Welcome to the **Single Phase Mass Balance** Course!

I designed this course is for general engineering fields. **Chemical and Process Engineers** will find it very relevant for their study curriculum but even Mechanical or Industrial Engineers will find it very interesting!

By the end of this course **you will learn**:

- The importance of Phases when Solving Mass Balance Problems
- Application of constant densities of Solid and Liquids in Chemical Proceses
- How to model Ideal Gases with the Ideal Gas Law
- Why are Standard Conditions of Temperature and Pressure used in the industry
- How to model Real Gases with the Virial Equation
- How to model Real Gases with the Z-Compressibility Factor Chart
- How to model Real Gas Mixtures with the Kay Rule

By the end of the Course **you will be able to**:

- Solve Mass Balance Problems of many real-life Chemical Processes involving Single-Phase Systems
- Model Ideal Gases vs. Real Gases

The course is structured as follow:

- 6 Sections of
**Theory**and**Applied Examples**(**Video-Based!**) - 22 Mass Balance
**Solved Exercises!** - 3
**Quizes**for Learning Review **Support**on the Discussion Board!

This is a very important Subject in Engineering and is the basis of further courses such as:

- Energy Balance and Thermodynamic
- Heat and Mass Transfer Operations and Unit Operations
- Reactor Engineering and Plant Design

I teach this course for about *$400 per semester*. You will get it as low as **$25 for a LIFETIME!**

Take the course and you will have a **greater advantage **than your classmates to get a better grade on your university courses!

** NOTE**: This is the continuation of my other course

**MB1: Introduction to Mass Balance**. I highly recommend you take first the other course in order to get the best of this course!

The Course Curriculum may be seen below!

### Course Overview

This is an overview of this Course. This course divides in:

- Solid and Liquids
- Gases - Ideal Gas Modeling and Mass Balance Problem solving
- Gases - Real Gases
- Virial Equation
- Z-Compressibility Factor

By the end of the course you should be able to perform more elaborate Mass Balance Problems including different phases (Single-Phase Problems).

### Solids and Liquids

The definition of Phase is explained. Single-Phase problems are those that only have 1 Phase (either liquid, solid or gas)

This Section covers solids and liquids. Since their densities are almost independent of temperature and can be considered constant, we pay special attention on this concept.

Solids and Liquids are very common phases in the industry!

An example regarding the density of a liquid

Another example reggarding densities!

The density of a liquid and how it is useful for other tasks

How to estimate densities of mixtures or other substances

Using the different type of deffinitions of density: Bulk and Absolute Densities.

Density of a Slurry, a mixture of a solid and liquid. Be aware of the correction in the Video

Density of a Slurry, a mixture of a solid and liquid. Be aware of the correction in the Video

### Ideal Gases and Mass Balances

A brief introduction to Gases, its importance in engineering and why it is harder to model

We present the Ideal Gas Model which is very important. You probably have already worked with it...

The typical limitations of the Ideal Gas. High pressures and low temperatures... the more near the molecules, the more interaciton they have and therefore, more non-ideal they became

Why we model with Ideal Gas. We explain the application to Mass Balance Solving

An applied example of the Ideal Gas Law

Standard Conditions are conditions for a Standard Use. Typical values of T, P and V varies dependeing o n the industry or institution.

SCMH is a "standardized" or "normalized" measurement of gases flowing in pipes. They give a reference value and comparable to other streams if they where on the same conditions

Examples of the use and application of the Standard Conditions of Temperature an Pressure AKA STP

Another example on how we can apply the SCMH concept

Last example of STP

Mixture of substance in gas phase are very common. Even though they are separate substances, they are still in one phase (gas phase). We apply the partial pressures and Ideal Gas in order to model such mixtures.

We finally apply the concepts seen in this sections to a Mass Balance. Get the idea of how we could model data. We get T, P and form there we get moles!

Using the Ideal Gas Law to calculate Volume and moles

The ideal gas constant "R" may vary depending on the values of units oyu choose. Here is a fastway to convert them

Using the ideal gas law to get the density of a flowign gas

We compare specific gravities using the ideal gas law

Very creative problem on how a company steals gas from another company.

Using the ideal gas law to a combusiton process

Hydrazine may be used as a propellant due to its expansion reaction (increase of moles and volume)

The problem is based on the vaporization of Acetone due to a stream of Nitrogen

Ideal Gas Law Application to Chlorine Tank

We use two concepts known by now: Equilibrium and Ideal Gas Law

We use two concepts known by now: Equilibrium and Ideal Gas Law

Once again, multiple equilibrium with ideal gases!

### Real Gases (Theory)

Definition of a Real gas. That gas that can not be modeled with ideal gas law

The Critical Point is a sepcial point. In this point the liquid and the gas are no longer separable. The gas has superfluid properties and the liquid has also superfluid properties

Reduced conditions are a type of "standardization" in order to compare substances. The reference is the critical point conditions such as Temperature and Pressure (critical)

Its very important to remark the difference between gas and vapor. Esentially is the critical point that makes the difference.

### Mass Balance with Real Gases

A common model for a Real Gas. This uses "virial" terms. It is good for pressure or temperature modeling. Its difficult for volume model due to the amount of volume terms.

An example of how to apply the Truncated Virial Equation. Remember that by theory, the virial equation is infinite. You should choose the number of terms you are going to work with.

Other Equations may be used. The Scope of this Course is only to:

- Virial Equation
- Z compressbility Factor

You may study other equations in typical courses such as Thermodynamics

This video introduces the concept of compressibility factor "Z". This is essentially just a direct correction to the ideal gas law. This is easy and very powerful!

A fast example of the compressibility factor "Z"

For some diatomic molceules, it is better to apply a correctino factor named by Newton. This should be done since they are some times very important and will correct your predictions

We present the compressibility chart for each substance. It show "Z" value for every substance, T and P

If we get ONE compressibility chart that applies to every single substance, would be awesome wouldnt it?

We could use the law of corresponding states which help us get ONE chart of Z values vs. T and P!

A compressibility factor "Z" example

How do we model Real Gases in mixtures? We must use the Kay Rule which is easy to understand but it takes a little bit of time to calculate...

The Kay Rule applied to a mixture of Gases!

Modeling Volume using the Truncated Virial Equation

Calculating the "Z" Factor

We apply the Z compressbility factor to Oxygen and then Use Newton's Correction.

As with previeous example, we apply Z factor to Nitrogen Purge system. Remember that Nitrogen is a diatomic molecule, therefore we apply Newton's Corrections

We "evaporate" the Liquid Nitrogen. Due to conditions, we can't model this as an ideal gas. We use Z-Compressibility Factor

We apply the Kay Rule to a mixture of gases. Be sure to use correctly the Kay Rule!

We compress a mixture of gases from State 1 to State 2. We model the mixture with the Kay Rule

Finally we apply the real gas concepts to a production process!

Application of the Kay Rule to a mixture of gases flowing in a pipe. We use many concpets here!

### Course Conlusion

Course Conclusion and some Final notes!

Please leave a Review guys! It helps a lot to the commnity and also helps me know what should I improve!

Hey there! Thank you very much for joining the course...

I kindly ask you to leave a review... It helps me to know what should I improve and helps other to know if the course is worth the time and money!

Thank you in advance and Good luck with your studies!