Question

A man consumes 3000 kcal, losing half as energy through evaporating water. How many kilograms of water evaporate?

a) 0.17 kg
b) 0.34 kg
c) 0.50 kg
d) 0.68 kg

Answer 1

To find out how many kilograms of water evaporate, we need to calculate half of the energy consumed and then convert it to mass using the heat of vaporization of water.

Step-by-step explanation:

To find out how many kilograms of water evaporate, we need to calculate half of the energy consumed, which is 3000 kcal divided by 2. This gives us 1500 kcal. We know that 1 kcal is equivalent to 4.18 kJ, so 1500 kcal is equal to 1500 x 4.18 kJ. This equals 6270 kJ.

The heat of vaporization of water is 40.7 kJ/mol. To find the mass of water evaporated, we can use the equation:

Mass of water evaporated = Heat of vaporization / Energy required

Plugging in the values, we get:

Mass of water evaporated = 6270 kJ / 40.7 kJ/mol

Using the molar mass of water (18.015 g/mol), we can convert the mass of water evaporated from moles to kilograms. The correct option is B) 0.34 kg.