# Charge-Balance Error (CBE)

One fundamental law of nature is that aqueous solutions must be electrically neutral. This means that in real solutions, the total sum of all the positive charges (cations) must equal the total sum of all negative charges (anions):

(1) | charge balance: | \(\sum \, \textrm{cations} \ = \ \sum \, \text{anions}\) |

However, analysis errors and/or unanalyzed constituents cause electrical imbalances. One measure of this imbalance is the charge-balance error in percent:^{1}

(2) | \(\textrm{CBE} \, = \, \dfrac{\sum \textrm{cations} \, - \mid\sum \textrm{anions}\mid}{\sum \textrm{cations} \, + \mid\sum \textrm{anions} \mid} \, \times \, 100\) |

We use CBE to judge the validity and quality of water analyses. In the program, the CBE is determined just before each reaction step (based on speciation calculations) and displayed in a separate panel.

The CBE can be positive or negative. A *positive* CBE indicates that the water sample has a higher concentration of cations than anions. Conversely, a *negative* CBE indicates that anions are more abundant.

Acceptable water analyses have CBE less than *±5 %.*

The CBE is a *relative* error (rather than an absolute one). Due to the presence of the denominator in *2*, low-concentrated waters are particularly sensitive to small deviations between total cations and total anions.

*Alternative Definitions*

In addition to *2* (which is used in PhreeqC and *aqion*) there are alternative definitions of CBE. In one alternative^{2}, for example, the denominator is multiplied by 0.5, which increases the CBE by a factor 2.

Thus, before comparing CBE values ensure that they are based on the same definition formula.

*Causes for Charge-Balance Errors*

Three possible causes for electrical imbalance are:

- lab errors (serious or systematic errors during analysis)
- some dissolved species (major ions) are not measured
- using
*unfiltered*samples that contain particulate matter which dissolves upon addition of acid (for preservation purposes)

*References*