One litre of mixture of `O_2` and `O_3` at STP was allowed to react with an excess of acidified solution of KI. The iodine liberated required 40 " mL of " `(M)/(10)` sodium thiosulphate solution for titration. What is the mass per cent of ozone in the mixture? Ultraviolet radiation of wavelength 300 nm can decompose ozone. Assuming that one photon can decompose one ozone molecule, how many photons would have been required for complete decomposition of ozone in the original mixture?

Explanation

`O_(3) + 2Kl + H_(2)O to 2KOH + l_(2) + O_(2)`
`2Na_(2)S_(2)O_(3) + l_(2) to Na_(2)S_(2)O_(3) + l_(2) to Na_(2)S_(4)O_(6)+2Nal`
Millimoles of `O_(3)` = Millimoles of `l_(2) = 1//2 xx " Millimoles of " Na_(2)S_(2)O_(3) `
` = 1//2 xx 40 xx 1/10 = 2 ` millimoles
= `0.002` moles
Total moles of `O_(3)" and " O_(2)` in the mixture .
PV = n RT
` 1 xx 1 = n xx 0.0821 xx 273`
` n = 0.044`
Moles of `O_(2) = 0.044 - 0.002 = 0.042`
`W_(O2) = 0.042 xx 32 g = 1.344 g `
`W_(O3) = 0.002 xx 48 g = 0.096 `g
`:. % " of " O_(3) = (0.096)/(1.144) xx 100 = 6.7 %`
No. of photons required for decomposition of Ozone molecules ` = 0.002 xx 6.023 xx 10^(23) `
` = 1.2 xx 10^(21)`