3.4 Isolation method and pseudo-order reactions

The isolation method simplifies determining rate laws for complex reactions by adjusting initial concentrations. It's a powerful tool when dealing with multiple reactants or unknown mechanisms. This approach allows us to focus on the effect of limiting reactants, making it easier to unravel reaction kinetics.

By keeping one reactant in excess, we create pseudo-order reactions. This simplification helps us determine rate laws and rate constants more easily. However, it's important to remember that this method has limitations and may not always provide the full picture of reaction kinetics.

Isolation Method

Isolation method for rate laws

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• Experimental technique simplifies determining rate law for complex reactions
  • Adjusts initial concentrations of reactants making one reactant concentration much larger than others
  • Effectively isolates effect of concentration of excess reactant on reaction rate
• Most useful when:
  • Reaction involves multiple reactants and rate law is unknown
  • Reaction mechanism is complex or involves multiple steps
  • Reaction order with respect to each reactant is difficult to determine using method of initial rates or graphical method

Simplification of rate laws

• General rate law, rate depends on concentrations of all reactants:
  • $Rate = k[A]^x[B]^y[C]^z$, where $k$ is rate constant and $x$, $y$, and $z$ are orders with respect to reactants $A$, $B$, and $C$
• When one reactant, $A$, is in large excess compared to others, its concentration remains essentially constant throughout reaction
  • Allows rate law to be simplified to: $Rate = k_{obs}[B]^y[C]^z$, where $k_{obs} = k[A]^x$ is observed rate constant
• Simplified rate law depends only on concentrations of limiting reactants ($B$ and $C$ in this example)
  • Makes it easier to determine orders with respect to these reactants using method of initial rates or graphical method

Pseudo-order reactions

• Reactions that appear to follow simpler rate law than actual rate law due to use of isolation method
  • Observed rate law has different order than true rate law because concentration of one reactant is held constant
• Arise from isolation method when one reactant is in large excess compared to others
  • Excess reactant's concentration remains essentially constant throughout reaction
  • Allows rate law to be simplified, with order of reaction with respect to excess reactant being incorporated into observed rate constant ($k_{obs}$)
• Examples:
  • Pseudo-first-order reaction: $Rate = k_{obs}[B]$, where $k_{obs} = k[A]^x$ and $[A]$ is concentration of reactant in excess
  • Pseudo-second-order reaction: $Rate = k_{obs}[B][C]$, where $k_{obs} = k[A]^x$ and $[A]$ is concentration of reactant in excess

Determining rate laws through isolation

• To determine rate law and pseudo-order rate constant using isolation method:
  1. Design experiments where concentration of one reactant is much larger than others
  2. Measure initial rates of reaction at different concentrations of limiting reactants while keeping concentration of reactant in excess constant
  3. Use method of initial rates or graphical method to determine orders with respect to limiting reactants
  4. Write simplified rate law in terms of limiting reactants and observed rate constant ($k_{obs}$)
  5. Calculate $k_{obs}$ using simplified rate law and measured initial rates
• Example:
  • For reaction $A + B + C \rightarrow Products$, if $[A]$ is much larger than $[B]$ and $[C]$, simplified rate law might be: $Rate = k_{obs}[B]^y[C]^z$
  • Values of $y$ and $z$ can be determined using method of initial rates or graphical method
  • $k_{obs}$ can be calculated using simplified rate law and measured initial rates at different concentrations of $B$ and $C$

Limitations and Applicability

Limitations of isolation method

• Assumes concentration of reactant in excess remains constant throughout reaction, which may not always be true
• Does not provide information about true rate law or reaction mechanism
• May not be applicable if reaction is reversible or if there are competing side reactions
• Most applicable when:
  • Reaction is irreversible and has no significant side reactions
  • Concentration of one reactant can be made much larger than others without affecting reaction mechanism
  • Orders with respect to limiting reactants are of primary interest
• May not be suitable for:
  • Reversible reactions, where reverse reaction becomes significant as reaction progresses
  • Reactions with competing side reactions that become more significant at high concentrations of reactant in excess
  • Reactions where concentration of reactant in excess affects reaction mechanism or rate-determining step