Question

If the concentration of a reaction product increases from 0.0882 \(\mathrm{mol} / \mathrm{L}\) to 0.1446 \(\mathrm{mol} / \mathrm{L}\) in 12.0 minutes, what is the average reaction rate during the time interval?

Short answer

The average reaction rate during the given time interval is \(7.83 \times 10^{-5} \frac{mol}{L \cdot s}\).

Step-by-step solution

Identify given information

We have the initial concentration of the product, \(C_i = 0.0882 mol/L\), the final concentration of the product, \(C_f = 0.1446 mol/L\), and the time interval, \(t = 12.0 min\).

Calculate the change in concentration

To find the change in concentration, subtract the initial concentration from the final concentration: \[\Delta C = C_f - C_i.\]Substitute the given values: \[\Delta C = 0.1446 - 0.0882 = 0.0564 mol/L.\]

Convert the time to seconds

For a reaction rate, we typically express time in seconds, so we need to convert the given time from minutes to seconds: \[t = 12.0 min \times \frac{60s}{1 min} = 720 s.\]

Calculate the average reaction rate

Now, we can find the average reaction rate by dividing the change in concentration by the change in time: \[Reaction\,rate = \frac{\Delta C}{\Delta t}.\]Substitute the values we found: \[Reaction\,rate = \frac{0.0564\,mol/L}{720\,s} = 7.83 \times 10^{-5} \frac{mol}{L \cdot s}.\]

State the final answer

The average reaction rate during the given time interval is \(7.83 \times 10^{-5} \frac{mol}{L \cdot s}\).

Key concepts

Chemical Kinetics

Chemical kinetics is the study of rates of chemical processes and the factors that affect these rates. It is a core concept in the field of chemistry that explains how fast reactions occur and helps predict the behavior of chemical systems over time. An average reaction rate, as seen in our exercise, is a measure of how much the concentration of a reactant or product changes per unit time during a reaction.

Understanding kinetics can inform the optimization of industrial processes, control pollution, and even help develop new energy sources. It operates under the general principle that a chemical reaction proceeds at a rate proportional to the concentration of the reactants and is often influenced by factors such as temperature, catalysts, and the presence of inhibitors.

Concentration Change

When chemists refer to concentration change in a reaction, they are describing the difference in concentration of a reactant or product over time. This change is essential for calculating reaction rates. In our example, the exercise focused on the increase in concentration of a product.

The concentration change can convey much about the reaction's progress. For instance, a rapid change suggests a swift reaction, while a slower change indicates the opposite. This information is critical for laboratory work, industrial applications, and can even dictate the safety measures necessary during a reaction.

Reaction Rate Calculation

To calculate a reaction rate, you need to take the change in concentration of a reactant or product and divide it by the time interval during which this change occurs. This formula was applied in our exercise to determine the average reaction rate. To perform this calculation effectively:

• Identify the initial and final concentrations of a reactant or product.
• Determine the time interval over which the concentrations were measured.
• Calculate the difference in concentrations, often represented as \( \Delta C \).
• Divide the concentration change by the time change, usually in seconds, yielding the reaction rate \( \frac{\Delta C}{\Delta t} \).

A comprehension of reaction rate calculations helps chemists in scaling reactions, adjusting conditions to optimize rates, and ensuring the reactions occur as expected in both laboratory and industrial settings.

Unit Conversion

Unit conversion is an essential skill in chemistry and many other scientific fields. It is the process of converting measurements from one unit to another. As shown in the exercise, we converted time from minutes to seconds to standardize the units for the reaction rate calculation.

This practice ensures consistency and accuracy in scientific calculations, allowing for clear communication and comparison of results. Without proper unit conversion, calculations could lead to incorrect results that might affect research outcomes, product quality, or safety. Always make sure your units match the expected units for the equations you're using.