What Would Happen To The Rate Of A Reaction With The Rate Law $\text{rate} = K[ \text{NO} ]^2[ \text{H}_2 ] If The Concentration Of NO Were Halved?A. The Rate Would Also Be Halved. B. The Rate Would Be One-fourth. C. The Rate Would Be Four

Introduction

In chemistry, the rate law is a mathematical expression that describes the relationship between the rate of a reaction and the concentrations of the reactants. It is a fundamental concept in chemical kinetics, and understanding the rate law is crucial in predicting the outcome of a reaction. In this article, we will explore the implications of the rate law on the rate of a reaction, specifically the rate law $\text{rate} = k[ \text{NO} ]^2[ \text{H}_2 ]$.

The Rate Law

The rate law is a mathematical expression that describes the relationship between the rate of a reaction and the concentrations of the reactants. It is typically expressed as:

$$\text{rate} = k[ \text{NO} ]^2[ \text{H}_2 ]$$

where $k$ is the rate constant, and $[ \text{NO} ]$ and $[ \text{H}_2 ]$ are the concentrations of the reactants NO and H$_2$, respectively.

The Effect of Halving the Concentration of NO

Now, let's consider what happens to the rate of the reaction if the concentration of NO is halved. To do this, we need to substitute the new concentration of NO into the rate law.

Let $[ \text{NO} ]_0$ be the original concentration of NO, and $[ \text{NO} ]_1$ be the new concentration of NO after it is halved. Then, we can write:

$$[ \text{NO} ]_1 = \frac{1}{2} [ \text{NO} ]_0$$

Substituting this expression into the rate law, we get:

$$\text{rate} = k \left( \frac{1}{2} [ \text{NO} ]_0 \right)^2 [ \text{H}_2 ]$$

Simplifying this expression, we get:

$$\text{rate} = k \frac{1}{4} [ \text{NO} ]_0^2 [ \text{H}_2 ]$$

Comparing this expression to the original rate law, we can see that the rate of the reaction is reduced by a factor of 4.

Conclusion

In conclusion, if the concentration of NO is halved, the rate of the reaction will also be reduced by a factor of 4. This is because the rate law is a quadratic function of the concentration of NO, and halving the concentration of NO will reduce the rate of the reaction by a factor of 4.

Answer

The correct answer is C. The rate would be four.

Additional Information

• The rate law is a mathematical expression that describes the relationship between the rate of a reaction and the concentrations of the reactants.
• The rate law is typically expressed as $\text{rate} = k[ \text{NO} ]^2[ \text{H}_2 ]$.
• If the concentration of NO is halved, the rate of the reaction will also be reduced by a factor of 4.
• The rate law is a fundamental concept in chemical kinetics, and understanding the rate law is crucial in predicting the outcome of a reaction.

References

• Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.
• Levine, I. N. (2009). Physical chemistry. McGraw-Hill.
• Moore, J. W., & Pearson, R. G. (2012). Kinetics and mechanism: A dynamic approach. John Wiley & Sons.

Chemical Kinetics

Chemical kinetics is the study of the rates of chemical reactions. It is a fundamental concept in chemistry, and understanding chemical kinetics is crucial in predicting the outcome of a reaction.

Rate Law

The rate law is a mathematical expression that describes the relationship between the rate of a reaction and the concentrations of the reactants. It is typically expressed as:

$$\text{rate} = k[ \text{NO} ]^2[ \text{H}_2 ]$$

where $k$ is the rate constant, and $[ \text{NO} ]$ and $[ \text{H}_2 ]$ are the concentrations of the reactants NO and H$_2$, respectively.

Order of Reaction

The order of a reaction is the power to which the concentration of a reactant is raised in the rate law. In the case of the rate law $\text{rate} = k[ \text{NO} ]^2[ \text{H}_2 ]$, the order of the reaction with respect to NO is 2, and the order of the reaction with respect to H$_2$ is 1.

Rate Constant

The rate constant is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants. It is typically denoted by the symbol $k$, and its value depends on the specific reaction and the conditions under which it occurs.

Units of Rate Constant

The units of the rate constant depend on the order of the reaction and the units of the concentrations of the reactants. In the case of the rate law $\text{rate} = k[ \text{NO} ]^2[ \text{H}_2 ]$, the units of the rate constant are typically expressed as:

$$k = \frac{\text{rate}}{[ \text{NO} ]^2 [ \text{H}_2 ]}$$

where the rate is expressed in units of concentration per unit time, and the concentrations of NO and H$_2$ are expressed in units of molarity.

Half-Life

The half-life of a reaction is the time it takes for the concentration of a reactant to decrease by half. It is a useful concept in chemical kinetics, as it provides a way to predict the outcome of a reaction over time.

Half-Life Equation

The half-life equation is a mathematical expression that describes the relationship between the half-life of a reaction and the rate constant. It is typically expressed as:

$$t_{1/2} = \frac{\ln 2}{k}$$

where $t_{1/2}$ is the half-life of the reaction, and $k$ is the rate constant.

Half-Life Units

The units of the half-life depend on the units of the rate constant. In the case of the rate law $\text{rate} = k[ \text{NO} ]^2[ \text{H}_2 ]$, the units of the half-life are typically expressed as:

$$t_{1/2} = \frac{\ln 2}{k} = \frac{\ln 2}{\frac{\text{rate}}{[ \text{NO} ]^2 [ \text{H}_2 ]}}$$

where the rate is expressed in units of concentration per unit time, and the concentrations of NO and H$_2$ are expressed in units of molarity.

Conclusion

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Q: What is the rate law, and why is it important in chemical kinetics?

A: The rate law is a mathematical expression that describes the relationship between the rate of a reaction and the concentrations of the reactants. It is a fundamental concept in chemical kinetics, and understanding the rate law is crucial in predicting the outcome of a reaction.

Q: What is the order of a reaction, and how is it related to the rate law?

A: The order of a reaction is the power to which the concentration of a reactant is raised in the rate law. In the case of the rate law $\text{rate} = k[ \text{NO} ]^2[ \text{H}_2 ]$, the order of the reaction with respect to NO is 2, and the order of the reaction with respect to H$_2$ is 1.

Q: What is the rate constant, and how is it related to the rate law?

A: The rate constant is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants. It is typically denoted by the symbol $k$, and its value depends on the specific reaction and the conditions under which it occurs.

Q: What is the half-life of a reaction, and how is it related to the rate constant?

A: The half-life of a reaction is the time it takes for the concentration of a reactant to decrease by half. It is a useful concept in chemical kinetics, as it provides a way to predict the outcome of a reaction over time. The half-life equation is a mathematical expression that describes the relationship between the half-life of a reaction and the rate constant.

Q: How do I determine the rate constant of a reaction?

A: The rate constant of a reaction can be determined experimentally by measuring the rate of the reaction at different concentrations of the reactants. The rate constant is then calculated using the rate law and the measured rates.

Q: What are some common mistakes to avoid when working with the rate law?

A: Some common mistakes to avoid when working with the rate law include:

• Failing to account for the order of the reaction
• Failing to account for the rate constant
• Failing to account for the concentrations of the reactants
• Failing to use the correct units for the rate constant and the concentrations of the reactants

Q: How do I apply the rate law to real-world problems?

A: The rate law can be applied to real-world problems in a variety of ways, including:

• Predicting the outcome of a reaction
• Optimizing the conditions for a reaction
• Designing experiments to measure the rate of a reaction
• Interpreting data from experiments to measure the rate of a reaction

Q: What are some common applications of the rate law?

A: Some common applications of the rate law include:

• Predicting the rate of a chemical reaction
• Optimizing the conditions for a chemical reaction
• Designing experiments to measure the rate of a chemical reaction
• Interpreting data from experiments to measure the rate of a chemical reaction

Q: What are some common misconceptions about the rate law?

A: Some common misconceptions about the rate law include:

• Believing that the rate law is only applicable to simple reactions
• Believing that the rate law is only applicable to reactions with a single reactant
• Believing that the rate law is only applicable to reactions with a single product
• Believing that the rate law is only applicable to reactions with a constant rate constant

Conclusion

In conclusion, the rate law is a fundamental concept in chemical kinetics that describes the relationship between the rate of a reaction and the concentrations of the reactants. Understanding the rate law is crucial in predicting the outcome of a reaction, and it has a wide range of applications in real-world problems. By avoiding common mistakes and misconceptions, and by applying the rate law to real-world problems, you can gain a deeper understanding of the rate law and its implications.