A container contains a 200 mL of 100% proof alcohol (i.e.,it has 50% ethyl alcohol and 50% water by volume)at the boiling point of the alcohol.How long does it take to distill (boil)all the alcohol if heat is supplied at a rate of 100 W? (The density and latent heat of vaporization of ethyl alcohol are 0.81 g/cm³,and 879 kJ/kg.) A)712 s B)1110 s C)450 s D)1450 s E)950 s

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Quizplus · Accepted Answer

First, calculate the mass of ethyl alcohol in the container. Given that the container has 200 mL of 100% proof alcohol, which means it has 50% ethyl alcohol by volume, the volume of ethyl alcohol is 100 mL or 0.1 L. The density of ethyl alcohol is 0.81 g/cm³, so the mass (m) of ethyl alcohol is:$$ m = density \times volume = 0.81 \, \text{g/cm}^3 \times 100 \, \text{cm}^3 = 81 \, \text{g} = 0.081 \, \text{kg} $$The latent heat of vaporization (L) of ethyl alcohol is 879 kJ/kg. The energy (Q) required to vaporize the alcohol is:$$ Q = m \times L = 0.081 \, \text{kg} \times 879 \, \text{kJ/kg} = 71.199 \, \text{kJ} $$Since power (P) is energy per unit time and is given as 100 W (or 0.1 kW), the time (t) required to supply this energy is:$$ t = \frac{Q}{P} = \frac{71.199 \, \text{kJ}}{0.1 \, \text{kW}} = 711.99 \, \text{s} $$Rounding to the nearest whole number gives approximately 712 seconds.

A Container Contains a 200 ML of 100% Proof Alcohol