# D32.1 Reaction Rate

The **rate of a chemical reaction** is usually defined as *the change in concentration of a reactant or a product per unit time. *Rates can be experimentally determined by measuring the concentration of a reactant or a product at a series of fixed time intervals after the reaction has started.

Often, it is easier to measure some property related to a substance’s concentration. For example, for a reaction involving a colored reactant, light absorption can be measured at different times after the start of the reaction. Then the reactant’s concentration at a given time can be calculated from the proportionality between light absorption and concentration.

Consider the decomposition reaction of cyclobutane in the gas phase:

_{4}H

_{8}(g) ⟶ 2 C

_{2}H

_{4}(g)

The rate at which cylcobutane decomposes can be expressed in terms of the rate of change of its concentration:

In this equation, Δ[C_{4}H_{8}] represents the change in concentration of cyclobutane during the time interval Δ*t*. The minus sign in front of the fraction is there because *reaction rate is defined to be positive*. The reactant concentration decreases as the reaction proceeds, making Δ[C_{4}H_{8}] a negative quantity, so a negative sign is needed to make the calculated rate positive.

The table below provides an example of data collected during the decomposition of C_{4}H_{8}. Notice that the reaction rate varies with time, decreasing as [C_{4}H_{8}] decreases.

Time (s) |
[C_{4}H_{8}] (M) |
Δ[C_{4}H_{8}] (M) |
Δt (s) |
Rate of decomposition (M/s) |

0.0 | 0.240 | |||

20.0 | 0.120 | -0.120 | 20.0 | 0.00600 |

40.0 | 0.060 | -0.060 | 20.0 | 0.0030 |

60.0 | 0.030 | -0.030 | 20.0 | 0.0015 |

80.0 | 0.015 | -0.015 | 20.0 | 0.00075 |

An **average rate** over a given time period can be calculated using the concentrations at the beginning and the end of the period. For example, the average rate for the first and last 20-second period are:

*The rate of reaction at* *any specific time* is known as the **instantaneous rate**. The *instantaneous rate when the reaction starts (at t _{0})*, is the

**initial rate**. The instantaneous rate of a reaction may be determined one of two ways:

- If concentration changes can be measured at very short time intervals, then average rates over these very short time intervals provide reasonably good approximations of instantaneous rates.
- If we plot reactant concentration vs. time, the instantaneous rate at any time
*t*is given by the negative of the slope of a straight line that is tangent to the curve at that time.

**Exercise: Reaction Rates from Concentration Graph
**

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