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Chapter 13: Problem 112

Is the rate law for a catalyzed reaction the same as that for the uncatalyzed reaction?

Short Answer

Expert verified
Answer: The rate laws for catalyzed reactions and uncatalyzed reactions differ in that the rate law for a catalyzed reaction takes into account the presence and influence of a catalyst, as well as its concentration, in the rate equation. In contrast, the rate law for an uncatalyzed reaction only considers the concentration of reactants and the reaction order with respect to the reactants.

Step by step solution

01

Understanding Reaction Rate

Reaction rate is a measure of how quickly the concentration of a reactant or product changes with time during a chemical reaction. The rate law is a mathematical expression that relates the reaction rate to the concentration of reactants and products in a chemical reaction.
02

Role of Catalysts

A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process. Catalysts work by providing a different reaction pathway, which has a lower activation energy than the original pathway of the reaction. This makes it easier for the reactants to collide, form products, and release energy.
03

Rate Law for an Uncatalyzed Reaction

The rate law for an uncatalyzed reaction is typically given by the equation:rate = k[reactants]^n, where k is the rate constant, [reactants] is the concentration of reactants, and n is the order of the reaction with respect to the reactants.
04

Rate Law for a Catalyzed Reaction

The rate law for a catalyzed reaction is given by a different equation, which takes into account the lower activation energy provided by the catalyst. It can be written as: rate = k'[reactants]^m[cat]^p, where k' is the rate constant for the catalyzed reaction, [reactants] is the concentration of reactants, m is the order of the reaction with respect to the reactants in the presence of the catalyst, [cat] is the concentration of the catalyst, and p is the order of reaction with respect to the catalyst. Now that we have established the general forms of the rate laws for both uncatalyzed and catalyzed reactions, we can compare them.
05

Comparing the Rate Laws for Catalyzed and Uncatalyzed Reactions

The rate law for catalyzed reactions and uncatalyzed reactions is different. The main difference is the inclusion of the catalyst (and its concentration) in the rate equation for a catalyzed reaction. This demonstrates that the presence of a catalyst affects not only the rate of the reaction, but also the role and impact of reactant concentrations on the reaction rate. In conclusion, the rate law for a catalyzed reaction is not the same as that for an uncatalyzed reaction, because it takes into account the presence and influence of a catalyst.

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Most popular questions from this chapter

In addition to being studied in the gas phase, the decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) has been evaluated in solution. In carbon tetrachloride (CC1,) at \(45^{\circ} \mathrm{C}\), $$2 \mathrm{N}_{2} \mathrm{O}_{5} \rightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}$$ is a first-order reaction and \(k=6.32 \times 10^{-4} \mathrm{s}^{-1} .\) How much \(\mathrm{N}_{2} \mathrm{O}_{5}\) remains in solution after \(1 \mathrm{h}\) if the initial concentration of \(\mathrm{N}_{2} \mathrm{O}_{5}\) was \(0.50 \mathrm{mol} / \mathrm{L} ?\) What percent of the \(\mathrm{N}_{2} \mathrm{O}_{5}\) has reacted at that point?

\(\mathrm{N}_{2} \mathrm{O}_{5},\) when dissolved in water, decomposes to produce \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2}\) $$2 \mathrm{N}_{2} \mathrm{O}_{5}(a q) \rightarrow 4 \mathrm{NO}_{2}(a q)+\mathrm{O}_{2}(a q)$$ The rate of formation of \(\mathrm{O}_{2}\) is \(4.0 \times 10^{-3} M \cdot \mathrm{min}^{-1}\) a. What is the rate of formation of \(\mathrm{NO}_{2}(a q) ?\) b. What is the rate of disappearance of \(\mathrm{N}_{2} \mathrm{O}_{5}(a q) ?\)

Why do the average rates of most reactions change with time?

The dimerization of ClO, $$2 \mathrm{ClO}(g) \rightarrow \mathrm{Cl}_{2} \mathrm{O}_{2}(g)$$ is second order in ClO. a. Use the following data to determine the value of \(k\) at \(298 \mathrm{K}\) $$\begin{array}{cc} \text { Time (s) } & \text { [ClO] (molecules/cm }^{3} \text { ) } \\ 0 & 2.60 \times 10^{11} \\ \hline 1.00 & 1.08 \times 10^{11} \\ \hline 2.00 & 6.83 \times 10^{10} \\ \hline 3.00 & 4.99 \times 10^{10} \\ \hline 4.00 & 3.93 \times 10^{10} \\ \hline \end{array}$$ b. Determine the half-life for the dimerization of C1O.

Bacterial Degradation of Ammonia Nitrosomonas bacteria convert ammonia into nitrite in the presence of oxygen by the following reaction: \(2 \mathrm{NH}_{3}(a q)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}^{+}(a q)+2 \mathrm{NO}_{2}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(\ell)\) A. How are the rates of formation of \(\mathrm{H}^{+}\) and \(\mathrm{NO}_{2}^{-}\) related to the rate of consumption of \(\mathrm{NH}_{3} ?\) b. How is the rate of formation of \(\mathrm{NO}_{2}^{-}\) related to the rate of consumption of \(\mathrm{O}_{2} ?\) c. How is the rate of consumption of \(\mathrm{NH}_{3}\) related to the rate of consumption of \(\mathrm{O}_{2} ?\)
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