Explain what is meant by the rate law of a reaction.

Short Answer

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The rate law of a reaction is a mathematical equation that describes the rate at which a reaction will occur based on the concentrations of the reactants. It's often written in the form: Rate = k [Reactant1]^x [Reactant2]^y, where k is the rate constant, x and y are the reaction orders, and [Reactant1] and [Reactant2] are the molar concentrations of the reactants. The rate constant and reaction order dictate how the reaction rate varies with changes in reactant concentration.

Step by step solution

01

General Explanation

The rate law of a chemical reaction is a mathematical equation that describes the rate at which a reaction will occur based on the concentrations of the reactants. It's often written in the form: Rate = k [Reactant1]^x [Reactant2]^y, where Rate is the rate of reaction, [Reactant1] and [Reactant2] are the molar concentrations of the reactants, x and y are the reaction orders, and k is the rate constant that is specific for the reaction at a given temperature.
02

Understanding rate constants and reaction orders

The rate constant, k, is a proportionality factor that is affected by factors like temperature, pressure etc. The reaction orders (x,y..), on the other hand, show how the rate is affected by each reactant's concentration. A reaction order can be 0 (reaction rate doesn't change with that reactant's concentration), 1 (reaction rate is directly proportional to that reactant's concentration) or 2 (reaction rate is dependent on the square of that reactant's concentration) etc.
03

Example

Let's consider a simple reaction between substances A and B. The rate law could be expressed as: Rate = k [A]^1 [B]^2. This means the rate of the reaction is directly proportional to the concentration of A and proportional to the square of the concentration of B.

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Key Concepts

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

Chemical Kinetics
Chemical kinetics is the branch of chemistry that deals with the speed or rate at which a chemical reaction occurs and the factors that affect this rate. It focuses on understanding the sequence of chemical processes that lead to product formation and how different conditions can influence the progress of a reaction. This includes studying variables such as temperature, pressure, reactant concentrations, and catalysts. By mastering this concept, you're able to predict how a reaction will behave under different circumstances, making it a crucial part of developing new chemical processes and products.

Understanding kinetics also allows chemists to control reactions to optimize output and safety. For example, if you know that increasing the temperature can make a reaction hazardous by causing it to proceed too quickly, you can design a process that mitigates this risk while still achieving the desired result.
Reaction Rates
The rate of a chemical reaction indicates the speed at which reactants are converted into products. It is usually measured by the change in concentration of reactants or products per unit time. To make this concept more understandable, consider a simple analogy: a runner's speed on a track. Just as the runner has a certain pace to complete a lap, reactants have a 'pace' at which they are transformed into products—a faster rate means more product is formed in less time.

Factors Influencing Reaction Rates

Several factors can influence these rates, including the physical state of the reactants, the presence of a catalyst, the concentrations of the reactants, and the temperature of the system. An increased concentration of reactants or a higher temperature generally results in a faster reaction, as particles collide more often and with greater energy, leading to more frequent and effective collisions.
Rate Constant
The rate constant, often denoted as 'k', is a crucial component in the rate law equation. It represents the relationship between the reaction rate and the concentrations of reactants for a given reaction at a specific temperature. The value of 'k' is determined experimentally and is unique for each reaction under constant conditions. It can be thought of as the inherent 'speed' at which a reaction can proceed.

It’s essential to recognize that the rate constant is not affected by the concentration of reactants, but it is temperature-dependent. Changes in temperature can significantly influence 'k', thus affecting the overall reaction rate. In other words, just as a car's maximum speed depends on the make and model, but can be adjusted by pressing the accelerator (temperature), the rate constant is a fixed characteristic of the reaction that can be influenced by external conditions.
Reaction Order
Reaction order is an aspect of the rate law that reveals the dependency of the rate on the concentrations of reactants. It's a value (often an integer or sometimes a fraction) assigned to each reactant based on how the rate of the reaction changes concerning its concentration. A zero-order reaction means the rate does not depend on the reactant's concentration, first-order points to a direct proportionality, and second-order suggests that the rate is proportional to the square of the reactant's concentration.

Determining the order of a reaction requires experimental data and analysis, often using methods such as the method of initial rates. Reaction order is not only critical in predicting how a rate will change with varying concentrations but also invaluable in understanding the mechanisms behind a reaction. Like following a recipe, knowing the quantities and how they interact can mean the difference between a delightful dish and a culinary disaster.

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Most popular questions from this chapter

Chlorine oxide (ClO), which plays an important role in the depletion of ozone (see Problem 13.101 ), decays rapidly at room temperature according to the equation $$ 2 \mathrm{ClO}(g) \longrightarrow \mathrm{Cl}_{2}(g)+\mathrm{O}_{2}(g) $$ From the following data, determine the reaction order and calculate the rate constant of the reaction. $$ \begin{array}{ll} \hline \text { Time (s) } & {[\mathrm{ClO}](M)} \\ \hline 0.12 \times 10^{-3} & 8.49 \times 10^{-6} \\ 0.96 \times 10^{-3} & 7.10 \times 10^{-6} \\ 2.24 \times 10^{-3} & 5.79 \times 10^{-6} \\ 3.20 \times 10^{-3} & 5.20 \times 10^{-6} \\ 4.00 \times 10^{-3} & 4.77 \times 10^{-6} \\ \hline \end{array} $$

The rate law for the reaction $$ 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g) $$ is given by rate \(=k[\mathrm{NO}]\left[\mathrm{Cl}_{2}\right] .\) (a) What is the order of the reaction? (b) A mechanism involving the following steps has been proposed for the reaction: $$ \begin{array}{c} \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g) \\ \mathrm{NOCl}_{2}(g)+\mathrm{NO}(g) \longrightarrow 2 \mathrm{NOCl}(g) \end{array} $$ If this mechanism is correct, what does it imply about the relative rates of these two steps?

Consider the following elementary step: $$ \mathrm{X}+2 \mathrm{Y} \longrightarrow \mathrm{XY}_{2} $$ (a) Write a rate law for this reaction. (b) If the initial rate of formation of \(\mathrm{XY}_{2}\) is \(3.8 \times 10^{-3} \mathrm{M} / \mathrm{s}\) and the initial concentrations of \(\mathrm{X}\) and \(\mathrm{Y}\) are \(0.26 \mathrm{M}\) and \(0.88 M\), what is the rate constant of the reaction?

What is the half-life of a compound if 75 percent of a given sample of the compound decomposes in \(60 \mathrm{~min} ?\) Assume first-order kinetics.

A certain first-order reaction is 35.5 percent complete in 4.90 min at \(25^{\circ} \mathrm{C}\). What is its rate constant?

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