 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/4/a/i/solution

The decadic Beer-Lambert law can be written

I = I_{0} 1 0^{- εl c}, lo g_{10} (I_{0} / I) = εl c .

Here

l

is the path length in metres,

c

mol L^{- 1}

or M, and

ε

M^{- 1} m^{- 1}

. The intensity ratio and the exponent are dimensionless. Equivalently

I = I_{0} e^{- κ l c}

with

κ = (ln 10) ε

in the same units. Defining the logarithm convention avoids a missing factor of

ln 10

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