Problem 47 - Chemistry Matter and Change

Question

In the gas-phase reaction, \(\mathrm{I}_{2}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{ICl},\left[\mathrm{I}_{2}\right]\) changes from 0.400 \(\mathrm{M}\) at 0.00 \(\mathrm{min}\) to 0.300 \(\mathrm{M}\) at 4.00 \(\mathrm{min.}\) Calculate the average reaction rate in moles of 12 con- sumed per liter per minute.

Step-by-Step Solution

Answer

The average reaction rate is 0.025 M/min.

Step 1: Write Down Initial and Final Concentrations

Identify the initial concentration of \( \mathrm{I}_2 \) as 0.400 M at 0.00 minutes and the final concentration as 0.300 M at 4.00 minutes.

Step 2: Determine Change in Concentration

Calculate the change in concentration of \( \mathrm{I}_2 \) by subtracting the final concentration from the initial concentration: \[\Delta [\mathrm{I}_2] = 0.300 \, \mathrm{M} - 0.400 \, \mathrm{M} = -0.100 \, \mathrm{M}\]

Step 3: Calculate Change in Time

Determine the time interval over which the reaction occurs by subtracting the initial time from the final time: \[\Delta t = 4.00 \, \text{minutes} - 0.00 \, \text{minutes} = 4.00 \, \text{minutes}\]

Step 4: Calculate Average Reaction Rate

The average reaction rate is given by the formula \[\text{Average rate} = -\frac{\Delta [\mathrm{I}_2]}{\Delta t}\]Plug the values into the formula:\[\text{Average rate} = -\frac{-0.100 \, \mathrm{M}}{4.00 \, \text{minutes}} = 0.025 \, \mathrm{M/min}\]

Key Concepts

Gas-Phase Reaction

Gas-phase reactions occur when reactants in the gaseous state interact to form products. Such reactions involve molecules moving freely with high kinetic energy, often resulting in faster reaction rates compared to reactions in other states. The reaction \( \mathrm{I}_{2} + \mathrm{Cl}_{2} \rightarrow 2 \mathrm{ICl} \) is an example of a gas-phase reaction, where iodine and chlorine gases react to form iodine monochloride. The kinetic energy and random movement of the molecules facilitate collisions between reactants, promoting the chemical transformation.
Gas-phase reactions are often investigated in terms of reaction dynamics, making them a staple in physical chemistry studies. Watching how the concentration of reactants decreases over time helps us explore the characteristics of the reaction.

Concentration Change

The concentration change is a critical concept in understanding reaction progress. It refers to the difference in the amount of a reactant or product over a specific time frame. In this context, the concentration of iodine gas \([\mathrm{I}_2]\) changes from 0.400 M to 0.300 M.
This means that 0.100 M of the iodine gas has been consumed as the reaction proceeds from start to end.
We can calculate the concentration change by taking the difference between initial and final concentrations using the formula:

• \( \Delta [\mathrm{I}_2] = [\mathrm{I}_2]_{\text{final}} - [\mathrm{I}_2]_{\text{initial}} \)

Understanding the concentration change is essential because it allows us to quantify the extent of a reaction and its rate.

Average Reaction Rate

Average reaction rate provides a measure of how fast a reactant is consumed or a product is formed in a reaction. It is calculated by dividing the change in concentration by the time over which the change occurred. In our exercise, this is indicated by the consumption of iodine gas. The formula used is:

• \( \text{Average rate} = -\frac{\Delta [\mathrm{I}_2]}{\Delta t} \)

The negative sign indicates the concentration of the reactant is decreasing. In the given exercise, the average reaction rate is 0.025 M/min, illustrating how quickly iodine was consumed, on average, over the 4-minute time interval.
Calculating average reaction rates aids in understanding the overall speed of chemical processes, which is crucial in many industrial and laboratory applications.

Time Interval Analysis

Time interval analysis is important to determine how reaction rates vary over specific time frames. By assessing how much time it takes for a concentration change to occur, we gain insights into the dynamics of the reaction.
In our case, the time interval was from 0.00 to 4.00 minutes, a duration that permits us to calculate the average rate of reaction. This is essential for understanding both the reaction mechanism and potential factors influencing the reaction.

• The time interval \(\Delta t\) is simply the difference between the end time and the start time of the observation.
• \(\Delta t = 4.00\, \text{minutes} - 0.00\, \text{minutes} = 4.00\, \text{minutes}\)

Understanding and analyzing time intervals allow chemists to manipulate conditions to optimize the rate of reactions, which is vital for efficient production in chemical industries and research.