Calculations with AT and CT measured

There is no analytical solution to this problem. The simplest method of solution is to solve Eq. (8-52) for (H ) by an iterative method (e.g., Newton-Raphson see Stephenson, 1969). Then/(C02) ean be ealculated using equation (8-51). 

This problem also lacks an analytical solution. The simplest method is again an iterative solution for H j, this time solving Eq. (8-50), following which Ct can be calculated using equation (8-49). 

This problem can be solved by rearranging Eq. (8-49) as a quadratic in H ) with the solution  

An important consideration when carrying out any of the calculations summarized in Section 8.6.3 is the anticipated uncertainty in the result. Since the equations themselves are non-linear, the uncertainties in the measured parameters and in the stability constants combine in a non-linear fashion. Dickson and Riley (1978) have compiled the partial derivatives which allow the errors associated with these calculations to be estimated. The values of r in 

The non-linearity in accumulation of errors can clearly be seen from Table 8-2. The measurement combinations At, Ct and pH, /(COz) are obviously unsuitable for calculation of other CO2 system parameters since the uncertainties in the measurements are magnified during the calculation. The results suggest, however, that with the right choice of measured parameters. At and Cj can be calculated with precision similar to that achieved in direct measurement (this also applies to pH measured by potentiometry). In contrast, /(CO2) cannot be calculated with the precision which can be achieved in direct measurement. 

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