Orders of Rates and Concentration Dependencies

Outline

• Concentrations and Rates
  • Graphical Methods
• Practice with Concepts
• Discussion Questions
• Optional Website Reading

Concentrations and Rates

We distinguish between different reaction situations use the order of a reaction to classify it. If [C] is the concentration of a species in a reaction, the reaction order for [C] can be:

• zeroth order: rate = k[C]⁰ = k. The rate is constant.
• first order: rate = k[C]¹. The rate decreases direction as the concentration [C] decreases.
• second order: rate = k[C]ⁿ. The rate decreases as the concentration, taken to some power n, decreases.

This gives us a brief working introduction to the reality that rates of reactions can be constant, or change in different ways. When the rate of concentration change depends on the actual moment-to-moment value of the concentration (or some power of that value), we need to use calculus to complete the mathematics...or we can use a quick graphical method to help us sort it out.

Graphical methods for analyzing reaction rates

In a real experimental situation, we may get data like this for a reactant "C":

In this spreadsheet, the leftmost column shows elapsed time in seconds. The [C] column records the concentration in moles/liter of one of the reactants in a particular reaction. We've gotten the spreadsheet to do some extra calculations for us, figuring out the ln[C] and 1/[C] values as well, in case we need them.

If we plot the concentration [C] values as a function of, we see that concentration drops quickly at first, but then slows down:

The changing slope of the reaction data tells us that the rate itself changing over time. Reaction rates can vary as the order (exponent) of the concentration. The rate isn't constant, so this is not a "zeroth" order reaction. We can get the rate at any moment from the slope of the line tangent to the curve at that point...but there may be an easier way to make some conclusions from our data.

Let's go ahead and plot the data as ln[C] against time and 1/[C] against time. The plot will be a straight line for the correct order of the reaction we are studying.

Since the plot for ln[C] vs. t is a straight line, our reaction is a first order reaction.

This preliminary survey lets us see the variety of reaction rates, since these rates can depend on several factors. For now, we will focus on how changing concentrations affects the rate of a reaction.

Practice with the Concepts

No practice yet.

Discussion Questions

Check out the UC Davis CHEMWiki page on the Rate Law for more discussion of how rate laws work.

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