Examples of Rate-Determining Steps in Multi-Step Reactions

📚 Quick Study Guide

• ⚛️ The rate-determining step (RDS) is the slowest step in a multi-step reaction. It determines the overall reaction rate.
• ⏱️ The RDS has the highest activation energy ($E_a$) compared to other steps.
• 📈 The rate law for the overall reaction is determined by the RDS. If $A + B \rightarrow C$ is the RDS, the rate law might be $rate = k[A][B]$.
• 🧊 Intermediates are formed in one step and consumed in a subsequent step; they are not part of the overall reaction's stoichiometry or the rate law expression.
• 🌡️ Changing conditions (temperature, catalyst) can sometimes change the RDS.
• Catalysts speed up reactions by lowering the activation energy of the RDS.
• 📉 A reaction mechanism is a series of elementary steps that describe the overall reaction. The RDS is one of these steps.

🧪 Practice Quiz

1. Which statement best describes the rate-determining step (RDS) in a multi-step reaction?
   1. It is the fastest step.
   2. It is the step with the lowest activation energy.
   3. It is the slowest step.
   4. It has no effect on the overall reaction rate.
2. The rate law for a reaction is found to be $rate = k[A]^2[B]$. Which of the following could be the rate-determining step?
   1. $A + B \rightarrow products$
   2. $A + A \rightarrow intermediate$
   3. $A + B + B \rightarrow products$
   4. $B \rightarrow products$
3. What is the role of a catalyst in relation to the rate-determining step?
   1. It speeds up all steps equally.
   2. It increases the activation energy of the RDS.
   3. It lowers the activation energy of the RDS.
   4. It changes the stoichiometry of the overall reaction.
4. Which of the following is NOT true about intermediates in a reaction mechanism?
   1. They appear in the overall balanced equation.
   2. They are formed in one step and consumed in another.
   3. They are not part of the rate law.
   4. They are typically unstable.
5. How does temperature generally affect the rate of the rate-determining step?
   1. Increasing temperature always slows down the RDS.
   2. Increasing temperature generally speeds up the RDS.
   3. Temperature has no effect on the RDS.
   4. Increasing temperature only affects the RDS if a catalyst is present.
6. In a reaction mechanism, if the first step is the RDS, what can you conclude about the subsequent steps?
   1. They must be slower than the first step.
   2. They must be faster than the first step.
   3. They have no effect on the overall reaction rate.
   4. They determine the equilibrium constant of the reaction.
7. If a proposed mechanism has multiple steps and only one of them involves the reactants, $X$ and $Y$, with rate $= k[X][Y]$, then:
   1. The other steps must be faster and the proposed mechanism is valid.
   2. The other steps must be slower and the proposed mechanism is invalid.
   3. It is impossible to determine if the proposed mechanism is valid.
   4. The proposed mechanism is definitely valid.