Rate equations and orders
Rate equations and orders
- A rate equation shows how the rate depends on the concentrations.
- The order is the power of each concentration.
- It can only be found by experiment, not from the balanced equation.
The rate equation
$$\text{rate} = k\,[\text{A}]^m[\text{B}]^n$$
- $m$ and $n$ are the orders (each 0, 1 or 2); the overall order is $m + n$.
- $k$ is the rate constant.
Practice
The rate equation of a reaction:
Orders must be measured experimentally; they cannot be deduced from the stoichiometric equation.
Practice
The overall order of a reaction is:
Add the orders with respect to each reactant to get the overall order.
Finding the order
- initial rates: change one concentration at a time. Double $[\text{A}]$ → rate ×2 = first order; rate ×4 = second; rate unchanged = zero.
- graphs: a rate–concentration graph is flat (zero), a straight line through the origin (first), or an upward curve (second).
Practice
If doubling [A] doubles the rate, the order with respect to A is:
Rate ∝ [A]¹, so doubling [A] doubles the rate — first order.
Practice
A rate–concentration graph that is a straight line through the origin shows:
First order gives a straight line through the origin; zero order is flat; second order is a curve.
You've got it
Key idea
- $\text{rate} = k[\text{A}]^m[\text{B}]^n$; overall order $= m + n$; found only by experiment
- initial rates: double a concentration — rate ×2 (1st), ×4 (2nd), unchanged (0)
- rate–concentration graph: flat (0), line through origin (1st), curve (2nd)