Question

The rate constant of a first-order reaction is \(66 \mathrm{~s}^{-1}\). What is the rate constant in units of minutes?

Short answer

The rate constant in minutes is approximately \(1.1 \text{ min}^{-1}\).

Step-by-step solution

Understanding the Given Information

We are given a rate constant for a first-order reaction as \(66 \text{ s}^{-1}\). The goal is to convert this rate constant from seconds to minutes.

Converting Seconds to Minutes

To convert the rate constant from seconds to minutes, note that 1 minute is equal to 60 seconds. Therefore, to convert the rate constant to \(\text{min}^{-1}\), divide the rate constant by 60.

Performing the Calculation

Use the formula \( k_{\text{min}^{-1}} = \frac{k_{\text{s}^{-1}}}{60} \). Substitute the given value, \(66\), into the formula: \[ k_{\text{min}^{-1}} = \frac{66}{60} \approx 1.1 \text{ min}^{-1} \].

Conclusion

The rate constant for the given reaction, when expressed in units of minutes, is approximately \(1.1 \text{ min}^{-1}\).

Key concepts

First-Order Reaction

First-order reactions are common in chemistry, where the rate of reaction is directly proportional to the concentration of a single reactant. In simple terms, the speed of the reaction depends on how much of one specific substance is present. This means that as the concentration of that substance decreases, the reaction rate slows down proportionally.

To identify a first-order reaction, you often use the rate equation:

• \[ ext{Rate} = k[A] \]

Where \(k\) is the rate constant, and \([A]\) is the concentration of the reactant. The unit of \(k\) is generally \( ext{s}^{-1}\) for first-order reactions, indicating how quickly the reaction occurs per second. Understanding the order of a reaction is key to predict how a reaction progresses over time.

Unit Conversion

Unit conversion is a fundamental skill in science, allowing measurements to be converted from one set of units to another for different contexts or requirements. For reactions, converting units helps standardize measurements for comparison and communication.

In the original problem, we converted units from seconds to minutes. This process involves understanding that 1 minute equals 60 seconds. To convert a rate constant from seconds to minutes:

• Divide the rate constant by 60.

For example, given a rate constant of \(66 \text{ s}^{-1}\), we find:

• \[ k_{\text{min}^{-1}} = \frac{66}{60} = 1.1 \text{ min}^{-1} \]

This conversion changes the perspective of time without altering the reaction's behavior.

Reaction Kinetics

Reaction kinetics explores how and at what rate chemical reactions occur. It delves into the factors influencing these rates and helps scientists understand and manipulate reaction processes. This is crucial in fields ranging from pharmaceuticals to environmental science.

A key aspect of reaction kinetics is the rate constant \(k\), unique to each reaction under certain conditions. It tells us how fast a reaction proceeds. In first-order reactions, the rate constant has specific units, such as \( \text{s}^{-1} \) or \( \text{min}^{-1} \), to indicate time involvement.

By studying reaction kinetics, one can determine the efficiency of the reaction, how temperature or concentration changes affect it, and much more. It's all about understanding the reaction's journey from start to finish.

Time Conversion

Time conversion is a practical tool in chemistry, helping translate between different time units to facilitate easier calculations and comparisons. For instance, converting seconds to minutes can provide a clearer sense of duration in everyday terms.

Consider the original exercise where the rate constant was given in \(\text{s}^{-1}\), and our goal was to express it in \(\text{min}^{-1}\). Here's how you can approach such conversions:

• Know the conversion factor: 1 minute equals 60 seconds.
• Divide the rate constant by this factor to convert from seconds to minutes.

Using these steps, the conversion becomes straightforward, making it easier to understand the time scale involved in a given process.