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 units of minutes is \(1.1 \mathrm{~min}^{-1}\).

Step-by-step solution

Identify the Conversion Factor

There are 60 seconds in a minute. Therefore, to convert from seconds to minutes, you divide the number of seconds by 60. The conversion factor between seconds and minutes is therefore \( \frac{1}{60} \) or 0.01667.

Apply the Conversion Factor

To change the units of the rate constant from seconds to minutes, multiply the rate constant in seconds by the conversion factor. In mathematical terms, this would be \( 66 \mathrm{~s}^{-1} \times \frac{1}{60} = 1.1 \mathrm{~min}^{-1} \).

Write the Final Answer

The rate constant of the first-order reaction in units of minutes is therefore \( 1.1 \mathrm{~min}^{-1} \).

Key concepts

Chemical Kinetics

Understanding chemical kinetics is akin to figuring out how a clock ticks, but instead of seconds and minutes, chemists are looking at how fast reactions proceed. At its core, chemical kinetics deals with studying the speed or rate at which chemical reactions occur. This rate is influenced by various factors such as temperature, concentration of reactants, and the presence of a catalyst.

For instance, if we take a first-order reaction where the rate depends linearly on the concentration of one reactant, knowing the rate constant—a number that quantifies the speed of the reaction—becomes essential. This constant is unique for every reaction and conditions under which the reaction occurs. In an analogy for ease of understanding, if the reaction were a race, the rate constant would represent the average speed of runners, influencing how quickly they reach the finish line.

A higher rate constant would mean a faster reaction, analogous to a faster runner. And just like planning race strategies changes with the distance of the race, chemists might employ different techniques or consider different conditions based on the reaction's rate constant to control or predict the progression of the reaction.

Unit Conversion

When we talk about unit conversion in chemistry, we're looking at the translation of quantities from one measurement system to another, ensuring that we're comparing apples to apples, instead of apples to oranges. Applied to our first-order reaction rate constant, it's vital to ensure that the units we use are consistent with the rest of the calculations in the problem or experimental setup.

Units such as seconds \(\mathrm{s^{-1}}\) and minutes \(\mathrm{min^{-1}}\) are essential to understand the time scale of a reaction. For those new to unit conversion, it may seem challenging, but it follows a logical method. Using the correct conversion factors, as in our example of converting seconds to minutes, plays a crucial role in ensuring accurate calculations.

It's just like converting currency when traveling to a different country; you want to know precisely how much value you're getting after the exchange. Similarly, scientists need to be fluent in converting units to make sure their experiments 'currency' aligns with their expectations and understanding of the reaction in question.

Rate Laws

Rate laws are equations that quantify the relationship between the concentration of reactants and the rate of a chemical reaction. They are the formulas that let chemists put numbers to their predictions and solutions. Understanding a rate law is crucial because it helps predict how concentrations will change over time and under various conditions.

For a first-order reaction, the rate law can be expressed simply: the rate is directly proportional to the concentration of one reactant. This means that if you double the amount of reactant, the rate of reaction will also double. The rate law for a first-order reaction is typically written as \(\text{rate} = k[\text{A}]\), where \(k\) is the first-order rate constant and \[\text{A}\] represents the concentration of the reactant.

In our example, understanding the rate law allows us to seamlessly convert the rate constant from one set of time units to another, preserving the integrity of the scientific calculations. Just as a recipe might require adjustment when switching from a tablespoon to a teaspoon, chemists must adjust their rate constants to match the units used in their 'recipe' for studying reactions.