Reaction Orders

(see molarity)

For the reaction :

where:

• is the order of the reaction with respect to
• is the order of the reaction with respect to
• is the overall order of the reaction
• is the rate constant (a function of temperature)

(see rate of change)

The order of a reaction means the relationship between how much reactant and how fast the reaction occurs

• Order 0 means no relation
• Order 1 means linear relation
• Order 2 means quadratic relation
• Etc

Consider a reaction with rate . What happens when we double the concentration of if:

• • No effect
• • Reaction rate doubles
• • Reaction rate quadruples

Experiments were performed using different initial concentrations of reactants, , , and (without or initially present) for the reaction:

initial rates of reaction are determined to be:

What is the order of the reaction with respect to , , and ? What is the value of the rate constant ?

solution
For , be need to find two experiments where the concentration of and do not change, but does. This is the case for experiments 1 and 2.
We see that when changes by a factor of 9, changes by a factor of .
Then with , we find that ("half order").

Similarly for , we find can use experiments 2 and 3.
We see that when changes by a factor of 2, changes by a factor of 4.
Then with , we find that (2nd order).

For , we use experiments 1 and 4.
We see that when changes by factor of , changes by a factor of .
Then with , we find that (0th order).

For the rate constant, use any experiment's values:

When all but one reactant is in excess, we have:

and we write:

then we can find as a function of time by integration.

For a zero-order reaction:

For a first-order reaction:

(see Logarithms, Euler's Number)

For a second-order-equation:

The reaction between ozone () and nitric oxide () proceeds as follows:

The reaction is first order with respect to both and :

Starting with of and of , exactly 75% of the is converted to in 46 seconds at 300k. Determine the reaction rate constant at a constant temperature.

solution
Since , and the stoichiometric ratio is 1:1, we can write:

which turns this into a second-order reaction:

Di--butyl peroxide (DTBP, ) decomposes in the gaseous state into acetone and ethane () according to the reaction:

In an experiment, pure gaseous DTBP is placed inside a closed reactor at an initial pressure of (see Measuring a Gas) and temperature of . Knowing that the rate constant for the decomposition reaction at is , determine the time when the total gas pressure inside the reactor is .

solution
We have:

Because the units of are , we have a first-order reaction:

To determine the final partial pressure of DTBP:

and

subsituting:

The half-life of a reactant is the amount of time it takes for half of the reactant to react