Page 100 - Gas Adsorption Equilibria

86 Chapter 2

least three times to guarantee reproducibility of data and reduce the
uncertainty by a factor (1 / 3). To be more explicit let us consider briefly an
arbitrary quantity (x) which has been measured times, the result of the
i-th measurement being

with the uncertainty or error Then the statistical mean value of all
measurements

has, according to Gauss’ law of propagation of error a dispersion (or variance
or mean square deviation, MSD) of

We consider this quantity as uncertainty of the representive value of the
quantity x. In (2.14) it has been assumed that the uncertainties of all single
measurements are equal and that measurements
themselves are statistically independent [2.16].

In view of space limitations we here consider only the uncertainty of the
Gibbs surface excess mass adsorbed according to Eq. (2.8). The Gauss law of
error propagation immediately leads to the expressions