Graphs of rate laws

[Baoying Li 1B]

Hey, can someone describe the characteristics of the graph of rate laws? Like what’s the between the first order and the second order? What about the zero order?

[Parker Smith]

A first order rate law forms a linear relationship when the natural log of [A] is plotted over time. A second d order rate law forms this relationship when 1/[A] is graphed over time. We derive these relationships from the integrated rate laws of each order of reaction. Since a 0th order rxn doesn't depend on the concentration, the relationship of simply [A] over time gives a linear graph

[Aarja Pavade 1H]

All of the graphs will be linear, but the slopes will vary. For instance, the graph of a first-order and zero-order reaction will have a decreasing slope of -k while a second-order reaction will have an increasing slope of k.

[405268063]

For zero order, the rate law makes a linear graph, which means that the rate just goes at constant k (slope). For first order reactions, the graph is also linear if you plot ln[A] versus time. For second order reactions, the graph is linear is you plot 1/[A] versus time.

[MeeraBhagat]

Depending on the different rate laws for the different ordered reactions, plotting the corresponding term on the y-axis against time will yield a straight line instead of a curve. For example, if given a graph with the y-axis as 1/ln[A] plotted against time, and the graph is a straight line, then you know it is a second order reaction. The same goes for a first and zero order reactions with y-axis ln[A] and [A], respectively.

[Gabriella Bates 2L]

The graphs for the different rate laws will all be linear, but what is plotted on the y axis varies. For a 0th order reaction, [A] vs time is linear, and the slop is equal to -k. For a 1st order reaction, ln[A] vs time is linear and the slope is equal to -k. For a 2nd order reaction, 1/[A] vs time will be linear and the slope is equal to k. The differences are important because looking a the graph can help us determine the order of the rate law for a given reaction.

[Justin Quan 4I]

Here's a diagram depicting the graphs of the three rate laws, zeroth, first, and second order reactions.

[105335337]

If you graph [R] v time & get a straight line: zero order

if you graph ln[R] v time & get a straight line: first order

if you graph 1/[R] v time & get a straight line: second order

[pmokh14B]

The first order graph is of ln[A] vs time, and the second-order is 1/[A], whichever is linear is the order of the reaction.