# How to Calculate Rate of Reaction

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The rate at which chemical substances react varies greatly. A nail can take years to rust, whereas explosives detonate in thousandths of a second. Generally, a reaction rate involves the change in the concentration of a substance over a given period of time. You calculate the rate of reaction by dividing the change in concentration by the elapsed time. You can also determine the rate of a reaction graphically, by finding the slope of the concentration curve.

#### TL;DR (Too Long; Didn't Read)

To calculate the rate of a chemical reaction, divide the moles of substance consumed or produced by the number of seconds the reaction took to complete.

## Instantaneous vs. Average Rate

The rate of a reaction can change over time. As a reactant is used up, for example, its rate typically decreases. So you need to distinguish between the instantaneous reaction rate, that is, the rate for a given instant, and the average rate, which determines the rate over the course of the reaction.

## Stoichiometric Dependency of Rates

The reaction rates for different products and reactants depend on one another according to the stoichiometry of the reaction. When you determine the rate for one substance in a reaction, finding the rates for the other substances is simply a matter of multiplying the molar ratios by the rate of the known substance. For example, consider the combustion of methane:

CH4 + 2O2 → CO2 + 2H2O

The reaction consumes two moles of oxygen for every mole of methane and produces one mole of carbon dioxide and two of water. The reaction rate for oxygen is double that of methane, but the rate for CO2 is the same as for methane.

## Positive Reaction Rate

A reaction rate should always be a positive number. When you calculate the reaction rate for a product, a positive rate comes naturally, as the concentration of the substance increases with time. But you multiply the calculation for a reactant by negative one (-1) to make it come out positive, because the concentration of a reactant decreases with time.

## Reaction Rate Assumptions

A few different environmental factors can alter the rate of a reaction, including temperature, pressure and the presence of catalysts. You need to be aware of these factors when doing rate calculations. Under conditions of standard temperature and pressure (STP), you can assume the reaction occurred at room temperature and standard atmospheric pressure.

## Numerical Calculation of Reaction Rate

You can express reaction rates in units of moles per liter per second, or mol × L-1 × s-1. To calculate a reaction rate, simply divide the moles of substance produced or consumed in the reaction and divide by the reaction time in seconds.

For example, .2 moles of hydrochloric acid in 1 liter of water react with the .2 moles of sodium hydroxide, forming water and sodium chloride. The reaction takes 15 seconds. You calculate the reaction rate for hydrochloric acid as follows:

.2 moles HCl ÷ 1 L = .2 moles per liter (mol × L-1 ).
.2 moles per liter ÷ 15 seconds = .0133 mol × L-1 × s-1.

## Graphical Rate Calculation

You can measure and record the concentration of a product or reactant during a reaction. This data typically produces a curve that decreases for reactants and increases for products. If you find the tangent line at any point along the curve, the slope of that line is the instantaneous rate for that point in time and for that substance.