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Question

Many chemical reactions can be brought about by the absorption of light of suitable wavelength. Such reactions are known as photochemical reactions. In a photochemical reaction, only the first step is photochemical and the rest are thermal. The energy of the absorbed photon is used for the chemical conversions. For the photochemical combination of hydrogen and chlorine to form hydrogen chloride, the following mechanism was suggested.
Cl2(hv)2Cl . . . . . . (i)
Cl+H2k1HCl+H
. . . . . . (ii)
H+Cl2k2HCl+Cl . . . . . . (iii)
2Clk3Cl2 . . . . . . (iv)
In the photochemical reaction of H2 and Cl2,Cl2 absorbs at wavelength of 488 nm.When the Cl2 gas is irradiated with a 60 watt lamp that emits radiation with 80% efficiency, 4.1 mmol of HCl were formed in 10 sec. Calculate the quantum yield for the reaction. (write the value to the nearest integer)

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Solution

H2+Cl22HCl
Energy of one photon E=hcλ=6.626×1034×3×108488×109
E=0.040733×1017J
Energy of one mol of photon =0.040733×1017×6.023×1023=0.24533×106J/mol=2.4533×105J/mol
Energy of one mmol of photon =245.33J/mmol
Power of 60 watt corresponds to 60 J per second. For 10 sec, 600 J of energy is emitted. This corresponds to
600245.33=2.4456 mmol of photons.
For 80 % efficiency, the number of mmol of photon =2.4456×80100=1.9565 mmol
1 mmol of photon should theoretically give 2 mmol of HCl
Quantum yield =4.12×1.9565=1.05

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