It requires 945.0 kJ/mol to break N2 molecules into atoms. Calculate the maximum wavelength of light that will still break these molecules apart.
I tried converting the energy to kj and using E=hc/wavelength but that didn't give me the right answer...
First you need to determine the energy required to break "one molecule" of nitrogen. You know how much is required to break 6.022E23 molecules(1 mole), so divide that 945,000 J/6.022E23 to find for 1 molecule. Then apply the E = hc/wavelength and see if that doesn't give you the correct answer.
it did work, thanks!
It looks like you've already made some good progress, but maybe the math just needs a little clowning around. Let's give it another shot!
To break apart N2 molecules, you need an energy of 945.0 kJ/mol. We can convert this energy to J/mol for simplicity. 1 kJ = 1000 J, so 945.0 kJ/mol is equal to 945,000 J/mol.
Next, let's use the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength of light.
Now we need to solve for λ. Rearranging the formula, we have λ = hc/E.
Plugging in the values:
λ = (6.626 x 10^-34 J·s) x (2.998 x 10^8 m/s) / (945,000 J/mol)
Now, let's convert the units to make things a bit easier. For convenience, we'll use nm (nanometers) as the unit for wavelength.
λ = (6.626 x 10^-34 J·s) x (2.998 x 10^8 m/s) / (945,000 J/mol) * (1 m/10^9 nm)
Calculating this, we find:
λ ≈ 20.99 nm
So, the maximum wavelength of light that will still break apart N2 molecules is approximately 20.99 nm. Keep in mind, my calculations may have a few clown-determined approximations in them, so please double-check!
To calculate the maximum wavelength of light that will still break N2 molecules apart, we can use the formula:
E = hc / λ
Where:
E is the energy required to break N2 molecules into atoms,
h is Planck's constant (6.626 x 10^-34 J·s or 4.135 x 10^-15 eV·s),
c is the speed of light (2.998 x 10^8 m/s),
λ is the wavelength of light.
First, we need to convert the given energy from kilojoules per mole (kJ/mol) to joules per molecule (J/molecule). Since there are 6.022 x 10^23 molecules in 1 mole, we will divide the given energy by Avogadro's number:
945.0 kJ/mol / (6.022 x 10^23 molecules/mol) = 1.57 x 10^-21 kJ/molecule
Next, we need to convert the energy from kilojoules to joules by multiplying by 1000:
1.57 x 10^-21 kJ/molecule * 1000 = 1.57 x 10^-18 J/molecule
Now, we have the energy in joules per molecule. We can plug this value into the formula and solve for the maximum wavelength. However, it's important to note that the energy given is in joules, not kilojoules. So, we should convert the energy back to its original unit:
1.57 x 10^-18 J/molecule * (1 eV / 1.602 x 10^-19 J) = 9.80 eV/molecule
Now, we can use the formula with the converted energy value:
E = hc / λ
Rearranging the formula to solve for wavelength:
λ = hc / E
Substituting the values:
λ = (6.626 x 10^-34 J·s) * (2.998 x 10^8 m/s) / (9.80 eV)
Converting eV to joules by multiplying by 1.602 x 10^-19 J/eV:
λ = (6.626 x 10^-34 J·s) * (2.998 x 10^8 m/s) / (9.80 * 1.602 x 10^-19 J)
Calculating the maximum wavelength:
λ = 2.008 x 10^-7 m
Therefore, the maximum wavelength of light that will still break N2 molecules apart is approximately 2.008 x 10^-7 meters (or 200.8 nm).