## Ozone Library

Half-life of Ozone

## Typical **Gaseous Ozone** Half-life time as a Function of Temperature

Half-life time | Temp |
---|---|

∼ 3 months | -50 ºC |

∼ 18 days | -35 ºC |

∼ 8 days | -25 ºC |

∼ 3 days | 20 ºC |

∼ 1.5 hours days | 120 ºC |

∼ 1.5 seconds | 250 ºC |

## Typical **Dissolved in Water Ozone** (PH=7) Half-life time as a Function of Temperature

Half-life time | Temp |
---|---|

∼ 30 minutes | 15 ºC |

∼ 20 minutes | 20 ºC |

∼ 15 minutes | 25 ºC |

∼ 12 minutes | 30 ºC |

∼ 8 minutes | 35 ºC |

## 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; is the concentration (number of the molecules per unit volume):

n= (M /μV)* N(2)_{A }

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 time into the volume and calculated per unit volume:

q= (m/μV) N(3)_{A}

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

## 2. Closed volume

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

n= (

n/1+_{o}n) (4)_{o }k t

where is the initial concentration. Using (2):

n(5)_{o}= (M_{o}/ μV)* N_{A}

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 factor of two, see Eq.(6). Comparing Eqs. (4) and (6) one obtains:

τ= 1 /

nk (7)_{o }

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(8)_{A }M_{o }k) = k1 / M_{o}

**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(10)_{o }/ τ

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

m = M(11)_{o }/ τ

**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.