Charge Balance Approximation

In summary, the Charge Balance Approximation is a simplifying assumption used in scientific and engineering calculations involving charged particles. It assumes that the number of positively charged particles is equal to the number of negatively charged particles, resulting in a net charge of zero. It is commonly used in situations where the exact number of charged particles is not known or is difficult to determine, and when the system has a large number of particles. However, this approximation has limitations as it does not always accurately reflect real-world situations and does not consider the distribution of charged particles. It simplifies calculations but may introduce errors. Alternative methods, such as the Poisson-Boltzmann equation, exist but may be more complex.
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Qube
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Homework Statement



Question: is the charge sum an approximation?

Homework Equations



E.g. consider 0.10 M [itex]Na_{2}SO_{4}[/itex] solution.

Charge sum appears to be 0.20 from elementary stoichiometric considerations.

The Attempt at a Solution



The charge sum, however, seems to be ignoring the auto-ionization of water, which forms two ions - hydronium and hydroxide. Am I correct? This doesn't make a significant difference for most solution considerations, right?
 
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  • #2
We often ignore ions present in very small concentrations, but full charge balance equation for sodium sulfate solution is

[tex][Na^+] + [H^+] = 2[SO_4^{2-}] + [OH^-][/tex]
 

What is the Charge Balance Approximation?

The Charge Balance Approximation is a simplifying assumption used in many scientific and engineering calculations involving charged particles. It assumes that the number of positively charged particles in a system is equal to the number of negatively charged particles, resulting in a net charge of zero.

When is the Charge Balance Approximation used?

The Charge Balance Approximation is commonly used in situations where the exact number of charged particles is not known or is difficult to determine. It is also used when the system under consideration has a large number of particles, making it impractical to account for each individual charge.

What are the limitations of the Charge Balance Approximation?

The Charge Balance Approximation is based on the assumption that the number of positively and negatively charged particles is equal. This may not always be the case in real-world situations, leading to errors in calculations. Additionally, it does not take into account the distribution or arrangement of charged particles, which can affect the overall charge of a system.

How does the Charge Balance Approximation affect calculations?

The Charge Balance Approximation simplifies calculations by reducing the number of variables involved. This can make calculations more manageable and easier to understand. However, it is important to note that the approximation may introduce some level of error, which should be considered when interpreting the results.

Are there alternative methods to the Charge Balance Approximation?

Yes, there are alternative methods to the Charge Balance Approximation, such as the Poisson-Boltzmann equation, which takes into account the distribution of charged particles in a system. However, these methods may be more complex and require more advanced mathematical techniques, making the Charge Balance Approximation a more practical choice in certain situations.

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