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QuestionHow much energy is in 2.50 mol2.50 \mathrm{~mol} of UV light at 235 nm235 \mathrm{~nm}?

Studdy Solution

STEP 1

Assumptions1. The wavelength of UV light is235 nm. . The number of moles of UV light is.50 mol.
3. We are using the Planck's equation to calculate the energy.
4. The Planck's constant (h) is 6.626×10−34 J s6.626 \times10^{-34} \, \text{J s}.
5. The speed of light (c) is 3.00×108 m/s3.00 \times10^{8} \, \text{m/s}.
6. Avogadro's number (_A) is 6.022×1023 mol−16.022 \times10^{23} \, \text{mol}^{-1}.

STEP 2

First, we need to convert the wavelength from nm to m, because the speed of light is given in m/s.
λ=235 nm=235×10−9 m\lambda =235 \, \text{nm} =235 \times10^{-9} \, \text{m}

STEP 3

Next, we use the Planck's equation to calculate the energy of one photon.
photon=hcλ_{\text{photon}} = \frac{hc}{\lambda}

STEP 4

Now, plug in the values for the Planck's constant, the speed of light, and the wavelength to calculate the energy of one photon.
photon=(6.626×10−34 J s)(3.00×108 m/s)235×10−9 m_{\text{photon}} = \frac{(6.626 \times10^{-34} \, \text{J s})(3.00 \times10^{8} \, \text{m/s})}{235 \times10^{-9} \, \text{m}}

STEP 5

Calculate the energy of one photon.
photon=8.46×10−19 J_{\text{photon}} =8.46 \times10^{-19} \, \text{J}

STEP 6

Now that we have the energy of one photon, we can find the energy of one mole of photons by multiplying the energy of one photon by Avogadro's number.
mol=photon×NA_{\text{mol}} =_{\text{photon}} \times N_A

STEP 7

Plug in the values for the energy of one photon and Avogadro's number to calculate the energy of one mole of photons.
mol=(.46×10−19 J)×(6.022×1023 mol−1)_{\text{mol}} = (.46 \times10^{-19} \, \text{J}) \times (6.022 \times10^{23} \, \text{mol}^{-1})

STEP 8

Calculate the energy of one mole of photons.
mol=509 kJ/mol_{\text{mol}} =509 \, \text{kJ/mol}

STEP 9

Now that we have the energy of one mole of photons, we can find the total energy by multiplying the energy of one mole of photons by the number of moles.
total=mol×number of moles_{\text{total}} =_{\text{mol}} \times \text{number of moles}

STEP 10

Plug in the values for the energy of one mole of photons and the number of moles to calculate the total energy.
total=509 kJ/mol×2.50 mol_{\text{total}} =509 \, \text{kJ/mol} \times2.50 \, \text{mol}

STEP 11

Calculate the total energy.
total=509 kJ/mol×.50 mol=1273 kJ_{\text{total}} =509 \, \text{kJ/mol} \times.50 \, \text{mol} =1273 \, \text{kJ}The total energy contained in.50 mol of UV light at235 nm is1273 kJ.

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