Question

A sample of gaseous acetone is irradiated with monochromatic light having a wavelength of 313 nm. Light of this wavelength decomposes the acetone according to the equation (CH3 )2 CO ---> C2H6 +CO The reaction cell used has a volume of 59 cm3 . The acetone vapor absorbs 91.5% of the incident energy. During the experiment the following data are obtained: Temperature of reaction = 56.7 °C Initial pressure = 102.16 kPa Final pressure = 104.42 kPa Time of radiation = 7h Incident energy = 48.1 × 10-4 J s-1 What is the quantum yield?

Answer 1

(CH3 )2CO       C2H6 + CO

Incident energy = 48.1 × 10-4 J s-1

Time of radiation = 7h = 25200 s

Total energy = 48.1 × 10-4 J s-1 * 25200 s

= 121.21 J

Energy absorbed = 0.915 * 121.21 J

= 110.91 J

wavelength of light = 313 nm = 313x10^-9 m

Energy of 1 photon = hc /

= 6.626x10^-34 * 3x10⁸ / 313x10^-9

= 6.35x10^-19 J

Total number of photons absorbed = 110.91 J / 6.35x10^-19 J

= 1.746x10²⁰ photons

Temperature = 56.7 oC = 329.7 K

Volume = 59 cm3 = 0.059 L

Initial pressure = 102.16 kPa = 1.008 atm

Final pressure = 104.42 kPa = 1.0305 atm

Initial moles = PV / RT

= 1.008 * 0.059 / 0.0821*329.7

= 0.00219

Final moles = 1.0305*0.059 / 0.0821*329.7

= 0.00224

Moles of acetone dissociated = 0.00224 - 0.00219

= 5x10^-5

Molecules of acetone dissociated = 5x10^-5 * 6.023x10²³

= 3.0115x10¹⁹ molecules

Quantum yield = molecules decomposed / photons absorbed

= 3.0115x10¹⁹ / 1.746x10²⁰

= 0.1724

= 17.24 %