How Reaction Rates Work

Quick Answer

A reaction rate is set by two separate things: how high the energy barrier is, and how the rate responds to concentration. The Arrhenius equation covers the first, k = A x e^(-Ea / RT), and the reaction order covers the second. Activation energy sits inside an exponent, so raising it by 20 kJ/mol at room temperature slows a reaction by a factor of about three thousand, while doubling the pre-exponential factor only doubles it. Order decides shape rather than speed: zero order falls in a straight line, first order decays exponentially, and second order drags out a long tail. Set both here and watch the flask empty at the rate the numbers actually give.

What Does The Arrhenius Equation Tell You?

The Arrhenius equation splits a rate constant into two parts. The pre-exponential factor A counts collisions with the right orientation. The exponential term is the fraction of those collisions carrying enough energy to clear the barrier. Multiply them and you have k. Everything a temperature change does to a rate happens inside that exponential.

• Temperature must be in kelvin, because the exponent divides by T rather than shifting it.
• The base-10 form log k = log A - Ea / (2.303 R T) is a straight line against 1/T, which is how Ea is measured.

Why Does Temperature Matter So Much?

Heating a flask by ten degrees changes the average molecular energy by a few percent. It changes the number of molecules above the barrier by far more, because that population sits in the tail of the distribution. The rate change readout puts a number on it for the current settings. Around 50 kJ/mol at room temperature that number is close to two, which is where the rule of thumb comes from.

How Do You Find The Half-Life Of A First Order Reaction?

Get k from the Arrhenius equation, then divide ln 2 by it. For example, a 60 kJ/mol barrier at 298 K with log A of 11 gives k near 3.0 per second, therefore the half-life is 0.69 / 3.0, about 0.23 seconds. Nothing in that arithmetic mentions concentration, which is what makes first order the easy case. This page doubles as an Arrhenius equation calculator and a half life calculator, because both readouts update from the same three sliders.

• The readouts are base-10 logarithms, so a half-life of 0.23 s reads as -0.64.
• However, the same k gives a different half-life at zero or second order, so check the order before you use ln 2 / k.

Zero vs First vs Second Order: What Changes?

Order describes how the rate responds to how much reactant is left. Zero order does not respond at all, so the line is straight and the reaction stops dead when the reactant runs out. First order halves in equal intervals forever. Second order slows faster than it consumes, so the tail drags. Plotting against half-lives rather than seconds strips out the rate constant and leaves those three shapes.

• Zero order finishes at exactly two half-lives, which no other order does.
• First order is the only one whose half-life ignores the starting concentration.
• Second order doubles its half-life every time, so the last percent takes the longest.

How Do You Read A Half-Life From The Order?

Each order has its own expression, and mixing them up is the most common error in a kinetics problem. First order is ln 2 / k. Zero order is [A]0 / 2k, which shrinks as the run proceeds. Second order is 1 / (k [A]0), which grows. Move the starting concentration slider and watch which of the three readouts responds.

What Does A Catalyst Actually Change?

A catalyst offers a lower barrier by way of a different mechanism. It leaves the reactant and product energies untouched, so the position of equilibrium does not move. Lower the activation energy slider and the half-life collapses while the final conversion stays the same. That is the difference between kinetics and thermodynamics in one slider.

Where Does Chemical Kinetics Get Used?

Shelf life is the everyday answer. An accelerated stability test runs a drug hot for weeks, fits the Arrhenius line, and extrapolates back down to storage temperature to predict how long it lasts. Food works the same way in reverse: a fridge at 4 C rather than 20 C cuts the rate of every spoilage reaction by a large factor, therefore milk keeps for days instead of hours. Chemical kinetics is what turns a barrier height into a date on a label.

• Accelerated testing only works while the mechanism stays the same at the higher temperature.
• For example, a 60 kJ/mol spoilage reaction slows by about a factor of four between 20 C and 4 C.

Common Mistakes