A cup of chicken soup (500.0 g) is heated from 20ºC to 98ºC in a microwave oven that operates at wavelength = 1.55 x 10–2 m. How many moles of photons are absorbed by the soup? Assume that the specific heat capacity of chicken soup is equal to that of water.

q = mass water x specific heat water x delta T = ?? Joules.

E = hc/wavelength.
Substitute h, c, and wavelength to calculate E (in joules/photon)

Convert to # photons, then divide by 6.022 x 10^23 to convert # photons to moles photons.

To find the number of moles of photons absorbed by the chicken soup, we need to calculate the energy absorbed by the soup and then convert it to the number of moles.

First, let's calculate the energy absorbed by the soup. The energy of a photon can be calculated using the equation:

E = hc/λ

Where:
E is the energy of the photon,
h is the Planck's constant (6.626 x 10^(-34) J·s),
c is the speed of light (3.00 x 10^8 m/s), and
λ is the wavelength of the microwave radiation.

We have the value for the wavelength (λ = 1.55 x 10^(-2) m), so we can calculate the energy of each photon.

E = (6.626 x 10^(-34) J·s) * (3.00 x 10^8 m/s) / (1.55 x 10^(-2) m)
E = 1.281 x 10^(-19) J

Next, let's calculate the heat energy absorbed by the soup. The heat energy absorbed can be calculated using the equation:

Q = mcΔT

Where:
Q is the heat energy,
m is the mass of the soup (500.0 g),
c is the specific heat capacity of water (4.184 J/g·°C), and
ΔT is the change in temperature (final temperature - initial temperature).

We have the mass of the soup (m = 500.0 g) and the change in temperature (ΔT = 98°C - 20°C = 78°C), so we can calculate the heat energy absorbed.

Q = (500.0 g) * (4.184 J/g·°C) * (78°C)
Q = 1.629 x 10^5 J

Since the energy absorbed by each photon is much smaller than the heat energy absorbed by the soup, we can assume all the energy is transferred by photons.

Finally, let's calculate the number of moles of photons absorbed by dividing the total energy absorbed by the energy of each photon.

Number of moles = Q / E
Number of moles = (1.629 x 10^5 J) / (1.281 x 10^(-19) J)
Number of moles ≈ 1.27 x 10^24 moles

Therefore, approximately 1.27 x 10^24 moles of photons are absorbed by the chicken soup.