P4.41 The lactic acid byproduct recovered from cheese plants can be used to make a variety of chemicals. For example, it may be hydrogenated to pro- duce 1,2-propanediol, which is in turn used as a polymer precursor and as a food additive: CH,CHOHCOOH + 2H, 2 CH,CHOHCH,OH + H,O The process feed is a vapor stream containg 1:3:2 lactic acid:H,:inert (mole ratios), at a total pressure of 5 atm and a flow rate of 300 mol/h. The reaction is reversible, with an equilibrium constant K, = 3.2 atm at the reactor temperature. What is the fractional conversion of the lim- iting reactant at equilibrium, and the reactor outlet composition? Will increasing the inert concentration in the feed increase or decrease the equilibrium fractional conversion? First give your answer by using qual- itative reasoning, then calculate the conversion at a higher inert concen- tration and see if your reasoning was right. Would changing the reactor pressure change the conversion? Prove your results by calculating the effect of an increase in pressure by 2 atm,

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**Title: Conversion of Lactic Acid Byproduct from Cheese Production**

**Introduction:**
The lactic acid byproduct recovered from cheese plants can be used to produce various chemicals. One notable application is its hydrogenation to create 1,2-propanediol, which serves as a polymer precursor and a food additive.

**Chemical Reaction:**
\[ \text{CH}_3\text{CHOHCOOH} + 2\text{H}_2 \rightleftharpoons \text{CH}_3\text{CHOHCH}_2\text{OH} + \text{H}_2\text{O} \]

**Process Feed Details:**
- The vapor stream feed has a molar ratio of 1:3:2 for lactic acid:H₂:inert gases.
- It is maintained at a total pressure of 5 atm.
- The flow rate is 300 mol/h.

**Reaction Characteristics:**
- This reversible reaction is governed by an equilibrium constant (Kₐ) of 3.2 atm⁻¹ at the given reactor temperature.

**Problem Statement:**
1. Determine the fractional conversion of the limiting reactant at equilibrium.
2. Calculate the composition of the reactor outlet.
3. Analyze whether increasing the concentration of the inert gas in the feed affects the equilibrium fractional conversion.
4. Provide an initial qualitative assessment, followed by a calculation to confirm the conversion at increased inert concentrations.
5. Investigate how changing the reactor pressure influences conversion and validate your findings by assessing the effect of a 2 atm increase in pressure.

**Conclusion:**
This activity allows students to explore chemical equilibria and the impact of variables such as inert concentrations and pressure on reaction conversion, providing an enriching understanding of chemical process optimization.
Transcribed Image Text:**Title: Conversion of Lactic Acid Byproduct from Cheese Production** **Introduction:** The lactic acid byproduct recovered from cheese plants can be used to produce various chemicals. One notable application is its hydrogenation to create 1,2-propanediol, which serves as a polymer precursor and a food additive. **Chemical Reaction:** \[ \text{CH}_3\text{CHOHCOOH} + 2\text{H}_2 \rightleftharpoons \text{CH}_3\text{CHOHCH}_2\text{OH} + \text{H}_2\text{O} \] **Process Feed Details:** - The vapor stream feed has a molar ratio of 1:3:2 for lactic acid:H₂:inert gases. - It is maintained at a total pressure of 5 atm. - The flow rate is 300 mol/h. **Reaction Characteristics:** - This reversible reaction is governed by an equilibrium constant (Kₐ) of 3.2 atm⁻¹ at the given reactor temperature. **Problem Statement:** 1. Determine the fractional conversion of the limiting reactant at equilibrium. 2. Calculate the composition of the reactor outlet. 3. Analyze whether increasing the concentration of the inert gas in the feed affects the equilibrium fractional conversion. 4. Provide an initial qualitative assessment, followed by a calculation to confirm the conversion at increased inert concentrations. 5. Investigate how changing the reactor pressure influences conversion and validate your findings by assessing the effect of a 2 atm increase in pressure. **Conclusion:** This activity allows students to explore chemical equilibria and the impact of variables such as inert concentrations and pressure on reaction conversion, providing an enriching understanding of chemical process optimization.
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