How long does it take to saturate H2O with O3
The solubility of ozone in water as per one website is:



First thing is to establish which curve you need. In 1 m$^3$ gas you have 70 L ozone:

$\frac{70\ L\ \ce{O3}}{1\ m^3}\frac{1\ mol}{0.082\cdot 298\ L}\frac{16\cdot 3\  g\ \ce{O3}}{1\ mol}= 138\ g\ \ce{O3}/m^3$

Let us take the curve of 150 g/m$^3$ which has an ozone solubility of 30 mg/L water. 
Then:

$\frac{30\cdot 10^{-3}\ g\ \ce{O3}}{1\ L\ \ce{H2O}}\frac{1\ mol}{16\cdot 3\ g\ \ce{O3}}\frac{0.082\cdot 298\ L}{1\ mol}\frac{1\ min}{5\cdot 0.07\ L\ \ce{O3}}= 0.044\ min$

Which is about 3 seconds.