## 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: $\sum \, cations \ = \ \sum \, anions$

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

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

We make use of CBE to judge the validity and quality of water analyses. Its value is determined just before any 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%.

It is important to note that CBE is a relative error (rather than an absolute one). Due to the presence of the denominator in 2, low-concentrated waters are especially sensitive to small deviation between total cations and anions.

Note. In addition to the CBE formula in 2 (which is used in PhreeqC and aqion) there are alternative definitions of CBE. In one alternative2, for example, the denominator is multiplied by 0.5, which increases CBE by a factor 2. Thus, before comparing CBE values ensure that they are based on the same equation/definition.

Causes for Charge-Balance Error

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

1. Hydrochemistry software PhreeqC (U.S.G.S.)

2. German technical standard DIN 38402-62