Understanding Watson's Law and Pathogen Resistance

This question relates to water disinfection, specifically how different pathogens react to chlorine treatment over time. We are given Watson's Law, which describes the relationship between the concentration of free residual chlorine ($C$) and the contact time ($t_p$) needed to achieve a 99% kill rate for various pathogens. The law is expressed as:

$$C^{0.86} t_p = \lambda$$

In this formula:

• $C$ is the concentration of chlorine.
• $t_p$ is the contact time required for 99% kill.
• $\lambda$ is a constant specific to each pathogen.

The constant $\lambda$ indicates the inherent resistance of a pathogen to chlorination. A higher value of $\lambda$ means that a longer contact time ($t_p$) is needed for a given chlorine concentration ($C$) to achieve the same level of disinfection (99% kill). Therefore, a pathogen with a higher $\lambda$ value is considered more resistant to chlorination.

Analyzing Pathogen Resistance Data

We can rearrange Watson's Law to see how contact time depends on the constant:

$$t_p = \frac{\lambda}{C^{0.86}}$$

This shows that for any given chlorine concentration ($C$), the contact time ($t_p$) is directly proportional to $\lambda$. Let's look at the provided data:

To find the pathogen with the maximum resistance, we need to identify the one with the highest $\lambda$ value:

• Adenovirus: $\lambda = 0.098$
• E.coli: $\lambda = 0.24$
• Coxsackievirus A2: $\lambda = 6.30$
• AA: $\lambda = 0.110$

Comparing these values, Coxsackievirus A2 has the largest $\lambda$ value (6.30).

Conclusion on Maximum Resistance

Since Coxsackievirus A2 has the highest $\lambda$ value, it requires the longest contact time ($t_p$) for a given chlorine concentration ($C$) to achieve a 99% kill compared to the other pathogens listed. This indicates that Coxsackievirus A2 exhibits the maximum resistance to chlorination among the given options.