Problem 23 - Chemistry The Science in Context

Question

In the decomposition reaction \(A \rightarrow B+C\), how is the rate at which \(\mathrm{A}\) is consumed related to the rate at which \(\mathrm{B}\) is produced?

Step-by-Step Solution

Answer

Answer: In the decomposition reaction A → B + C, the rate of consumption of A is equal to the rate of production of B.

Step 1: Write the balanced equation for the decomposition reaction

Start by writing the balanced decomposition reaction: A → B + C In this reaction, one molecule of A decomposes into one molecule of B and one molecule of C.

Step 2: Determine the reaction stoichiometry

The stoichiometric coefficients in the balanced equation give the molar ratios of the reactants and products involved in the reaction. In this case, the stoichiometric coefficients are all 1: 1 A → 1 B + 1 C

Step 3: Express the rate of reaction

To express the rate of reaction, we need to write the rate of change in the concentration of each species in terms of time. Given the stoichiometry of the reaction, we can write the rates as: Rate of consumption of A= -Δ[A]/Δt (since A is being consumed) Rate of formation of B= Δ[B]/Δt

Step 4: Relate the rates using stoichiometry

Using the stoichiometric coefficients (in this case, all equal to 1), we can now relate the rate of consumption of A to the rate of production of B: - Δ[A]/Δt = Δ[B]/Δt

Step 5: Final expression

The relationship between the rate of consumption of A and the rate of production of B is: Rate of consumption of A = Rate of production of B In other words, as A is consumed, B is produced at an equal rate in the decomposition reaction A → B + C.

Key Concepts

Decomposition Reaction

In chemistry, a decomposition reaction is a type of chemical reaction where one compound breaks down into two or more simpler substances. It is often expressed in a general form like:

• A single reactant yields multiple products: \[ \text{AB} \rightarrow \text{A} + \text{B} \]

Decomposition reactions are the opposite of synthesis reactions, where simpler substances combine to form more complex compounds. These reactions can be triggered by various forms of energy such as heat, light, or electricity.For the decomposition reaction in the original exercise:

• The compound \(A\) breaks down into two products: \(B\) and \(C\).
• This process is essential in many natural and industrial processes, such as the breakdown of organic matter or the analysis of compounds.

Understanding decomposition reactions helps predict how materials change and react under specific conditions.

Stoichiometry

Stoichiometry is the study of quantitative relationships in a chemical reaction. It involves calculating the amounts of reactants and products involved in the reactions based on the ratios given in a balanced equation. Consider the balanced equation:

• \[ \text{A} \rightarrow \text{B} + \text{C} \]

Here, stoichiometric coefficients signify the ratio at which substances react and form. For instance, for every 1 molecule of \(A\), 1 molecule of \(B\) and 1 molecule of \(C\) are formed. The coefficients direct the calculation of the molar rates at which compounds participate in the reaction. This is crucial because it ensures that the reaction adheres to the principle of conservation of mass.Stoichiometry provides valuable insight:

• It allows chemists to predict the amount of each substance required or produced.
• It is fundamental when scaling reactions for industrial purposes or laboratory synthesis.

Concentration Changes

In the context of chemical reactions, concentration changes refer to how the amounts of reactants and products vary over time. For a reaction to occur, the reactants need to collide with enough energy and correct orientation, which directly affects their concentrations.In decomposition reactions, the concentration of the reactant decreases as it transforms into products. For example, in our reaction \(A \rightarrow B + C\) :

• The concentration of \(A\) diminishes as it decomposes into \(B\) and \(C\).
• The concentration of \(B\) and \(C\) increases as they are formed from \(A\).

The rate at which these concentrations change is important for understanding the reaction dynamics. A common way to express the rate is:

• The rate of consumption of \(A\) is \(-\Delta[A]/\Delta t\).
• The rate of formation of \(B\) is \(\Delta[B]/\Delta t\).

By measuring these concentration changes over time, chemists can better understand and control the reaction conditions to achieve desired outcomes efficiently.