The surface coverage of CO molecules obtained is 4.5 x 1018 molecules m-2 or θ = 0.45

Rationale

We have calculated the incident flux, F , of CO under these conditions in a previous question; it is equal 3.83 x 1016 molecules m-2 s-1. We are also told that the maximum surface coverage, Nsat , is 6.5 x 1018 molecules m-2.

Let N(t) be the surface coverage in molecules m-2 at any time, t.
Then
whereS(N) = ( 1 - ( N / Nsat ) )

 
If we use the Langmuir definition for the surface coverage, i.e.   θ = ( N / Nsat )  ,

Then  dθ = dN / Nsat  and

where S(θ) = ( 1 - θ ) .

To answer this question we need to integrate the differential equation from t = 0 to t = 200 s which gives

  ⇒   θfinal = 0.692 (where θ is still defined in the Langmuir manner)

So, the absolute coverage of CO molecules is given by

  ⇒   Coverage = 0.692 x 6.5 x 1018 molecules m-2 = 4.5 x 1018 molecules m-2.

and the coverage defined in the standard surface science manner is obtained by ratioing with the atom density of substrate atoms in the first layer

  ⇒   θ = ( 4.5 x 1018 / 1.0 x 1019 ) = 0.450

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