Problem 30
Question
Write an equation relating the rates of change in the concentrations of the products and reactants in each of the following reactions: a. \(\operatorname{SOF}_{2}(g)+2 \mathrm{F}_{2}(g) \rightarrow \mathrm{F}_{5} \mathrm{SOF}(g)\) b. \(\mathrm{B}_{2} \mathrm{H}_{6}(g)+6 \mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{BCl}_{3}(g)+6 \mathrm{HCl}(g)\) c. \(\mathrm{N}_{2} \mathrm{H}_{4}(g)+2 \mathrm{NH}_{2} \mathrm{Cl}(g) \rightarrow 2 \mathrm{NH}_{4} \mathrm{Cl}(s)+\mathrm{N}_{2}(g)\)
Step-by-Step Solution
Verified Answer
Question: Write the rate equation for each of the following reactions:
a. \(\operatorname{SOF}_{2}(g)+2 \mathrm{F}_{2}(g) \rightarrow \mathrm{F}_{5} \mathrm{SOF}(g)\)
b. \(\mathrm{B}_{2} \mathrm{H}_{6}(g)+6 \mathrm{Cl}_{2}(g) \rightarrow 2\mathrm{BCl}_{3}(g)+6 \mathrm{HCl}(g)\)
c. \(\mathrm{N}_{2} \mathrm{H}_{4}(g)+2 \mathrm{NH}_{2} \mathrm{Cl}(g)\rightarrow 2 \mathrm{NH}_{4} \mathrm{Cl}(s)+\mathrm{N}_{2}(g)\)
Answer:
a. \(-\frac{d[\operatorname{SOF}_{2}]}{dt}=k_{1}[\operatorname{SOF}_{2}][\mathrm{F}_{2}]^{2}\)
b. \(-\frac{d[\mathrm{B}_{2}\mathrm{H}_{6}]}{dt}=k_{2}[\mathrm{B}_{2}\mathrm{H}_{6}][\mathrm{Cl}_{2}]^{6}\)
c. \(-\frac{d[\mathrm{N}_{2}\mathrm{H}_{4}]}{dt}=k_{3}[\mathrm{N}_{2}\mathrm{H}_{4}][\mathrm{NH}_{2}\mathrm{Cl}]^{2}\)
1Step 1: Identify the reactants and products
The given reaction is: \(\operatorname{SOF}_{2}(g)+2 \mathrm{F}_{2}(g) \rightarrow \mathrm{F}_{5} \mathrm{SOF}(g)\). The reactants are SOF2 and F2, and the product is F5SOF.
2Step 2: Write the rate equation for reactants and products
For reactants, the rate of consumption is negative, and for products, the rate of formation is positive. Also, the rate will be proportional to the stoichiometric coefficients of the species in the reaction. The rate equation is as follows:
\(-\frac{d[\operatorname{SOF}_{2}]}{dt}=k_{1}[\operatorname{SOF}_{2}][\mathrm{F}_{2}]^{2}\)
\(-2\frac{d[\mathrm{F}_{2}]}{dt}=2k_{1}[\operatorname{SOF}_{2}][\mathrm{F}_{2}]^{2}\)
\(\frac{d[\mathrm{F}_{5}\mathrm{SOF}]}{dt}=k_{1}[\operatorname{SOF}_{2}][\mathrm{F}_{2}]^{2}\)
b. \(\mathrm{B}_{2} \mathrm{H}_{6}(g)+6 \mathrm{Cl}_{2}(g) \rightarrow 2\mathrm{BCl}_{3}(g)+6 \mathrm{HCl}(g)\)
3Step 1: Identify the reactants and products
The given reaction is: \(\mathrm{B}_{2} \mathrm{H}_{6}(g)+6 \mathrm{Cl}_{2}(g) \rightarrow 2\mathrm{BCl}_{3}(g)+6 \mathrm{HCl}(g)\). The reactants are B2H6 and Cl2, and the products are BCl3 and HCl.
4Step 2: Write the rate equation for reactants and products
Apply the same concept as in the first reaction:
\(-\frac{d[\mathrm{B}_{2}\mathrm{H}_{6}]}{dt}=k_{2}[\mathrm{B}_{2}\mathrm{H}_{6}][\mathrm{Cl}_{2}]^{6}\)
\(-6\frac{d[\mathrm{Cl}_{2}]}{dt}=6k_{2}[\mathrm{B}_{2}\mathrm{H}_{6}][\mathrm{Cl}_{2}]^{6}\)
\(2\frac{d[\mathrm{BCl}_{3}]}{dt}=2k_{2}[\mathrm{B}_{2}\mathrm{H}_{6}][\mathrm{Cl}_{2}]^{6}\)
\(6\frac{d[\mathrm{HCl}]}{dt}=6k_{2}[\mathrm{B}_{2}\mathrm{H}_{6}][\mathrm{Cl}_{2}]^{6}\)
c. \(\mathrm{N}_{2} \mathrm{H}_{4}(g)+2 \mathrm{NH}_{2} \mathrm{Cl}(g)\rightarrow 2 \mathrm{NH}_{4} \mathrm{Cl}(s)+\mathrm{N}_{2}(g)\)
5Step 1: Identify the reactants and products
The given reaction is: \(\mathrm{N}_{2} \mathrm{H}_{4}(g)+2 \mathrm{NH}_{2} \mathrm{Cl}(g)\rightarrow 2 \mathrm{NH}_{4} \mathrm{Cl}(s)+\mathrm{N}_{2}(g)\). The reactants are N2H4 and NH2Cl, and the products are NH4Cl and N2.
6Step 2: Write the rate equation for reactants and products
Apply the same concept as in the first reaction:
\(-\frac{d[\mathrm{N}_{2}\mathrm{H}_{4}]}{dt}=k_{3}[\mathrm{N}_{2}\mathrm{H}_{4}][\mathrm{NH}_{2}\mathrm{Cl}]^{2}\)
\(-2\frac{d[\mathrm{NH}_{2}\mathrm{Cl}]}{dt}=2k_{3}[\mathrm{N}_{2}\mathrm{H}_{4}][\mathrm{NH}_{2}\mathrm{Cl}]^{2}\)
\(2\frac{d[\mathrm{NH}_{4}\mathrm{Cl}]}{dt}=2k_{3}[\mathrm{N}_{2}\mathrm{H}_{4}][\mathrm{NH}_{2}\mathrm{Cl}]^{2}\)
\(\frac{d[\mathrm{N}_{2}]}{dt}=k_{3}[\mathrm{N}_{2}\mathrm{H}_{4}][\mathrm{NH}_{2}\mathrm{Cl}]^{2}\)
Key Concepts
Chemical Kinetics and Reaction Rate EquationsDetermining Reaction RatesStoichiometric Coefficients in Rate EquationsThe Role of Reactants and Products
Chemical Kinetics and Reaction Rate Equations
Understanding the speed at which chemical reactions occur is a fundamental concept in chemistry, known as chemical kinetics. A critical tool used in this field is the rate equation, which quantifies the change in concentration of reactants and products over time.
A rate equation will look something like this: \(-\frac{d[A]}{dt} = k[A]^m[B]^n\), where \(A\) and \(B\) represent the concentrations of reactants, \(k\) is the rate constant, and \(m\) and \(n\) are the reaction orders that correspond to the concentration dependence of each reactant.
Rate equations are derived from experimental data and reflect how the rate is affected by concentrations. They are essential for predicting how long a reaction will take under different conditions and for understanding the mechanism behind the reaction.
A rate equation will look something like this: \(-\frac{d[A]}{dt} = k[A]^m[B]^n\), where \(A\) and \(B\) represent the concentrations of reactants, \(k\) is the rate constant, and \(m\) and \(n\) are the reaction orders that correspond to the concentration dependence of each reactant.
Rate equations are derived from experimental data and reflect how the rate is affected by concentrations. They are essential for predicting how long a reaction will take under different conditions and for understanding the mechanism behind the reaction.
Determining Reaction Rates
The reaction rate is the speed at which reactants convert to products in a chemical reaction. It is usually expressed as the change in concentration of a reactant or product per unit time. For example, if \(A\) is a reactant, the rate could be expressed as \(-\frac{d[A]}{dt}\).
These rates can change depending on temperature, pressure, and the presence of a catalyst. In classroom practice or homework assignments, students often measure reaction rates to understand better how different factors affect the speed of chemical reactions. Calculating and comparing reaction rates for various reactions allows students to gain insight into reaction dynamics and the efficiency of chemical processes.
These rates can change depending on temperature, pressure, and the presence of a catalyst. In classroom practice or homework assignments, students often measure reaction rates to understand better how different factors affect the speed of chemical reactions. Calculating and comparing reaction rates for various reactions allows students to gain insight into reaction dynamics and the efficiency of chemical processes.
Stoichiometric Coefficients in Rate Equations
In chemical equations, the stoichiometric coefficients indicate the proportion of molecules that participate in the reaction. These coefficients are essential when writing rate equations because they dictate the relative rates at which reactants are consumed and products are formed.
For example, in the reaction where \(A + 2B \rightarrow C\), the stoichiometric coefficient for \(B\) is 2, meaning that \(B\) is consumed at double the rate of \(A\). Consequently, the rate at which \(B\) decreases is twice that of \(A\): \(-\frac{d[A]}{dt} = -\frac{1}{2}\frac{d[B]}{dt}\).
For example, in the reaction where \(A + 2B \rightarrow C\), the stoichiometric coefficient for \(B\) is 2, meaning that \(B\) is consumed at double the rate of \(A\). Consequently, the rate at which \(B\) decreases is twice that of \(A\): \(-\frac{d[A]}{dt} = -\frac{1}{2}\frac{d[B]}{dt}\).
The Role of Reactants and Products
In the analysis of chemical reactions, reactants and products play distinct roles. Reactants are the starting substances that undergo chemical changes to form products, the new substances produced at the end of the reaction. Understanding how to identify them is crucial for writing balanced chemical equations and rate equations.
For most chemical reactions, the rate equation focuses on the reactants since they determine the progression of the reaction. However, for reversible reactions or those in equilibrium, both reactants and products can be critical for understanding the dynamics of the reaction and its rate equation. This balance and interaction are key in predicting the outcome and manipulating the conditions to favor the formation of the desired products.
For most chemical reactions, the rate equation focuses on the reactants since they determine the progression of the reaction. However, for reversible reactions or those in equilibrium, both reactants and products can be critical for understanding the dynamics of the reaction and its rate equation. This balance and interaction are key in predicting the outcome and manipulating the conditions to favor the formation of the desired products.
Other exercises in this chapter
Problem 28
Catalytic Converters in Automobiles (II) Catalytic converters also combat air pollution by promoting the reaction between \(\mathrm{CO}\) and \(\mathrm{O}_{2}\)
View solution Problem 29
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(\el
View solution Problem 32
In a study of the thermal decomposition of ammonia into nitrogen and hydrogen: $$ 2 \mathrm{NH}_{3}(g) \rightarrow \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) $$ the
View solution Problem 33
Power Plant Emissions Sulfur dioxide emissions in stack gases at power plants may react with carbon monoxide as follows: $$ \mathrm{SO}_{2}(g)+3 \mathrm{CO}(g)
View solution