Chemistry help please...

Question

Water photo dialysis H2O+ hv > 4H2+1/2O2 has been suggested as a hydrogen source.The ΔH^o of this reaction calculated from thermochemical data os 258.8 kj/mol of decomposed water.How long the maximum influx (in nm) that is sufficient to produce the required energy?

 

a.320 nm

b.419 nm

c.450 nm

d.520 nm

e.230 nm

Answer 1

I'm assuming this means, find the maximum wavelength of the light required to cause this reaction.

 

Here's the way I would do it.  I don't get an answer that's obviously any one of the choices.  See if you can figure out a problem in what I did.

 

Divide 258.8 kj by the number of molecules in a mole of water (Avogadro's number) to get the energy absorbed per molecule of water. 

 

So that's:

 

258.8 kj/mol

--------------------------------  = 4.299 x 10^-22 kj / molecule

6.02 x 10²³ molecules/mol

 

1 kj = 1000 joules, so that's 4.299 x 10^-19 joules = 4.299 x 10^-19 kg-m²/s²

 

Then divide by Planck's constant to get the frequency of the light that contains that amount of energy.

 

4.299 x 10^-19 kg-m² / s²

------------------------------------- = 6.488 x 10¹⁴ / s

6.626 × 10^-34 kg-m² / s

 

That's the minimum frequency of the light required to cause the reaction. But we need the wavelength, which is the speed of light divided by the frequency.

 

2.998 x 10⁸ m/s

-------------------   = 0.4621 x 10^-6 m

6.488 x 10¹⁴ / s

 

1 nm = 10^-9 m, so that's 0.4621 x 10^-6 x 10⁹ = 0.4621 x 10³ nm = 462 nm

 

So that's not equal to any of the choices.  Why?  I'm not sure.  462 is almost exactly twice the number in choice e.  Did I lose a factor of 2 somewhere in my analysis?  462 is also just a few percent different from choice c.  Is it just a little rounding error?

 

Anyway, if you review what I did, you might find the problem.