Problem 3 - General Chemistry: Principles and Modern Applications

Question

In the reaction \(A \longrightarrow\) products, \([A]\) is found to be \(0.485 \mathrm{M}\) at \(t=71.5 \mathrm{s}\) and \(0.474 \mathrm{M}\) at \(t=82.4 \mathrm{s} .\) What is the average rate of the reaction during this time interval?

Step-by-Step Solution

Answer

The average rate of the reaction for this time interval is \( -0.001 \, M/s \).

Step 1: Identify the Variables

The initial concentration of A is 0.485 M at t = 71.5 s and the final concentration of A is 0.474 M at t = 82.4 s. Here, it is important to note that since A is being consumed to form the product, the rate will be negative.

Step 2: Substitute into the formula

Substitute the initial and final concentrations and time into the average rate formula: \[Average \;Rate = \frac{(0.474 \, M - 0.485 \, M)}{(82.4 \, s - 71.5 \, s)}\]

Step 3: Do the arithmetic

Perform the arithmetic in the numerator and the denominator of the fraction separately before dividing them.

Step 4: Calculate the average rate

Finally, perform the division to calculate the average rate of reaction during the given time interval. The unit of rate would be M/s.

Key Concepts

Reaction Kinetics

Reaction kinetics is the branch of chemistry that explores the rates at which chemical reactions occur. It explains how quickly reactants are converted to products, providing insight into the reaction's speed under various conditions.

Understanding reaction kinetics can help us control and optimize industrial processes, biological functions, and even environmental phenomena. It addresses

• the factors affecting reaction rates
• the mechanisms by which reactions proceed
• the quantitative aspects and predictive models for these processes

Reaction rates can be influenced by many factors, including temperature, pressure, concentration of reactants, and the presence of a catalyst. As temperature increases, for example, reactant molecules move more vigorously, which can lead to faster reactions. Similarly, increasing the concentration of reactants usually increases the reaction rate because more molecules are available to collide and react.

By understanding reactant behavior and reaction kinetics, chemists can predict how a reaction will proceed, giving us the ability to maximize yields and minimize waste.

Chemical Concentration Change

The change in chemical concentration during a reaction is a crucial indicator of its progress. Concentration refers to how much of a substance is present in a given volume of solution, often expressed in moles per liter ( ext{Molarity, M}). In the context of a reaction from A to products, the change in the concentration of A over time gives us a snapshot of the reaction kinetics at that moment.

As chemicals react, the concentrations of reactants typically decrease, while the concentrations of products increase. The rate of decrease in the concentration of a reactant or the rate of increase in the concentration of a product can give us valuable insights into the reaction kinetics and mechanisms.

For example, in the given exercise, the concentration of A decreases from 0.485 M to 0.474 M over a specific time frame. This decrease signifies the consumption of reactant A as it turns into products. Tracking concentration changes helps chemists understand the progress and extent of a reaction, allowing them to manipulate conditions to control the reaction outcomes.

Calculation of Average Rate

Calculating the average rate of reaction provides a straightforward way to measure how swiftly a reaction progresses within a particular interval. It reflects the change in concentration of a reactant or product over a given time period and is typically expressed in ( ext{M/s}), or molarity per second.

The average rate formula is:

• \[Average \;Rate = \frac{[A]_{final} - [A]_{initial}}{t_{final} - t_{initial}}\]

where ([A]_{final}) and ([A]_{initial}) are the final and initial concentrations, and (t_{final}) and (t_{initial}) are the final and initial times, respectively. This formula reflects the rate at which reactants disappear or products form.

In the given exercise, the rate of reaction is calculated over a specific interval: from 71.5 s to 82.4 s. The decrease in concentration of reactant A is plugged into the formula, and after performing the arithmetic: \[ Average \;Rate = \frac{(0.474 \, M - 0.485 \, M)}{(82.4 \, s - 71.5 \, s)} = -0.001 \text{ M/s}\]This negative sign indicates that the concentration of A is decreasing. The calculated average rate helps in understanding how fast the reaction is going over the given time period. It's essential for evaluating the efficiency and feasibility of a reaction under certain conditions.