Question

Nitriles are converted readily to amides with hydrogen peroxide in dilute sodium hydroxide solution. The reaction is $$ \mathrm{RC} \equiv \mathrm{N}+2 \mathrm{H}_{2} \mathrm{O}_{2} \stackrel{\mathrm{OH}^{\ominus}}{\longrightarrow} \mathrm{RCONH}_{2}+\mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} $$ The rate equation is $$ v=k\left[\mathrm{H}_{2} \mathrm{O}_{2}\right][\stackrel{\ominus}{\mathrm{O}} \mathrm{H}][\mathrm{R} \mathrm{C} \equiv \mathrm{N}] $$

Short answer

The reaction order is 3.

Step-by-step solution

Understanding the Reaction

We're given the conversion of nitriles to amides in the presence of hydrogen peroxide and dilute sodium hydroxide. The chemical formula of the reaction involves the transformation of a nitrile (RC≡N) with the aid of \[2 \text{H}_2\text{O}_2\text{ and } \text{OH}^- \] to eventually produce an amide (RCONH2), along with oxygen and water as by-products.

Identifying Reactants and Products

The reactants for the reaction are \[\text{RC} \equiv \text{N}, \text{H}_2 \text{O}_2, \text{ and } \text{OH}^- \]. The primary product formed is an amide (RCONH2), along with O2 and H2O as by-products.

Analyzing the Rate Equation

The given rate equation is\[v = k\left[\text{H}_2 \text{O}_2\right]\left[\stackrel{\ominus}{\text{O}}\text{H}\right]\left[\text{R} \text{C} \equiv \text{N}\right] \]. This indicates that the reaction rate depends linearly on the concentration of each reactant, meaning it's first order regarding \[\text{H}_2 \text{O}_2, \text{OH}^-, \] and \[\text{RC} \equiv \text{N} \].

Determining Reaction Order

The combined order of the reaction is calculated by summing the powers of the concentrations in the rate equation. Since each reactant appears to the power of one, the overall reaction order is first order with respect to each reactant, providing a total reaction order of three.

Key concepts

Reaction Kinetics

Reaction kinetics is the study of how fast chemical reactions occur and the factors that affect them. In the nitrile conversion to amides, reaction kinetics examines how quickly the nitrile (RC≡N) transforms into an amide (RCONH₂) through the interaction with hydrogen peroxide (H₂O₂) and hydroxide ions (OH⁻).
Understanding the reaction rate is crucial because it influences how efficiently the products are formed. The reaction speed can depend on several factors, such as temperature, concentration of reactants, and presence of catalysts or inhibitors.

• Temperature: Typically, increasing the temperature speeds up the reaction.
• Concentration of Reactants: Higher concentrations of reactants usually increase the reaction rate.
• Catalysts: Substances that increase the reaction rate without being consumed in the process.

The study of reaction kinetics helps in designing chemical processes that are both efficient and cost-effective, especially important in industrial applications.

Rate Equation

The rate equation provides a mathematical expression that relates the rate of a chemical reaction to the concentration of its reactants. For the conversion of nitriles to amides, the rate equation is given as:
\[ v = k \left[ \text{H}_2 \text{O}_2 \right] \left[ \stackrel{\ominus}{\text{O}} \text{H} \right] \left[ \text{RC} \equiv \text{N} \right] \]
This equation implies that the reaction rate \( v \) is proportional to the concentrations of hydrogen peroxide, hydroxide ions, and nitriles. The constant \( k \) is the rate constant, which is specific to the particular reaction under given conditions like temperature and pressure.

The rate equation is essential because it allows chemists to predict how changes in concentrations of reactants affect the reaction speed, aiding in optimization and control of chemical processes.

Reaction Order

The reaction order provides insight into the relationship between the concentration of reactants and the rate of reaction. In this particular nitrile conversion, each reactant ( H₂O₂, OH⁻, and RC≡N) affects the rate of reaction proportionally to its concentration, indicating a first order reaction for each reactant.

The overall reaction order is the sum of these individual orders. Since all reactants have an order of 1, the total reaction order is:

• First order with respect to H₂O₂
• First order with respect to OH⁻
• First order with respect to RC≡N

Summing these gives us an overall reaction order of three.
The significance of knowing the reaction order is paramount for understanding how different concentrations affect the speed at which the reaction proceeds, which is useful for reaction scaling and industrial application.

Organic Chemistry Transformation

Organic chemistry transformation involves changing one organic compound into another, usually more complex molecule. In the case of nitrile conversion, it's the transformation of nitriles (RC≡N) into amides (RCONH₂) using hydrogen peroxide and hydroxide ions.

This transformation is critical in organic chemistry because amides are fundamental components in various chemical products, including pharmaceuticals, plastics, and synthetic fibers. The process adds functionality to the original nitrile compound, enhancing its utility in various chemical synthesis pathways.

Understanding how to foster such transformations efficiently can lead to advancements in developing new materials and drugs, showcasing the practical applications of organic chemistry beyond theoretical knowledge.