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Using the Beer-Lambert law to calculate vapour pressure

Hi Guys,

The absorption cross section of atomic iodine for the transition from * 2P(3/2) to 2P(1/2) at 7603 cm-1 is, sigma = 2.1x10^-22 m^2

*spectroscopic term values just to be clear

using a 10cm long gas cell containing iodine atoms at room temperature, 1% of light at 7603 cm-1 is absorbed. What is the partial vapour pressure of I?

I know I have to use the beer lambert law and possibly Daltons Law or pV=nRT? But not sure how to proceed.

Some of the other questions ask about the term values but Im not sure they're particularly relevant to this part of the question.

Any takers?

Thanks in advance

Reply 1

BJack

The Beer-Lambert law is

T = \mathrm{e}^{-\sigma l N'}

where N' is the number density = N/V. You can use the data given to find N', then use the ideal gas law (pV = NkT) to find the pressure.

Reply 2

DonnieBrasco

Original post by BJack

The Beer-Lambert law is

T = \mathrm{e}^{-\sigma l N'}

where N' is the number density = N/V. You can use the data given to find N', then use the ideal gas law (pV = NkT) to find the pressure.

Ah ok thanks. I dont know this version of the Beer-Lambert law. So once we've found the number density N we plug this into the ideal gas law but what do we use for the volume?

Thanks

Reply 3

BJack

Original post by DonnieBrasco

Ah ok thanks. I dont know this version of the Beer-Lambert law. So once we've found the number density N we plug this into the ideal gas law but what do we use for the volume?

Thanks

You don't need to calculate the volume explicitly. You just rearrange the ideal gas law to p = (N/V)kT and use the value of (N/V), i.e. the number density, you get from Beer-Lambert.