The graphing calculator can run a program that can tell you the order of a chemical reaction, provided you indicate the reactant concentrations and reaction rates for two experiments involving the same reaction. Go to Appendix C. If you are using a TI-83 Plus, you can download the program RXNORDER and run the application as directed. If you are using another calculator, your teacher will provide you with key-strokes and data sets to use. At the prompts, enter the reactant concentrations and reaction rates. Run the program as needed to find the order of the following reactions. (All rates are given in M/s.) a. \(2 \mathrm{N}_{2} \mathrm{O}_{5}(g) \rightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\) \(\mathrm{N}_{2} \mathrm{O}_{5} :\) conc. \(1=0.025 \mathrm{M} ;\) conc. \(2=0.040 \mathrm{M}\) rate \(1=8.1 \times 10^{-5} ;\) rate \(2=1.3 \times 10^{-4}\) b. \(2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) \(\mathrm{NO}_{2} : \mathrm{conc.} 1=0.040 \mathrm{M} ; \mathrm{conc} .2=0.080 \mathrm{M}\) rate \(1=0.0030 ;\) rate \(2=0.012\) c. \(2 \mathrm{H}_{2} \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{O}_{2}(g)\) \(\mathrm{H}_{2} \mathrm{O}_{2} :\) conc. \(1=0.522 \mathrm{M} ;\) conc. \(2=0.887 \mathrm{M}\) rate \(1=1.90 \times 10^{-4} ;\) rate \(2=3.23 \times 10^{-4}\) d. \(2 \mathrm{NOBr}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)\) NOBr: conc. \(1=1.27 \times 10^{-4} \mathrm{M} ;\) conc. \(2=\) \(4.04 \times 10^{-4} \mathrm{M}\) rate \(1=6.26 \times 10^{-5} ;\) rate \(2=6.33 \times 10^{-4}\) e. \(2 \mathrm{HI}(g) \rightarrow \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)\) HI: conc. \(1=4.18 \times 10^{-4} \mathrm{M} ;\) conc. \(2=\) \(8.36 \times 10^{-4} \mathrm{M}\) rate \(1=3.86 \times 10^{-5} ;\) rate \(2=1.54 \times 10^{-4}\)

Step by step solution

01

Inputting Data

Open the RXNORDER program, when prompted, input the concentrations and reaction rates for the first reaction, \(2 N_{2} O_{5}(g) \rightarrow 4 NO_{2}(g)+ O_{2}(g)\), from the exercise. These values are: Concentration 1 = 0.025 M, Concentration 2 = 0.040 M, Rate 1 = 8.1 x 10^{-5} M/s and Rate 2 = 1.3 x 10^{-4} M/s.

02

Calculating Reaction Orders

Run the program and it will output the order of reaction. Repeat the process for the remaining reactions provided in the exercise with the given concentrations and reaction rates.

03

Repeat for Other Reactions

The same steps must be repeated for the remaining reactions. Input the relevant concentrations and reaction rates, run the program, and note down the reaction orders for each of the given chemical reactions. This process allows the determination of reaction orders only if the concentrations and rates relatable experimentally.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Reaction Kinetics

Reaction kinetics is a central concept in chemistry that deals with the rates at which chemical reactions occur and the mechanisms by which they proceed. It provides insight into the speed of chemical changes and is essential in predicting the behavior of reactions under different conditions.

In the context of the given exercises, we are particularly interested in the orders of reactions, which are a part of the reaction kinetics. The order of a reaction can be zero, first, second or any other integer or fraction, which is determined based on how the rate of a reaction depends on the concentration of reactants. In simple terms, it tells us how sensitive a reaction rate is to changes in reactant concentrations.

For example, in a first-order reaction, the rate is directly proportional to the concentration of one reactant, meaning if you double the concentration, the reaction rate also doubles. In a second-order reaction, the rate is proportional to the square of the concentration of one reactant, or to the product of the concentrations of two reactants. To determine the order experimentally, one typically measures the reaction rates at various concentrations, as illustrated in the exercise solutions with the use of the RXNORDER program.

Concentration and Reaction Rates

The relationship between concentration and reaction rates is fundamental to chemical kinetics. In general, the rate of a reaction increases when the concentration of the reactants is raised, due to more frequent collisions between the reacting particles.

The step by step solution demonstrates this relationship. By entering the concentrations and rates into the RXNORDER program, students can see how changes in concentration affect the rate, thereby determining the reaction order.

• In case a, the rate nearly doubles when the concentration increases from 0.025 M to 0.040 M, suggesting a reaction order greater than zero.
• In case b, the rate increases fourfold when the concentration doubles, hinting at a second order reaction, as the rate change is in line with the square of the concentration change.

In practical applications, understanding this relationship helps chemists control the speed of reactions, an essential aspect when designing reactors in chemical engineering or when conducting sensitive chemical reactions in research laboratories.

Graphing Calculator Applications in Chemistry

Graphing calculators are versatile tools that can extend far beyond basic mathematical computations. In chemistry, specifically, they can be used to run specialized programs like RXNORDER, which aid in analyzing reaction kinetics and determining reaction orders, as highlighted in the provided exercise.

These calculators enable students and chemists to input experimental data such as reactant concentrations and reaction rates, and promptly calculate the complex relationships that constitute the core of chemical kinetics. The instant processing capability of a graphing calculator simplifies what would otherwise be a tedious and error-prone manual calculation.

Moreover, advanced calculators can graph these relationships, displaying how reaction rates vary with concentration. This visual representation is vital for understanding the concept of reaction rates deeply, as it illustrates the actual impact of concentration changes on the speed of a reaction. Therefore, leveraging graphing calculator applications in chemistry education helps students to concretely grasp theoretical concepts through practical application.