Half-life of Ozone

The half-life of ozone refers to the amount of time required for half of a given quantity of ozone to decay into oxygen. Ozone is an unstable gas and readily decomposes into oxygen. Therefore, the half-life of ozone is an essential factor to consider when determining its effectiveness in various applications.

CHANGES IN OZONE OVER TIME

1. General equation

The equation that describes the temporal evolution of the ozone concentration has the following form:

dn/dt = −kn² + q             (1)

Where t is the time, k is the reaction rate constant, which is independent of concentration but probably, depends on the temperature, and n is the concentration (number of the molecules per unit volume):

n= (M /μV)* N_A                 (2)

μ is the molar weight of ozone, M is the mass of ozone inside the volume, V, in a given moment of time, NA is the Avogadro number

In Eq.(1), is the number of molecules delivered per unit of time into the volume and calculated per unit volume:

q= (m/μV) N_A       (3)

Where m is the mass of ozone delivered into volume, V, per unit of time.

2. Closed volume

Consider the case of q = 0. For such a case, integration of Eq. (1) yields

n= (n_o/1+n_o k t)              (4)

where is the initial concentration. Using (2):

n_o = (M_o/ μV)* N_A         (5)

Where M0 is the initial mass of ozone. Eq.(4) can be rewritten as

n= n_o/ (1 + t / τ) (6)

where we introduced the time scale parameter τ: when t =τ, the concentration of molecules (and the mass of ozone, for a given volume) decreases by a factor of two. See Eq.(6). Comparing Eqs. (4) and (6) one obtains:

τ= 1 / n_o k         (7)

Since k is independent of the concentration, we arrive at an important conclusion: the parameter τ depends on the initial concentration and, for a given volume and pressure, on the initial mass, M0.

τ= (μ / (N_A M_o k) = k1 / M_o         (8)

Stationary regime

Inspecting Eq.(1), one can conclude that the concentration does not change when

q = kn²            (9)

When Eq.(9) is satisfied, the rate of concentration changes, dn/dt, becomes zero, see Eq.(1). Realizing that the concentration is maintained to be constant in time, i.e., and using Eqs. (7) we obtain from (9) that

q = n_o  / τ          (10)

Using Eqs. (3) and (5) one can rewrite (10) in terms of mass

m = M_o / τ        (11)

Conclusion

Thus, to maintain a given mass of ozone, M0, within a fixed volume at a given temperature, one should deliver ozone with the rate (mass per unit time) given by Eq.(11). The time scale parameter m τ on the right-hand side of (11) is determined from an independent experiment. This experiment is to observe a decrease in the ozone mass with time in the same closed volume. The parameter τ coincides with the time corresponding to the ozone mass. It should be stressed that, for a given volume and temperature, the measured value of 0 M M= / 2 τ is strictly linked to the initial mass of ozone M0, which should be common for both experiments.