Rate Law

Introduction

The rate of chemical reactions applies to various fields, from pharmaceuticals to environmental science. Imagine baking a cake—the result changes significantly depending on ingredient amounts and temperature adjustments. Similarly, every chemical reaction depends on the concentration of reactants and the order of the reaction. One of the cardinal principles of chemical kinetics concerns mathematical expressions for the relationship of pure rate to the concentration of reactants, more properly called the rate law.

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This Story also Contains

1. Introduction
2. Rate Order and Law of Reaction
3. Real-world and Practical Significance
4. Solved Examples Based On Reaction Rates
5. Summary

Understanding the rate of chemical reactions is crucial across multiple disciplines. For example, in pharmaceuticals, the reaction rate of a drug in the body informs its efficacy and concentration. In environmental science, the reaction rates of pollutants help determine appropriate waste treatment methods. These examples highlight the importance of understanding reaction rates and rate laws.

This paper aims to describe the rate law, which involves reaction orders, their definitions, and how they determine the rate of a chemical reaction. We will delve into the mathematical formulation of the rate law and explore how experimentally obtained reaction orders differ from stoichiometric coefficients. Furthermore, we will consider the units of rate constants for different reaction orders and their practical and academic significance. By the end of this paper, readers should have a comprehensive understanding of how reaction rates are quantified and applied in real-world situations.

Rate Order and Law of Reaction

The Rate Law Equation

The Rate Law Equation

The order of the reactants has implications for how any chemical reaction runs, specifically upon the concentration of its reactants. It goes in math like this:

Rate =$k[A{]}^p[B{]}^q$

Where:
k is a rate constant depending only on a particular reaction and temperature.
[A] and [B] are the molar concentrations of reactants A and B respectively; p and q are the reaction orders with respect to reactants A and B respectively. These are experimentally determined quantities that indicate the power to which the concentration of each reactant is raised.

It is not necessarily the case that pq is equal to the stoichiometric coefficients x and y of reactants A and B in the balanced chemical equation. The rate law is determined experimentally, and the form cannot be predicted from the stoichiometric coefficients alone.

The role of the rate constant k in this new equation of rate law becomes very huge because it now carries with itself whatever temperature dependence the reaction rate has.

Experimental Quantities vs. Stoichiometric Coefficients

In many reactions, the exponents p and q are not necessarily equal to the stoichiometric coefficients x and y in the balanced chemical equation. These exponents must be determined experimentally, and the order of each reactant is often referred to as the experimental order of reaction. The order concerning each reactant is often different and independent of the reaction's stoichiometry.

Unit of Rate Constant

Differential Rate Expression for an nth Order Reaction

For a reaction of order, the differential rate expression is given by:

Rate =-[dA]/[dt] =[A]ⁿ

In this expression,
– [A] is the concentration of reactant A, in moles per liter (often expressed in M).
– t is time, usually expressed in minutes.
- k is the rate constant, whose value differs depending on the reaction order $n$.

Units of the Rate Constant for Different Reaction Orders

The units of the rate constant $k$ are related to the order of the reaction:

Zero-Order Reaction
For a zero-order reaction, equation (2.6.1) takes the form:

Rate = k

The unit of k is: molL^-1 min^-1

First-Order Reaction
The formula for the rate expression of a first-order reaction is given as:

Rate =k[A]

In this case, the rate constant is independent of the concentration of the reactant and depends only on time. The unit is:

min⁻¹

The numerical value remains constant for any concentration but changes with different time units.

Real-world and Practical Significance

Reaction rates are widely applied and highly relevant in both practical and academic contexts. Understanding the rate of reaction enables the pharmaceutical industry to develop fast and effective drugs. Rate laws help environmental scientists project how long it will take for various pollutants in water bodies to degrade and design appropriate remediation measures. Therefore, mastering these core concepts is essential for students aspiring to study chemistry, as they form the basis for advanced topics in physical chemistry and kinetics.

You can enhance your knowledge by youtube video

Solved Examples Based On Reaction Rates

Example 1

Identify the reaction order for rate constant, $(k=7.06\times {10}^{-3}mol{L}^{-1}{s}^{-1})$.

1. First
2. Second
3. Zero (correct)
4. Third

Solution:

The given units of the rate constant match the form for a zero-order reaction: $concentration{)}^{1-0}\times time{)}^{-1})$.

Thus, the reaction is zero-order.

Therefore, the answer is option (3)

Example 2

If the rate constant for the forward and backward reactions of $A+B\to C)$ are $(1.5\times {10}^{-2}{min}^{-1})$ and $(0.5\times {10}^{-3}{min}^{-1})$ respectively, the rate constant of the reaction is:

1. $(\frac{1}{30})$
2. 50
3. 30 (correct)
4. $(\frac{1}{50})$

Solution:

The rate constant for the reaction is given by:

$[K=\frac{K_{forward}}{K_{backward}}=\frac{1.5\times {10}^{-2}}{0.5\times {10}^{-3}}=30]$

Hence, the answer is option (3)

Example 3

Identify the incorrect statement concerning the rate constant.

1. Rate constant is defined as the rate of the reaction when the concentration of each reactant is unity.
2. The rate constant for any particular reaction is constant at constant temperature.
3. Rate constant does not change with concentration, volume, pressure, time, etc.
4. None of the above (correct)

Solution:

All the statements about the rate constant are correct.

Hence, the answer is option (4)

Example 4

The rate constant for the reaction $(H_2+I_2\rightleftharpoons 2HI)$ is 0.2. What is the rate constant for the reaction $(2HI\rightleftharpoons H_2+I_2)$?

1. 0.2
2. 2
3. 5 (correct)
4. 1

Solution:

The rate constant for the reverse reaction is the reciprocal of the forward reaction:

$[K_{backward}=\frac{1}{K_{forward}}=\frac{1}{0.2}=5]$

Hence, the answer is option (3).

Example 5

For the conversion $(R\to S)$, the rate constant for the reaction was found to be$(2.8\times {10}^{-6}L{mol}^{-1}{s}^{-1})$. What is the order of the reaction?

1. 2 (correct)
2. 1
3. 0
4. 0.5

Solution:

Given units match those for a second-order reaction: $({concentration}^{1-2}\times time{)}^{-1})$.

Thus, the reaction is second-order.

Hence, the answer is option (1).

Summary

This paper identifies critical concepts in reaction rates and rate laws, emphasizing how reactant concentration and reaction order influence the rate. We derived the mathematical expression of the rate law and distinguished between experimental quantities and stoichiometric coefficients. We also derived the units of different orders of the rate constant, highlighting their relation to time and concentration. Finally, we discussed real-life applications and the academic significance of understanding reaction rates, emphasizing their wide-ranging impacts. These concepts are fundamental for students and professionals dealing with chemistry across various fields.