Calculating Rates

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Determining Reaction Rates

The rate of a reaction is expressed three ways:

  • The average rate of reaction.
  • The instantaneous rate of reaction.
  • The initial rate of reaction.

Determining the Average Rate from Change in Concentration over a Time Period

We calculate the average rate of a reaction over a time interval by dividing the change in concentration over that time period by the time interval. For the change in concentration of a reactant, the equation, where the brackets mean "concentration of", is

Average rate equals the negative of the change in concentration divided by change in time

Note: We use the minus sign before the ratio in the previous equation because a rate is a positive number. We do not need the minus sign when calculating average rates from products.

Average rate equals the negative of delta concentration of reactants divided by delta time or equals delta conc of products divided by delta time

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Determining the Instantaneous Rate from a Plot of Concentration Versus Time

An instantaneous rate is the rate at some instant in time. An instantaneous rate is a differential rate: -d[reactant]/dt or d[product]/dt.

We determine an instantaneous rate at time t:

  • by calculating the negative of the slope of the curve of concentration of a reactant versus time at time t.

  • by calculating the slope of the curve of concentration of a product versus time at time t.

Graph of concentration vs time used to determine an instantaneous rate Top

Determining the Initial Rate from a Plot of Concentration Versus Time

The initial rate of a reaction is the instantaneous rate at the start of the reaction (i.e., when t = 0). The initial rate is equal to the negative of the slope of the curve of reactant concentration versus time at t = 0.

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