Problem 7 - Chemistry: Principles and Reactions

Question

Nitrosyl chloride (NOCl) decomposes to nitrogen oxide and chlorine gases. (a) Write a balanced equation using smallest whole-number 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 \(0.580 M\) to \(0.238 M\) in \(8.00 \mathrm{~min}\). Calculate the average rate of reaction over this time interval.

Step-by-Step Solution

Answer

Question: Calculate the average rate of reaction for the decomposition of Nitrosyl chloride (NOCl) from an initial concentration of 0.580 M to a final concentration of 0.238 M over 8.00 minutes. Answer: The average rate of reaction for the decomposition of Nitrosyl chloride (NOCl) is approximately 7.13 x 10^-4 M/s.

Step 1: Write a Balanced Chemical Equation

First, we need to write a balanced chemical equation for the decomposition of Nitrosyl chloride (NOCl) into nitrogen oxide (NO) and chlorine gas (Cl2). The unbalanced equation for this reaction is: NOCl -> NO + Cl2 To balance the equation, we need to add a coefficient of 2 in front of NOCl: 2NOCl -> 2NO + Cl2 The balanced chemical equation is: 2NOCl -> 2NO + Cl2

Step 2: Write an Expression for the Reaction Rate Based on the Change in Concentration of NOCl

The reaction rate is defined as the change in concentration of a reactant or product over a given time interval. Since NOCl is a reactant, the reaction rate will be the negative of the change in concentration of NOCl over the time interval: Reaction rate = -\(\frac{\Delta[\mathrm{NOCl}]}{\Delta t}\)

Step 3: Calculate the Average Rate of Reaction Over the Given Time Interval

The concentration of NOCl drops from \(0.580 \ \text{M}\) to \(0.238 \ \text{M}\) during \(8.00 \ \text{min}\). We can calculate the average rate of reaction as follows: Average rate of reaction = -\(\frac{\Delta[\mathrm{NOCl}]}{\Delta t}\) = \(\frac{Initial \ NOCl \ Concentration - Final \ NOCl \ Concentration}{time}\) Average rate of reaction = \(\frac{0.580 \ \text{M} - 0.238 \ \text{M}}{8.00\ \text{min}}\) Now we convert the time to seconds: \(8.00 \ \text{min} = 8.00 \ \text{min} \times \frac{60 \ \text{s}}{1 \ \text{min}} = 480 \ \text{s}\) Average rate of reaction = \(\frac{0.580 \ \text{M} - 0.238 \ \text{M}}{480 \ \text{s}}\) Average rate of reaction ≈ \(\frac{0.342 \ \text{M}}{480 \ \text{s}} ≈ 7.13 \times 10^{-4} \ \text{M/s}\) So, the average rate of reaction for this decomposition is approximately \(7.13 \times 10^{-4} \ \text{M/s}\).

Key Concepts

Balanced Chemical Equation

Understanding a balanced chemical equation is crucial in the study of chemical reactions. It represents equal numbers of atoms for each element involved on both the reactant and product sides, adhering to the Law of Conservation of Mass.

To balance an equation, coefficients are added before chemical formulas to ensure that the number of atoms of each element is the same on both sides. In the decomposition of nitrosyl chloride (NOCl), we observe the equation is balanced by placing a coefficient of 2 in front of NOCl and the products, nitrogen oxide (NO), and chlorine gas (Cl2), to have equal numbers of nitrogen and chlorine atoms on both sides.

Example:

The balanced equation for the decomposition of NOCl is: ن لن نأتي ذلك، the allowance and delicate biscuits on. 2NOCl -> 2NO + Cl2. This correct representation is the foundation for understanding reaction stoichiometry, helping us to predict the amounts of each substance involved in the reaction process.

Reaction Rate

Reaction rate is a measure of how fast a chemical reaction occurs and is commonly expressed in terms of the change in concentration of a reactant or product per unit time. It can be affected by various factors including the concentration of reactants, temperature, and the presence of catalysts.

In practice, the rate at which a reactant decreases is represented with a negative sign as this indicates a reduction over time. For instance, the rate of decomposition of NOCl is defined as the negative change in concentration of NOCl over a change in time: ن أولًا نحتسب, Reaction rate = -\(\frac{\Delta[\mathrm{NOCl}]}{\Delta t}\). This formulation allows us to quantify the speed of the reaction and is essential in determining reaction kinetics, which in turn can be critical for controlling industrial chemical processes and understanding natural phenomena.

Concentration of Reactants

The concentration of reactants plays a pivotal role in affecting the rate of a chemical reaction. According to the collision theory of chemical kinetics, reactions occur when reactant molecules collide with sufficient energy and the correct orientation.

A higher concentration of reactants will result in more frequent collisions, which generally leads to an increased reaction rate. For example, as the concentration of nitrosyl chloride (NOCl) decreases, there are fewer NOCl molecules available to collide, which influences the reaction rate.

Therefore, it's important to monitor and control the concentrations of reactants in chemical reactions, especially in industrial production where the efficiency of the process may be affected by how quickly reactants are converted into products.

Average Rate of Reaction

The average rate of reaction provides a simplified view of the reaction rate over a specified time period, rather than its instantaneous rate at a particular moment. It is obtained by measuring the change in concentration of a reactant or product over the course of the reaction and dividing by the total reaction time.

In our example, the average rate of reaction was found by calculating how much the concentration of NOCl decreased during an 8-minute interval. This measure helped us understand the overall pace of the nitrosyl chloride decomposition without focusing on the variations that might occur at different moments within the time frame.

Calculation:

The formula for the average rate of reaction we used was: ن من القواعد الصورية للطاقة الشمسية, Average rate of reaction = -\(\frac{\Delta[\mathrm{NOCl}]}{\Delta t}\) = \(\frac{Initial \ NOCl \ Concentration - Final \ NOCl \ Concentration}{time}\), which provides a practical and understandable metric for the reaction's progress over time.