Podcast
Questions and Answers
What is the vapor phase mole fraction of CO2 when x1 is 0.01 in carbonated water?
What is the vapor phase mole fraction of CO2 when x1 is 0.01 in carbonated water?
Henry's law applies only under high pressure conditions.
Henry's law applies only under high pressure conditions.
False
What is the value of Henry's constant for CO2 in water at 100°C?
What is the value of Henry's constant for CO2 in water at 100°C?
990 bar
According to Raoult's law, the total pressure P can be expressed as P = x1H1 + x2P2sat, where x1 is the mole fraction of component 1 and P2sat = _____ at 100°C.
According to Raoult's law, the total pressure P can be expressed as P = x1H1 + x2P2sat, where x1 is the mole fraction of component 1 and P2sat = _____ at 100°C.
Signup and view all the answers
Match the following terms with their definitions:
Match the following terms with their definitions:
Signup and view all the answers
What point is referred to as the bubble point in a phase diagram?
What point is referred to as the bubble point in a phase diagram?
Signup and view all the answers
Raoult’s Law states that the liquid phase is an ideal solution only when species are chemically different.
Raoult’s Law states that the liquid phase is an ideal solution only when species are chemically different.
Signup and view all the answers
What is the definition of the dew point in a phase equilibrium context?
What is the definition of the dew point in a phase equilibrium context?
Signup and view all the answers
In a phase equilibrium diagram, the line connecting liquid and vapor compositions is called a _________.
In a phase equilibrium diagram, the line connecting liquid and vapor compositions is called a _________.
Signup and view all the answers
Which law is applicable to describe the behavior of ideal gases in vapor phase?
Which law is applicable to describe the behavior of ideal gases in vapor phase?
Signup and view all the answers
Henry’s Law is valid for solutions with chemically similar components only.
Henry’s Law is valid for solutions with chemically similar components only.
Signup and view all the answers
What assumption is made regarding the vapor phase in the context of Raoult’s Law?
What assumption is made regarding the vapor phase in the context of Raoult’s Law?
Signup and view all the answers
What is the main purpose of Raoult's Law in the context of phase calculations?
What is the main purpose of Raoult's Law in the context of phase calculations?
Signup and view all the answers
The bubble point calculation requires knowledge of the total pressure and the liquid phase mole fractions.
The bubble point calculation requires knowledge of the total pressure and the liquid phase mole fractions.
Signup and view all the answers
What is the Antoine equation used for in vapor pressure calculations?
What is the Antoine equation used for in vapor pressure calculations?
Signup and view all the answers
In a binary mixture, the sum of the mole fractions in the vapor phase must equal ______.
In a binary mixture, the sum of the mole fractions in the vapor phase must equal ______.
Signup and view all the answers
Match the calculations to their corresponding conditions:
Match the calculations to their corresponding conditions:
Signup and view all the answers
Which of the following statements about dew point calculations is FALSE?
Which of the following statements about dew point calculations is FALSE?
Signup and view all the answers
The vapor pressures of the pure species in a binary system always increase with temperature.
The vapor pressures of the pure species in a binary system always increase with temperature.
Signup and view all the answers
What is the definition of equilibrium in a thermodynamic context?
What is the definition of equilibrium in a thermodynamic context?
Signup and view all the answers
In the bubble point calculation, what do you calculate using the given liquid phase mole fractions and temperature?
In the bubble point calculation, what do you calculate using the given liquid phase mole fractions and temperature?
Signup and view all the answers
The Phase Rule states that all variables in a system can be independently fixed.
The Phase Rule states that all variables in a system can be independently fixed.
Signup and view all the answers
What is the formula to calculate the degrees of freedom (F) according to the Phase Rule?
What is the formula to calculate the degrees of freedom (F) according to the Phase Rule?
Signup and view all the answers
According to Duhem's theorem, a closed system is completely determined when any two independent ____________ are fixed.
According to Duhem's theorem, a closed system is completely determined when any two independent ____________ are fixed.
Signup and view all the answers
Match the following terms with their explanations:
Match the following terms with their explanations:
Signup and view all the answers
What is the maximum number of variables that must be specified to fix the intensive state of a system with two chemical species?
What is the maximum number of variables that must be specified to fix the intensive state of a system with two chemical species?
Signup and view all the answers
The total number of equations required for a completely determined state is given by πN.
The total number of equations required for a completely determined state is given by πN.
Signup and view all the answers
State the two independent variable types mentioned in Duhem's theorem.
State the two independent variable types mentioned in Duhem's theorem.
Signup and view all the answers
What is the saturated pressure P1 at 75°C according to the Antoine equation?
What is the saturated pressure P1 at 75°C according to the Antoine equation?
Signup and view all the answers
At a fixed pressure of 70 kPa, T1sat is greater than T2sat.
At a fixed pressure of 70 kPa, T1sat is greater than T2sat.
Signup and view all the answers
What equation is used to calculate the temperature T for species 1?
What equation is used to calculate the temperature T for species 1?
Signup and view all the answers
At a pressure of 70 kPa, the value of T2sat is _____ °C.
At a pressure of 70 kPa, the value of T2sat is _____ °C.
Signup and view all the answers
Match the following variables to their corresponding values:
Match the following variables to their corresponding values:
Signup and view all the answers
What is the relationship between x1 and y1 according to Raoult's law?
What is the relationship between x1 and y1 according to Raoult's law?
Signup and view all the answers
The value of α can be calculated using the difference between lnP2sat and lnP1sat.
The value of α can be calculated using the difference between lnP2sat and lnP1sat.
Signup and view all the answers
What is the value of P at x1 = 0.6, according to the provided calculation?
What is the value of P at x1 = 0.6, according to the provided calculation?
Signup and view all the answers
Study Notes
Chemical Engineering Thermodynamics
- Vapor/liquid equilibrium is a static condition where macroscopic properties of a system remain unchanged over time.
- Equilibrium occurs when the T, P, and composition of a system reach a final fixed value.
- Equilibrium states are determined by the Phase Rule and Duhem's Theory.
Phase Rule & Duhem's Theory
- Equilibrium states depend on the Phase Rule and Duhem's Theory.
- The Phase Rule defines the number of variables that can be independently fixed in a system at equilibrium.
- Duhem's Theory applies to the extensive state of a closed system at equilibrium.
- A completely determined system has both extensive and intensive states fixed.
- Variables in a completely determined system = 2 + (N - 1)π + π = 2 + Nπ variables
- Number of equations = (π - 1)(N) + N = πN equations
- Difference between variable count and equation count = 2 + Nπ - Nπ = 2
Vapor/Liquid Equilibrium: Qualitative Behavior
- For two chemical species (N = 2), the phase rule is F = 4 – π.
- With one phase (π = 1), the intensive state is defined by fixing three variables (P, T, and one mole fraction).
- All equilibrium states can be represented in a three-dimensional P-T-composition space.
- Under the surface of a P-T-y diagram are saturated vapor states.
- Above the surface of a P-T-x diagram are saturated liquid states.
- Droplets of liquid appear at the bubble point (FG).
- The last drop of liquid disappears at the dew point (W).
- The tie line (LV) connects vapor and liquid compositions in equilibrium.
Quantitative Descriptions of VLE
- Simple models for VLE determine T, P, and composition.
- Raoult's Law assumptions: vapor phase is ideal gas and liquid phase is ideal solution.
- Raoult's law is applicable at low to moderate pressures and when species are chemically similar.
- Henry's Law assumptions: very low pressure where the gas is assumed as an ideal gas and liquid phase is a dilute solution.
Excess Gibbs Energy And Activity Coefficients
- Partial Gibbs energy for a solution is G₁ = (T) + RT ln ƒ₁.
- From the Lewis-Randall rule for an ideal solution, ƒᵢᵈ = xᵢ ƒᵢ.
- The difference Gᵢ - Gᵢᵈ = RT ln(yᵢ / xᵢ).
- Gᵢ - Gᵢᵈ is partial excess Gibbs energy and yᵢ is the activity coefficient of species i.
Analogous Expression for Excess Gibbs Energy
- An analogous expression for excess Gibbs energy can be developed for residual Gibbs energy.
- Complex equations relate changes in excess Gibbs energy/ residual Gibbs energy to changes in pressure and temperature; these involve intensive phase rule variables and are expressed in terms of mole fractions, vapor pressure, temperatures and pressures.
Phase Equilibrium Criteria
- Vapor and liquid phase fugacities must be equal at equilibrium for the same T and P.
- Raoult's law is an ideal case of VLE, providing vapor-phase ideal gas state and liquid-phase ideal solution.
Dew Point & Bubble Point Calculations
- Dew point: calculate xᵢ given yᵢ, P, and T
- Bubble point: calculate yᵢ given xᵢ, P, and T
- Calculations use Raoult's Law and the Antoine equation.
- Antoine equation: In Psat = A - (B/(T + C))
For Binary Systems
- T is given, solving for bubble point.
- Iteration is required for temperature if x and P are given; use the Antoine equation to calculate Psat for each component..
- To find the correct temperature, iterating using a series of steps is required.
Henry's Law
- Applicable at very low pressures and very dilute solutions in the liquid phase.
- The vapor pressure of a component in a solution is directly proportional to its mole fraction in the liquid phase.
- Henry's Law applies to gases dissolving in liquids, where the constant (H) accounts for the solubility of a gas in a liquid at a particular temperature.
Worked Examples
- Worked examples demonstrate calculating equilibrium compositions (V-phase and L-phase) in different scenarios such as carbonated water (CO2 and H2O) at a certain temperature and pressure, and binary systems like acetonitrile/nitromethane at specific temperatures and pressures.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Test your understanding of vapor/liquid equilibrium and its relation to the Phase Rule and Duhem's Theory. This quiz covers key concepts such as equilibrium states and the variables involved in thermodynamic systems. Perfect for students studying chemical engineering thermodynamics.
