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 I 2 consumed per liter per minute.

Step-by-Step Solution

Answer

The average reaction rate for the given reaction is \(-0.025 \frac{\text{M}}{\text{min}}\) in terms of the consumption of I2.

Step 1: Identify the given information

In this problem, we are given the initial concentration of I2 as 0.400 M, the final concentration of I2 as 0.300 M, and the time interval as 4.00 minutes.

Step 2: Calculate the change in concentration of I2

To find the change in concentration of I2, we need to subtract the final concentration (on the completion of given time) from the initial concentration: Change in concentration = Final concentration - Initial concentration Δ[I2] = 0.300 M - 0.400 M

Step 3: Calculate the average reaction rate

Now, we will calculate the average reaction rate by dividing the change in concentration by the time interval: Average reaction rate = (Δ[I2]) / (Δt) Where Δt is the time interval. In this case, Δ[I2] = -0.100 M (from Step 2) and Δt = 4.00 min. Average reaction rate = (-0.100 M) / (4.00 min)

Step 4: Simplify the expression to find the average reaction rate

Now, we can simplify the expression to get the answer: Average reaction rate = -0.025 M/min The negative sign indicates that the concentration of I2 is decreasing over time, as expected in a reaction where I2 is being consumed. Thus, the average reaction rate for the given reaction is -0.025 M/min in terms of the consumption of I2.

Key Concepts

Gas-Phase Reaction

In chemistry, a gas-phase reaction involves reactants and products in the gaseous state. These reactions occur when gas molecules collide with enough energy to overcome activation energy, leading to chemical changes.

Gas-phase reactions are crucial in several fields, from industrial processes like the Haber process to atmospheric chemistry, where they affect air quality and climate.

• Understanding these reactions helps predict reaction behavior under changing conditions.
• Gas-phase reactions are often faster than reactions involving liquid or solid reactants due to higher kinetic energy of gas molecules.

Mastering this concept aids in grasping broader topics in chemical kinetics.

Concentration Change

Concentration change refers to the difference in the concentration of a reactant or product during a reaction over time. This change is essential as it informs about the speed and extent of a reaction.

In the context of a gas-phase reaction, like the one involving Iodine ( I_2 ) and Chlorine ( Cl_2 ), the concentration of reactants can change as they are consumed to form products.

• It is calculated by subtracting the final concentration from the initial concentration.
• A negative change indicates consumption of the reactant.

Tracking these changes helps in determining the average reaction rate accurately.

I2 Consumption

Iodine ( I_2 ) consumption depicts how much iodine is used up during a chemical reaction. In our gas-phase reaction, iodine is one of the reactants, and as the reaction proceeds, the concentration of I_2 decreases.

Consumption is an integral part of measuring reaction rates because it directly correlates with how fast or slow a reaction proceeds.

• The rate of consumption indicates efficiency and speed of reactant conversion into products.
• Understanding iodine's consumption helps in predicting necessary amounts of reactants for desired reaction outcomes.

Such insights are vital for both experimental and industrial chemical applications.

Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the rate of chemical reactions and the factors affecting them. It involves understanding how changing conditions like temperature, concentration, and catalysts influence reaction speed.

In the specific reaction of iodine with chlorine to form iodine chloride ( 2ICl ), kinetics tell us how fast I_2 is being consumed.

• Average reaction rate is a basic component of chemical kinetics, calculated by dividing concentration change by time.
• Knowing these rates is crucial for applications like chemical manufacturing and pharmacology.

Adopting chemical kinetics principles allows chemists to control and optimize reaction conditions for better efficiency.