Question

Nitrosyl chloride (NOCl) decomposes to nitrogen oxide and chlorine gases. (a) Write a balanced equation using smallest wholenumber coefficients for the decomposition. (b) Write an expression for the reaction rate in terms of \(\Delta[\mathrm{NOCl}]\) (c) The concentration of NOCl drops from \(0.580 \mathrm{M}\) to \(0.238 \mathrm{M}\) in \(8.00 \mathrm{~min} .\) Calculate the average rate of reaction over this time interval.

Short answer

Answer: The average rate of the reaction is \(3.56 \times 10^{-4} \frac{\mathrm{M}}{\mathrm{s}}\).

Step-by-step solution

Write a balanced equation for the decomposition of Nitrosyl chloride (NOCl)

The balanced equation for the decomposition of Nitrosyl chloride (NOCl) can be written as: $$2\mathrm{NOCl}(g) \rightarrow 2\mathrm{NO(g)} + \mathrm{Cl_2}(g)$$

Write an expression for the reaction rate in terms of \(\Delta[\mathrm{NOCl}]\)

The reaction rate can be defined as the change in concentration of a reactant or product per unit time. For this reaction, the rate can be expressed as: $$\textrm{Rate} = -\frac{1}{2} \frac{\Delta[\mathrm{NOCl}]}{\Delta t}$$ Since \(2\mathrm{NOCl}\) molecules are required to produce \(2\mathrm{NO}\) and \(\mathrm{Cl_2}\), we divide by 2 to account for the stoichiometry of the reaction.

Calculate the average rate of reaction

Given the initial concentration of NOCl is \(0.580 \mathrm{M}\), the final concentration is \(0.238 \mathrm{M}\), and the reaction proceeds for \(8.00 \mathrm{min}\). First, we need to convert minutes to seconds, then, we can plug these values into the reaction rate expression. Time in seconds: $$ 8.00 \mathrm{~min} \times \frac{60 \mathrm{~s}}{1 \mathrm{~min}} = 480 \mathrm{~s} $$ Now, we can calculate the average rate of reaction: $$ \textrm{Rate} = -\frac{1}{2} \frac{0.580 \mathrm{M} - 0.238 \mathrm{M}}{480 \mathrm{~s}} $$ $$ \textrm{Rate} = -\frac{1}{2} \frac{0.342 \mathrm{M}}{480 \mathrm{~s}} $$ $$ \textrm{Rate} = -\frac{0.342 \mathrm{M}}{960 \mathrm{~s}} $$ $$ \textrm{Rate} = -3.56 \times 10^{-4} \frac{\mathrm{M}}{\mathrm{s}} $$ The negative sign indicates that the concentration of NOCl decreases over time. Therefore, the average rate of reaction is \(3.56 \times 10^{-4} \frac{\mathrm{M}}{\mathrm{s}}\).

Key concepts

Chemical Kinetics

Chemical kinetics is the study of the speed or rate at which chemical reactions occur. It's crucial in understanding how various factors such as temperature, concentration, and the presence of catalysts affect the reaction rates. The decomposition of nitrosyl chloride (NOCl) into nitrogen oxide and chlorine gases is an example that reflects these principles.

Knowing the kinetics of a chemical reaction helps to predict the concentration of reactants or products at any given time. The rate of reaction is often expressed in terms of the rate of change in concentration of the reactants, as demonstrated in the exercise above. By determining this rate, chemists can make predictions about the reaction's behavior in different conditions, optimize processes, and control product formation effectively.

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry. It involves adjusting the coefficients of the reactants and products to ensure that the same number of each type of atom appears on both sides of the equation. This reflects the conservation of mass—matter is neither created nor destroyed in a chemical reaction.

In the example given, the balanced equation for the decomposition of nitrosyl chloride shows that two molecules of NOCl produce two molecules of NO and one molecule of Cl₂. This balance is crucial for calculations related to the reaction rate and stoichiometry, as it ensures that the ratio in which reactants combine and products form is accurately represented.

Concentration Change

The concentration change of a reactant or product in a chemical reaction is an indicator of the reaction progress. It's defined by the difference in concentration over a specific time interval and is essential for calculating the reaction rate. In the initial step, the exercise provided the change in concentration of NOCl over an 8-minute period, which is fundamental to computing the average rate of reaction.

Understanding concentration change is not only about finding the difference in molarity but also about recognizing its impact on the reaction dynamics. A higher rate of concentration change implies a faster reaction, which can be crucial for industrial applications where time and efficiency are key factors in productivity.

Stoichiometry

Stoichiometry is the aspect of chemistry that pertains to the quantity of reactants and products in a chemical reaction. It uses the relationships within a balanced equation to determine the relative amounts of each substance needed or produced. The balanced equation for the decomposition of NOCl illustrates the stoichiometric relationships involving two mole ratios of NOCl to NO and a one mole ratio to Cl₂.

In calculating the reaction rate, the stoichiometry of the chemical equation provides the coefficients that factor into the expression. For instance, the rate expression involves dividing by 2 to match the stoichiometric coefficient of NOCl in the balanced equation. Thus, stoichiometry plays a critical role in quantitatively analyzing chemical reactions and contributes significantly to predicting and measuring the outcomes of reactions.