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

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

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

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

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