In producing chlorine through electrolysis, 100 W power at 125 V is being consumed. The liberation of chlorine

Question

In producing chlorine through electrolysis, 100 W power at 125 V is being consumed. The liberation of chlorine per min is: (ECE of chlorine is $0.367 	imes 10^{-6} 	ext{ kg/C}$)

Accepted Answer

Given:
Power ($P$) = 100 W
Voltage ($V$) = 125 V
Time ($t$) = 1 min = 60 s
Electrochemical Equivalent ($Z$) = $0.367 	imes 10^{-6} 	ext{ kg C}^{-1} = 0.367 	ext{ mg C}^{-1}$

First, we find the current ($I$) using the relation $P = VI$:
$I = \frac{P}{V} = \frac{100}{125} = 0.8 	ext{ A}$

Now, calculate the total charge ($Q$) passed in 1 minute (60 seconds):
$Q = I 	imes t = 0.8 	ext{ A} 	imes 60 	ext{ s} = 48 	ext{ C}$

According to Faraday's First Law of Electrolysis, the mass ($m$) liberated is given by:
$m = Z 	imes Q$
$m = (0.367 	imes 10^{-6} 	ext{ kg C}^{-1}) 	imes 48 	ext{ C}$
$m = 17.616 	imes 10^{-6} 	ext{ kg}$

Converting kilograms to milligrams:
$m = 17.616 	imes 10^{-6} 	imes 10^{6} 	ext{ mg} \approx 17.6 	ext{ mg}$

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