Question

Die gnt of 425 nm. 2. A typical microwave oven uses radiation of wavelength 12.2 cm a. How many moles of photons of this radiation are required to raise the temperature of 500.0 mL of water from 25°C to its boiling point? b. A watt (W) is a unit of power the rate at which energy is delivered or consumed (Power (W) = Energy (J)/time (s) or 1 W= 1 J/s. If all the energy of a 700-W microwave oven is used to heat the water in part a. how long will it take to heat the water? Page 2

Answer 1

Q2. (a) Wavelength of radiation = 12.2 cm = 12.2 x 10^-2 m

energy of photon = [(Planck's constant) * (speed of light)] / (Wavelength of radiation)

energy of photon = [(6.626 x 10^-34 J.s) * (3.0 x 10⁸ m/s)] / (12.2 x 10^-2 m)

energy of photon = 1.63 x 10^-24 J

volume of water = 500.0 mL

mass of water = (volume of water) * (density of water)

mass of water = (500.0 mL) * (1.00 g/mL)

mass of water = 500.0 g

Energy required to heat water = (mass of water) * (specific heat water) * (final temp. - initial temp.)

Energy required to heat water = (500.0 g) * (4.184 J/g.^oC) * (100 ^oC - 25 ^oC)

Energy required to heat water = 156900 J

Total photons required = (Energy required to heat water) / (energy of photon)

Total photons required = (156900 J) / (1.63 x 10^-24 J)

Total photons required = 9.63 x 10²⁸ photons

moles of photons required = (Total photons required) / (Avogadro's number)

moles of photons required = (9.63 x 10²⁸ photons) / (6.022 x 10²³ photons/mol)

moles of photons required = 1.60 x 10⁵ moles

(b) power of microwave = 700 W = 700 J/s

Energy required to heat water = 156900 J

Time required to heat water = (Energy required to heat water) / (power of microwave)

Time required to heat water = (156900 J) / (700 J/s)

Time required to heat water = 224.1 s