The heat of fusion of ice is 6.00 kJ/mol. Find the number of photons of wavelength = 6.42 x 10e-6 m that must be absorbed to melt 2.00 g of ice.

To find the number of photons of a given wavelength that must be absorbed to melt a certain mass of ice, we can follow these steps:

Step 1: Convert the mass of ice from grams to moles.

To do this, we need to know the molar mass of water. The molar mass of water (H₂O) is approximately 18.02 g/mol.

Given:
Mass of ice (m) = 2.00 g

Molar mass of H₂O = 18.02 g/mol

Number of moles (n) = Mass (m) / Molar mass

n = 2.00 g / 18.02 g/mol
n ≈ 0.111 moles

Step 2: Calculate the energy required to melt the given amount of ice.

The heat of fusion of ice is given as 6.00 kJ/mol.

Given:
Heat of fusion (ΔH) = 6.00 kJ/mol

Energy (E) = ΔH * n

E = 6.00 kJ/mol * 0.111 moles
E ≈ 0.666 kJ

Step 3: Calculate the energy per photon for the given wavelength.

The energy per photon (Ephoton) can be calculated using the formula:

Ephoton = hc / λ

Where:
h = Planck's constant = 6.626 x 10^-34 J·s
c = speed of light = 3.00 x 10^8 m/s
λ = wavelength of the photon = 6.42 x 10^-6 m

Ephoton = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (6.42 x 10^-6 m)
Ephoton ≈ 3.09 x 10^-19 J

Step 4: Calculate the number of photons required.

Number of photons (Nphoton) = Energy (E) / Ephoton

Nphoton = 0.666 kJ * (1000 J/1 kJ) / (3.09 x 10^-19 J)

Nphoton ≈ 2.16 x 10^21 photons

Therefore, approximately 2.16 x 10^21 photons of wavelength 6.42 x 10^-6 m must be absorbed to melt 2.00 g of ice.

To find the number of photons that must be absorbed to melt 2.00 g of ice, you will need to calculate the amount of heat required to melt the ice and then relate it to the number of photons absorbed.

Here's how you can approach the problem step by step:

Step 1: Calculate the moles of ice.

Molar mass of water (H2O) = 18.02 g/mol.
Given mass of ice = 2.00 g.

Using the formula:
moles = mass / molar mass

moles of ice = 2.00 g / 18.02 g/mol

Step 2: Calculate the heat required to melt the ice.

Heat of fusion of ice = 6.00 kJ/mol.

Using the formula:
heat = moles × heat of fusion

heat required to melt the ice = moles of ice × heat of fusion

Step 3: Convert the heat required to energy in joules.

1 kJ = 1000 J

heat required to melt the ice in joules = (heat required to melt the ice in kJ) × 1000

Step 4: Calculate the energy of each photon using the wavelength.

The energy of a photon can be calculated using the equation:

energy = (Planck's constant × speed of light) / wavelength

where
Planck's constant (h) = 6.626 x 10^-34 J·s
speed of light (c) = 3.00 x 10^8 m/s
wavelength = 6.42 x 10^-6 m

energy of each photon = (6.626 x 10^-34 J·s × 3.00 x 10^8 m/s) / (6.42 x 10^-6 m)

Step 5: Calculate the number of photons absorbed.

The number of photons can be obtained by dividing the total energy required (in joules) by the energy of each photon.

number of photons absorbed = (heat required to melt the ice in joules) / (energy of each photon)

Now, you can plug in the values into the respective formulas and perform the calculations to find the number of photons absorbed.

Eice to melt ice = mass x heat fusion.

Ephoton is hc/wavelength.
#photons = Eice/Ephoton