Chapter 5: Problem 9

Does the catalyst concentration affect the reaction rate?

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Step by step solution

Understand the Role of Catalysts

A catalyst is a substance that increases the rate of a chemical reaction without being consumed or undergoing any chemical change itself. Catalysts work by providing an alternative reaction pathway or mechanism with lower activation energy. This allows more reactant molecules to have enough energy to form products, thus increasing the rate of the reaction.

Examine Reaction Kinetics

Reaction kinetics is the study of the rates of chemical reactions and the factors that affect them, such as concentration, temperature, and presence of a catalyst. To investigate catalyst concentration's effect on reaction rate, we will examine the rate equation for a general reaction with a catalyst.

Derive the Rate Equation with a Catalyst

For a general reaction with reactants A and B and a catalyst C, one possible mechanism might look like this: 1. A + C -> AC 2. AC + B -> ABC 3. ABC -> P + C Where P represents the final products of the reaction. The rate of the reaction can be determined by analyzing the rates of each step. We have three expressions for these rates: 1. Rate1 = k1[A][C] 2. Rate2 = k2[AC][B] 3. Rate3 = k3[ABC] Since the reaction forms intermediate species AC and ABC, these are assumed to be in steady-state, which means their concentrations remain approximately constant: d[AC]/dt = d[ABC]/dt = 0.

Analyze the Steady-State Approximation

Using the steady-state approximation (d[AC]/dt = 0), we can equate the rate of formation of AC to the rate of its consumption: k1[A][C] = k2[AC][B] We can rearrange this equation to find the concentration of AC: [AC] = (k1[A][C])/(k2[B]) Similarly, using the steady-state approximation (d[ABC]/dt = 0), we can equate the rate of formation of ABC to the rate of its consumption: k2[AC][B] = k3[ABC] We can rearrange this equation to find the concentration of ABC: [ABC] = (k2[AC][B])/(k3)

Calculate the Effect of Catalyst Concentration on Reaction Rate

The overall rate of the reaction can be represented by the rate of formation of P: Rate = k3[ABC] Substitute the expression for [ABC] from the previous step: Rate = k3[(k2[AC][B])/(k3)] Substitute the expression for [AC] from the previous step: Rate = k3[(k2((k1[A][C])/(k2[B]))[B])/(k3)] Simplifying the expression: Rate = k1[A][C] Thus, the overall reaction rate depends on the concentration of the catalyst.

Conclusion

Based on the derived rate equation, the catalyst concentration does indeed affect the reaction rate. As the concentration of the catalyst increases, the rate of the reaction will also increase, assuming all other factors remain constant.

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Does the catalyst concentration affect the reaction rate?

Short Answer

Step by step solution

Understand the Role of Catalysts

Examine Reaction Kinetics

Derive the Rate Equation with a Catalyst

Analyze the Steady-State Approximation

Calculate the Effect of Catalyst Concentration on Reaction Rate

Conclusion

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