane Produced from CO2 and Water Without Combustion?

    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...
  36. X

    Static equilibrium: setting up the equation

    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...
  37. defaultusername

    Breakdown of a Logistic Equation

    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...
  38. doulyftbruh

    Change in Gibbs free energy at equillibrium

    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?
  39. R

    I am sure I am doing this Acid/Base problem wrong

    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...
  40. Blockade

    How to find if equilibrium points of a force is un/stable?

    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...
  41. K

    Calculating Force Exerted on Table Legs by Mass and Dimensions

    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...
  42. Z

    Find the displacement from the equilibrium position

    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...
  43. heartshapedbox

    Determining equilibrium position between two springs

    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.
  44. slymme

    Swinging, equilibrium, kinetic energy problem

    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...
  45. slymme

    Mass hangs in equilibrium on a spring (oscillation)(MCQ)

    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...
  46. heartshapedbox

    Minimum force to make box slide down slope

    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...
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