AP Chem Integrated Rate Law

Summary

In this video, Mrs. Oliver introduces integrated rate laws, a key concept in AP Chemistry. Unlike differential rate laws, which relate the concentration of reactants to reaction rates, integrated rate laws focus on the relationship between concentration and time. The video covers three types of integrated rate laws—zero, first, and second order—explaining how to identify them using graphs. Mrs. Oliver emphasizes recognizing linear relationships in these graphs to determine reaction order and calculating rate constants (K) from slope values. Practical graphing techniques and calculations are also demonstrated.

Takeaways

• 📚 Integrated rate laws relate concentration to time, unlike differential rate laws which relate concentration to reaction rate.
• 📊 There are three integrated rate laws to know: zero-order, first-order, and second-order.
• 📉 For a zero-order reaction, plotting concentration versus time gives a linear relationship, where the slope is negative K (the rate constant).
• 📝 Zero-order reactions follow the equation: [A] = -Kt + [A]₀, which is in slope-intercept form (Y = MX + B).
• 🔢 For a first-order reaction, a linear graph is obtained by plotting the natural log (ln) of concentration versus time.
• 📈 The first-order integrated rate law is: ln[A] = -Kt + ln[A]₀, also in slope-intercept form.
• 🧮 Second-order reactions give a linear plot when time is graphed versus the inverse of concentration (1/[A]).
• 🔍 To determine the reaction order, graph the data three ways: concentration versus time, ln(concentration) versus time, and 1/concentration versus time, and see which graph is linear.
• 🧠 For a first-order reaction, the slope of the ln(concentration) vs. time graph equals -K, and calculating this slope gives the rate constant.
• 💡 Use the slope of the linear graph to find K, with the rate constant being positive even if the slope is negative in the calculation.

Q & A

What is the difference between differential rate laws and integrated rate laws?

Differential rate laws show the relationship between the concentration of reactants and the rate of reaction, while integrated rate laws focus on the relationship between concentration and time.

How do you identify a zero-order reaction using a graph?

For a zero-order reaction, if you graph concentration versus time and get a straight line with a constant slope, the reaction is zero-order.

What is the significance of the slope in an integrated rate law graph?

The slope of the line in an integrated rate law graph represents the rate constant (K). In a zero-order reaction, the slope is the rate constant, while in a first-order or second-order reaction, it corresponds to the natural log or the inverse of the concentration.

How can you identify a first-order reaction from a graph?

A first-order reaction can be identified if the graph of time versus the natural log of the concentration gives a straight line.

What do the variables in the zero-order integrated rate law equation represent?

In the zero-order integrated rate law equation [A] = -Kt + [A]₀, [A] is the concentration at time t, K is the rate constant, and [A]₀ is the initial concentration.

What is the equation for the first-order integrated rate law?

The equation for the first-order integrated rate law is ln[A] = -Kt + ln[A]₀, where [A] is the concentration at time t, K is the rate constant, and [A]₀ is the initial concentration.

How do you determine if a reaction is second-order from a graph?

For a second-order reaction, a graph of time versus 1/[A] should yield a straight line if the reaction follows second-order kinetics.

What steps do you follow to determine the order of a reaction using graphing techniques?

You graph time versus concentration, time versus the natural log of concentration, and time versus 1/concentration. The graph that results in a straight line indicates the order of the reaction.

How is the rate constant (K) calculated from a graph?

The rate constant (K) is calculated by finding the slope of the linear graph that corresponds to the correct order of the reaction (e.g., concentration, natural log of concentration, or 1/concentration).

Why is it important to double-check the graphs for first- and second-order reactions?

Double-checking ensures that the reaction order is correct. For example, if the natural log of concentration versus time gives a straight line, it suggests a first-order reaction. However, you should also verify that the second-order graph does not give a linear relationship.