A gas stream containing acetone in air flows from a solvent recovery unit at a rate of 142 L/s at 150°C and 1.3 atm. The stream flows into a condenser which condenses most of the acetone, and the liquid and gas outlet streams are in equilibrium at -18°C and 5.0 atm. Shaft work is delivered to the system at a rate of 25.2 kW to achieve the compression from 1.3 atm to 5.0 atm. To determine the condenser feed stream composition, a 3.00-liter sample of the gas is taken and cooled to a temperature at which essentially all the acetone in the sample is recovered as a liquid. The liquid is poured into an empty flask with a mass of 4.017g. The flask containing the liquid acetone is weighed and found to have a mass of 4.973 g. Q(KW) W-25.2 kW 142 L/s, 150°C, 1.3 atm acetone(v), air CONDENSER 3-liter sample Condense and weigh acetone Gas at -18°C, 5 atm acetone(v), air Acetone(1) at -18°C, 5 atm (a) Carry out a degree-of-freedom analysis to show that enough information is available to determine the compositions of all streams and the required heat transfer rate. (b) Write out a complete set of equations for the molar flow rates of all streams, the mole fractions of acetone in the feed and product gas streams, and the rate (kW) at which heat must be removed in the condenser. Do no calculations.

Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
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### Educational Resource: Gas Stream Condensation Process

#### Overview:

A gas stream containing acetone in air flows from a solvent recovery unit at a rate of 142 L/s at 150°C and 1.3 atm. The stream is directed into a condenser where almost all the acetone condenses out, while the liquid and gas outlet streams reach equilibrium at -18°C and 5.0 atm. Shaft work is applied to the system at a rate of 25.2 kW to manage the compression from 1.3 atm to 5.0 atm. 

To determine the composition of the feed stream, a 3-liter sample of gas is observed, and the temperature is adjusted to recover the acetone as a liquid. The liquid is poured into a flask weighing 4.017 g, and the combined weight of the flask and acetone is found to be 4.973 g.

#### Diagram Explanation:

![Gas Stream Condensation Process Diagram]

- **Left Section**: 
  - **Input Stream**: 
    - **Flow Rate**: 142 L/s
    - **Conditions**: 150°C, 1.3 atm
    - **Composition**: Acetone (\(x_{acetone}^v\)), Air
  - **Shaft Work Delivered (\(\dot{W_s}\))**: 25.2 kW

- **Center Section (Condenser)**:
  - Condensation occurs here, separating the gas and liquid streams.

- **Right Section**:
  - **Gas Outlet**: 
    - **Conditions**: -18°C, 5 atm
    - **Composition**: Acetone (\(y_{acetone}^v\)), Air
  - **Liquid Outlet**: 
    - **Conditions**: -18°C, 5 atm
    - **Composition**: Acetone (\(x_{acetone}^l\))

#### Tasks and Questions:

1. **Degree-of-Freedom Analysis**:
   - Analyze the system to confirm enough data is available to establish the compositions of all streams and calculate the required heat transfer rate.

2. **Equation Writing**:
   - Formulate a complete set of equations for:
     - Molar flow rates of all streams.
     - Molar fractions of acetone in the feed and product gas streams.
     - Heat rate (\(kW\)) that must
Transcribed Image Text:### Educational Resource: Gas Stream Condensation Process #### Overview: A gas stream containing acetone in air flows from a solvent recovery unit at a rate of 142 L/s at 150°C and 1.3 atm. The stream is directed into a condenser where almost all the acetone condenses out, while the liquid and gas outlet streams reach equilibrium at -18°C and 5.0 atm. Shaft work is applied to the system at a rate of 25.2 kW to manage the compression from 1.3 atm to 5.0 atm. To determine the composition of the feed stream, a 3-liter sample of gas is observed, and the temperature is adjusted to recover the acetone as a liquid. The liquid is poured into a flask weighing 4.017 g, and the combined weight of the flask and acetone is found to be 4.973 g. #### Diagram Explanation: ![Gas Stream Condensation Process Diagram] - **Left Section**: - **Input Stream**: - **Flow Rate**: 142 L/s - **Conditions**: 150°C, 1.3 atm - **Composition**: Acetone (\(x_{acetone}^v\)), Air - **Shaft Work Delivered (\(\dot{W_s}\))**: 25.2 kW - **Center Section (Condenser)**: - Condensation occurs here, separating the gas and liquid streams. - **Right Section**: - **Gas Outlet**: - **Conditions**: -18°C, 5 atm - **Composition**: Acetone (\(y_{acetone}^v\)), Air - **Liquid Outlet**: - **Conditions**: -18°C, 5 atm - **Composition**: Acetone (\(x_{acetone}^l\)) #### Tasks and Questions: 1. **Degree-of-Freedom Analysis**: - Analyze the system to confirm enough data is available to establish the compositions of all streams and calculate the required heat transfer rate. 2. **Equation Writing**: - Formulate a complete set of equations for: - Molar flow rates of all streams. - Molar fractions of acetone in the feed and product gas streams. - Heat rate (\(kW\)) that must
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