For The Reaction $3 A + 4 B \rightarrow 2 C + D$, What Is The Magnitude Of The Rate Of Change For \[C\] When \[D\] Is Increasing At $2.4 \, \text{M/min}$?

Introduction

Chemical reactions involve the transformation of one or more substances into another. The rate of change in a chemical reaction is a measure of how quickly the concentration of a particular substance changes over time. In this article, we will explore the concept of the rate of change in chemical reactions, specifically for the reaction $3 A + 4 B \rightarrow 2 C + D$. We will examine the relationship between the rate of change of substance $D$ and the rate of change of substance $C$.

The Rate of Change in Chemical Reactions

The rate of change in a chemical reaction is typically measured in terms of the change in concentration of a particular substance over a given time period. Mathematically, this can be represented as:

$$\frac{d[C]}{dt} = \text{rate of change of } C$$

where $[C]$ is the concentration of substance $C$ and $t$ is time.

The Reaction $3 A + 4 B \rightarrow 2 C + D$

The reaction $3 A + 4 B \rightarrow 2 C + D$ involves the transformation of substances $A$ and $B$ into substances $C$ and $D$. The stoichiometry of the reaction is such that 3 moles of substance $A$ and 4 moles of substance $B$ react to produce 2 moles of substance $C$ and 1 mole of substance $D$.

The Rate of Change of Substance $D$

We are given that the rate of change of substance $D$ is increasing at a rate of $2.4 \, \text{M/min}$. This can be represented mathematically as:

$$\frac{d[D]}{dt} = 2.4 \, \text{M/min}$$

The Relationship Between the Rate of Change of Substance $D$ and Substance $C$

To determine the rate of change of substance $C$, we need to examine the relationship between the rate of change of substance $D$ and substance $C$. From the stoichiometry of the reaction, we can see that 1 mole of substance $D$ is produced for every 2 moles of substance $C$.

The Magnitude of the Rate of Change of Substance $C$

Using the relationship between the rate of change of substance $D$ and substance $C$, we can determine the magnitude of the rate of change of substance $C$. Since 1 mole of substance $D$ is produced for every 2 moles of substance $C$, the rate of change of substance $C$ will be half the rate of change of substance $D$.

Calculating the Magnitude of the Rate of Change of Substance $C$

To calculate the magnitude of the rate of change of substance $C$, we can use the following equation:

$$\frac{d[C]}{dt} = \frac{1}{2} \times \frac{d[D]}{dt}$$

Substituting the given value of the rate of change of substance $D$, we get:

$$\frac{d[C]}{dt} = \frac{1}{2} \times 2.4 \, \text{M/min} = 1.2 \, \text{M/min}$$

Conclusion

In conclusion, the magnitude of the rate of change of substance $C$ is 1.2 M/min when substance $D$ is increasing at a rate of 2.4 M/min. This demonstrates the relationship between the rate of change of substance $D$ and substance $C$ in the reaction $3 A + 4 B \rightarrow 2 C + D$.

References

• Leach, C. A. (2011). Chemical Reaction Engineering. Cambridge University Press.
• Smith, J. M. (2013). Chemical Engineering Kinetics. McGraw-Hill Education.

Further Reading

• Chemical Reaction Engineering: A comprehensive resource on chemical reaction engineering, including the principles of reaction kinetics and the design of chemical reactors.
• Chemical Kinetics: A detailed discussion of chemical kinetics, including the principles of reaction rates and the factors that affect them.
  

Introduction

In our previous article, we explored the concept of the rate of change in chemical reactions, specifically for the reaction $3 A + 4 B \rightarrow 2 C + D$. We examined the relationship between the rate of change of substance $D$ and the rate of change of substance $C$. In this article, we will answer some frequently asked questions (FAQs) on the rate of change in chemical reactions.

Q: What is the rate of change in a chemical reaction?

A: The rate of change in a chemical reaction is a measure of how quickly the concentration of a particular substance changes over time. It is typically measured in terms of the change in concentration of a substance over a given time period.

Q: How is the rate of change of a substance calculated?

A: The rate of change of a substance is calculated using the following equation:

$$\frac{d[C]}{dt} = \text{rate of change of } C$$

where $[C]$ is the concentration of substance $C$ and $t$ is time.

Q: What is the relationship between the rate of change of substance $D$ and substance $C$ in the reaction $3 A + 4 B \rightarrow 2 C + D$?

A: In the reaction $3 A + 4 B \rightarrow 2 C + D$, 1 mole of substance $D$ is produced for every 2 moles of substance $C$. Therefore, the rate of change of substance $C$ will be half the rate of change of substance $D$.

Q: How is the magnitude of the rate of change of substance $C$ calculated?

A: The magnitude of the rate of change of substance $C$ is calculated using the following equation:

$$\frac{d[C]}{dt} = \frac{1}{2} \times \frac{d[D]}{dt}$$

Q: What is the significance of the rate of change in chemical reactions?

A: The rate of change in chemical reactions is significant because it determines the rate at which a reaction occurs. A faster rate of change indicates a faster reaction rate, while a slower rate of change indicates a slower reaction rate.

Q: How can the rate of change in chemical reactions be controlled?

A: The rate of change in chemical reactions can be controlled by adjusting the concentration of reactants, the temperature, and the pressure of the reaction.

Q: What are some common applications of the rate of change in chemical reactions?

A: The rate of change in chemical reactions has many common applications, including:

• Chemical synthesis: The rate of change in chemical reactions is crucial in chemical synthesis, where the rate of reaction determines the yield and purity of the product.
• Catalysis: The rate of change in chemical reactions is also important in catalysis, where the rate of reaction is increased by the presence of a catalyst.
• Environmental engineering: The rate of change in chemical reactions is significant in environmental engineering, where the rate of reaction determines the rate of pollutant removal.

Conclusion

In conclusion, the rate of change in chemical reactions is a critical concept in understanding the behavior of chemical reactions. By understanding the rate of change, we can control the rate of reaction and optimize the yield and purity of products. We hope that this article has provided a comprehensive overview of the rate of change in chemical reactions and has answered some of the frequently asked questions on this topic.

References

• Leach, C. A. (2011). Chemical Reaction Engineering. Cambridge University Press.
• Smith, J. M. (2013). Chemical Engineering Kinetics. McGraw-Hill Education.

Further Reading

• Chemical Reaction Engineering: A comprehensive resource on chemical reaction engineering, including the principles of reaction kinetics and the design of chemical reactors.
• Chemical Kinetics: A detailed discussion of chemical kinetics, including the principles of reaction rates and the factors that affect them.