Iteration Steps for Bubble Temperature

This page delves deeper into the iteration steps for bubble temperature calculations. It provides a step-by-step guide to solve the non-linear problem presented in the previous page.

The iteration process is clearly outlined:

1. Assume an arbitrary temperature value
2. Calculate vapor pressures using Antoine's equation
3. Determine compositions using the calculated vapor pressures
4. Recalculate temperature using the new compositions
5. Compare assumed and calculated temperatures
6. Repeat if necessary

Example: For an initial assumed temperature of 75°C, the page demonstrates the calculations for vapor pressures, compositions, and the new temperature value.

Highlight: The iteration process continues until the assumed and calculated temperatures converge within an acceptable tolerance.

The page concludes with the final results after multiple iterations, providing the bubble point temperature, vapor pressures, and compositions for the acetonitrile-nitromethane mixture.

Vocabulary: Convergence - The point at which the assumed and calculated values become sufficiently close, indicating a solution has been found.

This detailed explanation of the iteration process is crucial for understanding how to perform bubble point temperature calculations in practice.

Creating a T-x-y Diagram

This page focuses on how to make a T-x-y diagram for the acetonitrile-nitromethane mixture at a constant pressure of 70 kPa. It provides a step-by-step approach to generate the necessary data points for plotting the diagram.

The process involves:

1. Calculating saturation temperatures for pure components
2. Determining liquid and vapor compositions at various temperatures
3. Using Antoine's equation to find vapor pressures
4. Applying equilibrium relationships to find compositions

Definition: A T-x-y diagram is a graphical representation of the relationship between temperature and composition for both liquid $x$ and vapor $y$ phases in a binary mixture at constant pressure.

Highlight: The T-x-y diagram spans from the saturation temperature of the more volatile component to that of the less volatile component.

The page provides specific equations and calculations for finding key points on the diagram, such as the compositions at the pure component saturation temperatures.

Example: For acetonitrile at 70 kPa, the saturation temperature is calculated as 70.0611°C, and the corresponding liquid composition $x₁$ is determined to be 0.8746.

This detailed guide on how to make a T-x-y diagram in Excel or other plotting software is essential for visualizing phase behavior in binary mixtures.

Dew Temperature Calculations

This page introduces dew point temperature calculations for the acetonitrile-nitromethane mixture. It presents an example problem to determine the temperature $T$ and liquid composition $x₁$ at a given pressure and vapor composition.

The dew point calculation process is explained, including:

1. The governing equations for vapor-liquid equilibrium
2. The relationship between vapor and liquid compositions
3. The iterative approach needed to solve for temperature

Definition: Dew point temperature is the temperature at which the first droplet of liquid forms when cooling a vapor mixture at constant pressure.

Highlight: The dew point calculation uses a similar iterative approach to the bubble point calculation, but with different initial assumptions and equations.

The page outlines a sample iteration procedure, starting with an assumed temperature of 75°C and demonstrating the calculations for the relative volatility, vapor pressures, and temperature correction.

Vocabulary: Relative volatility - A measure of the difference in volatility between two components in a mixture, calculated from the ratio of their vapor pressures.

This explanation of dew point temperature calculations complements the earlier discussion on bubble point temperatures, providing a comprehensive view of phase equilibrium calculations for binary mixtures.

Final Results and Verification

This page concludes the calculation examples by presenting the final results of the dew point temperature iteration for the acetonitrile-nitromethane mixture. It shows the converged temperature and the corresponding vapor pressures and liquid compositions.

The final results are:

• Dew point temperature: 79.735°C
• Vapor pressures: P₁ᢰᵃᵗ = 95.0178 kPa, P₂ᢰᵃᵗ = 49.9392 kPa
• Liquid compositions: x₁ = 0.4392, x₂ = 0.5607

Highlight: The final temperature is significantly different from the initially assumed value, demonstrating the importance of the iterative process in these calculations.

The page also includes the final forms of Antoine's equation used for each component, emphasizing the temperature dependence of vapor pressure.

Example: For acetonitrile, ln$P₁ᢰᵃᵗ$ = 14.8950 - 3413.10 / $79.735 + 250.523$

This conclusion ties together the concepts of bubble point and dew point calculation, providing a complete picture of the vapor-liquid equilibrium calculations for the binary mixture. The results can be used in conjunction with the T-x-y diagram to fully characterize the phase behavior of the system.

Bubble Temperature Calculations

This page introduces the concept of bubble temperature calculation for an ideal binary mixture of acetonitrile and nitromethane. It presents an example problem to determine the vapor composition $y₁$ and temperature $T$ at a given pressure and liquid composition.

The page outlines the necessary equations and steps for solving the problem, including the use of Antoine's equation for vapor pressure calculations. It emphasizes the need for an iterative approach due to the non-linear nature of the problem.

Definition: Bubble point temperature is the temperature at which the first bubble of vapor forms when heating a liquid mixture at a constant pressure.

Highlight: The calculation process involves assuming an initial temperature and iterating until the assumed and calculated temperatures converge.

Vocabulary: Antoine's equation - A mathematical formula used to relate vapor pressure and temperature for pure components.

The page provides a detailed breakdown of the equations used, including those for calculating vapor pressures, composition relationships, and temperature corrections. It sets the foundation for understanding bubble point and dew point calculation methods in binary systems.