Question

The human body obtains 835 kJ of energy from a chocolate chip cookie. If this energy were used to vaporize water at 100 ∘C, how many grams of water could be vaporized? The heat of vaporization of water at 100 ∘C is 40.7 kJ/mol. Assume that the density of water is 1.0 g/mL.

Answer 1

Amount of water that can be vaporized = 369 g

Step-by-step explanation:

Heat content of the cookie (q) = 835 kJ

Latent heat of vaporization of water (ΔHvap) = 40.7 kJ/mol

Density of water = 1 g/ml

Calculation:

Heat content of cookie = Heat absorbed by water

q = n(ΔHvap)

n = moles of water

n = q/ΔH = 835 kJ/ 40.7 kJ/mol = 20.516 moles

Molar mass of water = 18 g/mol

Mass of water = moles * molar mass = 20.516 moles * 18 g/mol = 369.3 g

Answer 2

If there is 1 mol vaporized per 40.7 kJ of heat, that means 20.516 mol of water can be vaporized, found by the equation 835 kJ/40.7 kJ = 20.516 mol. To find the mass of 20.516 mol of water, you take the mass of one mol of water, 18.0148 grams, found by multiplying avogadro's number (6.022 x 10^23) by the mass of one water molecule, and multiply it by 20.516. This results in 369.5916368 grams of water vaporized.