The Dependence of Rate on Concentration

During a chemical reaction:

• The reaction often starts out at a fast rate and then slows down as time goes on
• Also, the concentration of reactants also decreases over time (as they are consumed in the reaction)
• We can speed the reaction back up by adding more reactant(s), i.e. increasing the concentration of reactant(s)

Consider the following reaction of ammonium ion (NH₄⁺) with Nitrite ion (NO₂^-):

NH₄⁺(aq) + NO₂^-(aq) -> N₂(g) + 2H₂O(l)

• As far as the stoichiometry is concerned, NH₄⁺ NO₂^- N₂. Therefore, we could monitor the reaction rate by monitoring the changes in concentration, over time, of NH₄⁺ or NO₂^-, or by the volume of the released N₂ gas; all of these rates will be equal

How does this data look?

• Situation #1: let's keep the concentration of nitrite ion constant, and vary the concentration of ammonium ion (You might be asking how could we do this if we have an ionic compound of ammonium nitrite. Surely we would end up adding equal amounts of each ion. However, we could add a different ammonium salt, and it's counter ion could be unreactive and is thus a spectator ion in the reaction. The net result would be the addition of ammonium ion)

• The general relationship between concentration and initial reaction rate for the NH₄⁺ ion, is that the reaction rate is directly proportional; if we double the concentration of NH₄⁺ ion, then the reaction rate doubles
• Situation #2: let's keep the concentration of ammonium ion constant, and vary the nitrite ion concentration

• The general relationship is pretty much the same thing as seen when varying the ammonium ion. In other words, the reaction rate is directly proportional to the concentration of nitrite ion.

Conclusion:

• For example, if the concentration of ammonium ion were doubled, and the concentration of nitrite ion were doubled, we would expect the initial reaction rate to increase by a factor of 4
• We can write an exact equation by introducing a proportionality constant, k:

How is the rate constant, k, determined for a particular reaction?

• We need to know the particular rate law for a reaction
• We need a set of data that provides us with reaction rate information for different concentrations of reactant(s)
• Rearranging the rate law for the above reaction to solve for k:

• Let's try one of the data points from above:

• k is a constant, and the same value for k is found when using any data point from above
• If we know the rate law for a particular reaction, and the rate constant, k, then we can determine the instantaneous initial reaction rate for any given concentration of reactants

Rate laws have the general form of:

Rate = k [reactant 1]^m [reactant 2]ⁿ …

• The exponents m, and n, are called reaction orders
• The sum of the reaction orders (m + n +…) is the overall reaction order
• In the above reaction of ammonium ion with nitrite ion, the reaction order with respect to ammonium is 1 (or first order), and the reaction order with respect to nitrite is 1 (or first order). The overall reaction order is 2 (or second order overall)

• Reaction orders are commonly 0, 1 or 2. However, they can also be fractional, or negative

The units of the rate constant, k, depends upon the overall reaction order of the rate law

• In the above reaction of ammonium ion with nitrite ion, the overall reaction order was second order:

• k will therefore have units of:

• Units of k for a first order overall reaction order would be:

• Rate laws (Reaction Orders) must be determined experimentally

• The key is to characterize the initial rates of reaction for different concentrations of reactants
• If a reaction is zero order for a particular reactant, then changing it's concentration will have no effect upon the reaction rate

• If a reaction is first order for a particular reactant, then changing it's concentration will cause a direct, proportional change in the reaction rate. In other words, doubling the concentration will double the reaction rate, etc.
• If a reaction is second order for a particular reactant, then changing its concentration will cause an exponential change in the reaction rate. In other words, doubling the concentration will result in a four-fold increase (2²) in reaction rate; tripling the concentration will result in a nine-fold increase (3²) in reaction rate.