Problem 29 - Chemistry The Science in Context

Question

Write an equation relating the rates of change in the concentrations of the products and reactants in each of the following reactions: a. \(F_{2}(g)+H_{2} O(\ell) \rightarrow H O F(g)+H F(g)\) b. \(\mathrm{Si}(s)+3 \mathrm{HCl}(g) \rightarrow \mathrm{SiHCl}_{3}(\ell)+\mathrm{H}_{2}(g)\) c. \(4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-Step Solution

Answer

Based on the given step by step solutions, write a short answer that provides the equations relating the rates of change in the concentrations for each of the three reactions: a. For the first reaction, the equation relating the rates of change is: \(\frac{d[F_2]}{dt} = - \frac{d[H_2O]}{dt} = \frac{d[HOF]}{dt} = \frac{d[HF]}{dt}\) b. For the second reaction, the equation relating the rates of change is: \(\frac{d[Si]}{dt} = - \frac{1}{3} \frac{d[HCl]}{dt} = \frac{d[SiHCl_3]}{dt} = \frac{d[H_2]}{dt}\) c. For the third reaction, the equation relating the rates of change is: \(- \frac{1}{4} \frac{d[NH_3]}{dt} = - \frac{1}{3} \frac{d[O_2]}{dt} = \frac{1}{2} \frac{d[N_2]}{dt} = \frac{1}{6} \frac{d[H_2O]}{dt}\)

Step 1: Identify Reactants and Products

In this reaction, the reactants are \(F_2(g)\) and \(H_2O(\ell)\), and the products are \(HOF(g)\) and \(HF(g)\).

Step 2: Determine Stoichiometric Coefficients

The stoichiometric coefficients are already given in the balanced equation. They are 1 for each species.

Step 3: Write Equations for Rates of Change

The rates of change are: -(-1) for \(F_2(g)\) as reactant -1 for \(H_2O(\ell)\) as reactant 1 for \(HOF(g)\) as product 1 for \(HF(g)\) as product So the equation relating the rates of change is: \(\frac{d[F_2]}{dt} = - \frac{d[H_2O]}{dt} = \frac{d[HOF]}{dt} = \frac{d[HF]}{dt}\) b. $\mathrm{Si}(s)+3 \mathrm{HCl}(g) \rightarrow \mathrm{SiHCl}_{3}(\ell)+\mathrm{H}_{2}(g)$

Step 1: Identify Reactants and Products

In this reaction, the reactants are \(\mathrm{Si}(s)\) and \(3 \mathrm{HCl}(g)\), and the products are \(\mathrm{SiHCl}_{3}(\ell)\) and \(\mathrm{H}_{2}(g)\).

Step 2: Determine Stoichiometric Coefficients

The stoichiometric coefficients are already given in the balanced equation. They are 1 for \(\mathrm{Si}(s)\), 3 for \(\mathrm{HCl}(g)\), 1 for \(\mathrm{SiHCl}_{3}(\ell)\), and 1 for \(\mathrm{H}_{2}(g)\).

Step 3: Write Equations for Rates of Change

The rates of change are: -(-1) for \(\mathrm{Si}(s)\) as reactant -(-3) for \(\mathrm{HCl}(g)\) as reactant 1 for \(\mathrm{SiHCl}_{3}(\ell)\) as product 1 for \(\mathrm{H}_{2}(g)\) as product So the equation relating the rates of change is: \(\frac{d[Si]}{dt} = - \frac{1}{3} \frac{d[HCl]}{dt} = \frac{d[SiHCl_3]}{dt} = \frac{d[H_2]}{dt}\) c. $4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$

Step 1: Identify Reactants and Products

In this reaction, the reactants are \(4 \mathrm{NH}_{3}(g)\) and \(3 \mathrm{O}_{2}(g)\), and the products are \(2 \mathrm{N}_{2}(g)\) and \(6 \mathrm{H}_{2} \mathrm{O}(g)\).

Step 2: Determine Stoichiometric Coefficients

The stoichiometric coefficients are already given in the balanced equation. They are 4 for \(\mathrm{NH}_{3}(g)\), 3 for \(\mathrm{O}_{2}(g)\), 2 for \(\mathrm{N}_{2}(g)\), and 6 for \(\mathrm{H}_{2} \mathrm{O}(g)\).

Step 3: Write Equations for Rates of Change

The rates of change are: -(-1/4) for \(\mathrm{NH}_{3}(g)\) as reactant -(-1/3) for \(\mathrm{O}_{2}(g)\) as reactant 1/2 for \(\mathrm{N}_{2}(g)\) as product 1/6 for \(\mathrm{H}_{2} \mathrm{O}(g)\) as product So the equation relating the rates of change is: \(- \frac{1}{4} \frac{d[NH_3]}{dt} = - \frac{1}{3} \frac{d[O_2]}{dt} = \frac{1}{2} \frac{d[N_2]}{dt} = \frac{1}{6} \frac{d[H_2O]}{dt}\)

Key Concepts

Stoichiometry

Stoichiometry is the heart of understanding chemical reactions. It involves the calculation of reactants and products in chemical reactions. Essentially, stoichiometry helps us to know exactly how much of a substance is involved, both before and after a chemical reaction. This is crucial for creating a balanced chemical equation.

• **Balanced Equations**: It's important to balance the chemical equations to respect the Law of Conservation of Mass. This means that the number of each type of atom must be the same on both sides of the equation.
• **Stoichiometric Coefficients**: They are numbers written before reactants and products which indicate their proportions. For example, in the reaction \(2H_2 + O_2 \rightarrow 2H_2O\), the stoichiometric coefficients are 2 for \(H_2\), 1 for \(O_2\), and 2 for \(H_2O\).
• **Fractional Coefficients**: Sometimes, you may encounter fractional stoichiometric coefficients when converting to rate equations, to simplify comparisons between different species' rates of reaction.

Chemical Reactions

Chemical reactions are processes where substances, called reactants, are transformed into different substances, called products. Reactions are represented by chemical equations, which show the starting substances and the substances formed. Understanding chemical reactions requires identifying reactants, products, and their proportions.

• **Reactants and Products**: These are the starting materials and the new materials you end up with in a reaction. Recognizing them is the first step in analyzing any chemical reaction.
• **Phases and States**: Chemical equations often include states of matter (solid, liquid, gas, aqueous) to show the physical form of each substance. For example, \(g\) for gas, \(\ell\) for liquid, \(s\) for solid, and \(aq\) for aqueous solutions.
• **Types of Reactions**: There are numerous types of reactions, such as combination, decomposition, single displacement, and double displacement. Each type follows a different rearrangement of atoms or molecules.

Rate Equations

Rate equations describe how the rate of a chemical reaction relates to the concentration of reactants. These equations are key to understanding how fast reactions proceed, which is critical in both academic and industrial settings.

• **Reaction Rate**: This is a measure of how quickly reactants are converted into products. It can be expressed as the change in concentration over time, such as \(\frac{d[A]}{dt}\).
• **Rate Determining Step**: In multi-step reactions, the slowest step determines the reaction rate. Understanding this can aid in predicting the speed of the entire reaction.
• **Proportionality**: The rate of consumption of reactants and formation of products is governed by their stoichiometry in the reaction. For example, if the stoichiometric ratio between two reactants is 1:3, the rate equation will reflect this ratio, such as \(\frac{1}{3} \frac{d[B]}{dt} = \frac{d[A]}{dt}\), meaning for every molecule of \(A\) consumed, three molecules of \(B\) are consumed.