Question

Indicate the order of reaction consistent with each observation. \begin{equation} \begin{array}{l}{\text { a. A plot of the concentration of the reactant versus time yields a }} \\ {\text { straight line. }} \\ {\text { b. The reaction has a half-life that is independent of initial }} \\ {\text { c. A plot of the inverse of the concentration versus time yiclds a }} \\ {\text { straight line. }}\end{array} \end{equation}

Short answer

Observation a and b indicate a first-order reaction; observation c indicates a second-order reaction.

Step-by-step solution

- Observation a Analysis

If a plot of the concentration of the reactant versus time yields a straight line, this suggests that the concentration of the reactant decreases linearly over time. This behavior is characteristic of a first-order reaction, in which the rate of reaction is directly proportional to the concentration of the reactant.

- Observation b Analysis

When the half-life of a reaction is independent of the initial concentration, it implies that the half-life remains constant. This is a property specific to first-order reactions.

- Observation c Analysis

If a plot of the inverse of the concentration versus time yields a straight line, this indicates that the reaction rate is inversely proportional to the reactant concentration as it changes over time. This is characteristic of a second-order reaction.

Key concepts

First-Order Reaction

In a reaction where the rate is directly proportional to the concentration of a single reactant, we are dealing with what's known as a first-order reaction. This concept can be a bit abstract, so let's simplify it. Picture this: you're drinking a milkshake. The more milkshake you have, the faster you can drink it because you get more with each sip. If you had less milkshake, you'd sip it slower because there's less to grab each time. Similarly, in a first-order reaction, the rate at which the reactants turn into products speeds up or slows down depending on how much is left—more reactant, faster reaction; less reactant, slower reaction.

Linear Relationship

Now, to nail down this concept, a plot showing the amount of reactant over time for a first-order reaction gives you a straight line. This is because the rate at which the reactant's concentration decreases is constant when considered on a logarithmic scale. Imagine our milkshake again—if you're drinking at a steady rate, the level of milkshake drops consistently over time.

Constant Half-Life

Another key point is half-life—the time it takes for half of the reactant to be used up. For a first-order reaction, this half-life is constant; it doesn't matter if you start with a full cup or half a cup of milkshake, the time to drink half remains the same. This equal half-life, regardless of starting amount, is unique to first-order reactions.

Second-Order Reaction

Moving onto another type of reaction kinetics, we have the second-order reaction, which is like the more complex cousin of the first-order reaction. Here, the reaction rate depends on the concentration of two reactants or the square of the concentration if just one reactant is involved. This might sound complex, but we can break it down.

Inverse Proportionality

Put simply, if a second-order reaction has only one reactant, doubling the concentration of the reactant will make the reaction rate go up by four times—not just double, as you might expect. It's a bit like trying to arrange a meet-up with a friend: the likelihood of it happening depends not just on your schedule but on your friend's as well. So, if both of you have more free time (higher concentration), the meet-up (reaction) is much more likely to happen swiftly.

When graphing reactant concentration versus time for a second-order reaction, you won't get a simple straight line, but plotting the inverse of concentration versus time would yield one. It's because the relationship between the reaction rate and the reactant concentration is inversely proportional when plotted normally. This means that as the concentration of the reactant increases, the time it takes for the reaction to proceed decreases at a rate that is quicker than you'd guess.

Reaction Kinetics

Reaction kinetics is a term used to describe the speed of chemical reactions and the factors that influence this speed. Think of it as the study of how quickly ingredients in a recipe turn into a delicious cake, or how long it takes for certain chemicals to react in fireworks to create a dazzling display. It's all about the 'how fast' and 'what influences the speed' of reactions.

Measuring Reaction Rates

The speed of a chemical reaction can change based on several factors, including the concentration of reactants (like we've discussed in first and second-order reactions), temperature, and the presence of catalysts. Measuring how these factors affect reaction rates helps chemists to control and optimize reactions, whether it's in making pharmaceuticals or ensuring your car's engine runs efficiently.

Chemists measure these reaction rates in a variety of ways, such as tracking changes in concentration over time, observing energy changes, or even using color changes in a solution. By understanding reaction kinetics, chemists can predict how a reaction will progress, speed it up or slow it down, and harness the chemical changes to our benefit.