Problem 31 - Chemistry in 30 days

Question

\(A+B \rightarrow\) products \begin{tabular}{|l|l|l|} \hline\([A]\) & {\([B]\)} & Rate \\ \hline \(0.1\) & \(0.1\) & \(x\) \\ \hline \(0.1\) & \(0.2\) & \(4 x\) \\ \hline \(0.4\) & \(0.2\) & \(16 x\) \\ \hline \end{tabular} What is the order of the reaction ? (a) 1 (b) 2 (c) 3 (d) 4

Step-by-Step Solution

Answer

The reaction is third order (option c).

Step 1: Understand the Reaction Setup

We have a reaction where the rate depends on concentrations of reactants A and B. The table provides the rate for different combinations of concentrations of A and B.

Step 2: Determine Rate Law Structure

The rate of a reaction can be expressed as \( \text{Rate} = k[A]^m[B]^n \), where \( k \) is the rate constant and \( m \) and \( n \) are the reaction orders with respect to A and B, respectively.

Step 3: Analyzing Rate Change with B

Raise \( [B] \) from \( 0.1 \) to \( 0.2 \) while keeping \( [A] = 0.1 \). From the table: when \( [B] = 0.1 \), rate = \( x \); when \( [B] = 0.2 \), rate = \( 4x \). Thus, doubling \( [B] \) quadruples the rate, suggesting reaction order \( n = 2 \) with respect to B.

Step 4: Analyzing Rate Change with A

Raise \( [A] \) from \( 0.1 \) to \( 0.4 \) while keeping \( [B] = 0.2 \). From the table: \( [A] = 0.1 \), \( \, \text{rate} = 4x \); \( [A] = 0.4 \), \( \, \text{rate} = 16x \). Since \( 0.4 = 4 \, \times\, 0.1 \) and the rate quadruples, the reaction is first order \( m = 1 \) with respect to A.

Step 5: Calculate Total Reaction Order

The total order of reaction is \( m + n = 1 + 2 = 3 \).

Key Concepts

Rate of Reaction

The rate of reaction is a measure of how quickly a chemical reaction occurs. It can be thought of as the speed at which reactants are converted into products. This rate is typically expressed in terms of concentration change per unit time, such as moles per liter per second (M/s).

• In our exercise, the provided table helps illustrate how changes in concentrations of reactants affect the rate of the reaction.
• By examining the concentration of reactants [A] and [B], we can determine how these changes correlate with changes in the rate to understand the order of the reaction.

Understanding the rate of reaction is essential for predicting how fast a reaction will occur under given conditions, which is critical in many industrial and laboratory processes.

Rate Law

The rate law is an equation that links the rate of a chemical reaction to the concentration of the reactants. It includes the rate constant (k) and the reaction orders with respect to each reactant.

• The general form is given by \( \text{Rate} = k[A]^m[B]^n \), where \([A]\) and \([B]\) are concentrations of the reactants.
• The exponents \(m\) and \(n\) indicate the reaction order in relation to that reactant, representing how the rate depends on their concentrations.

To determine the specific form of the rate law for a reaction, experimental data, like the table in the original exercise, are analyzed to find the values of \(m\) and \(n\).
With this information, chemists can predict how changes in concentration will impact the rate, making the rate law quite instrumental for controlling reactions.

Reaction Order with Respect to Concentration

The reaction order with respect to a reactant describes how the rate of the reaction changes as the concentration of that particular reactant changes.

Determining Reaction Orders

• In our exercise, we observed that doubling \([B]\) while keeping \([A]\) constant resulted in a quadrupling of the rate. This provided us with \(n = 2\), showing that the reaction order with respect to B is second order.
• Similarly, doubling \([A]\) had a proportional effect on the rate, establishing \(m = 1\), which indicates a first order with respect to A.

Overall, the reaction order helps determine how sensitive the reaction rate is to changes in reactant concentrations, guiding scientists in optimizing conditions to achieve desired reaction speeds.

Chemical Kinetics

Chemical kinetics is the study of the rates of chemical processes and the factors affecting them. It delves into how different conditions and variations in reactant concentrations influence the speed of reactions.

• Key factors include concentrations of reactants, temperature, presence of a catalyst, and surface area.
• By understanding chemical kinetics, chemists can design more efficient chemical processes and synthesize products within a desired timeframe.

This field of study provides critical insights into the dynamics of reactions, enabling the development of new technologies and the improvement of current industrial processes. It connects deeply with the concepts of rate laws and reaction orders, as comprehensively explored in our exercise, highlighting the practical applications and theoretical foundations in chemistry.