Let's take a stab at a first-order approximation assuming simple random sampling and a constant proportion of infection for any treatment. Assume the sample size is large enough that a normal approximation can be used in a hypothesis test on proportions so we can calculate a z statistic like so
$z = \frac{p_t - p_0}{\sqrt{p_0(1-p_0)(\frac{1}{n_1}+\frac{1}{n_2})}}$
This is the sample statistic for a two-sample test, new formula vs. bleach, since we expect the effect of bleach to be random as well as the effect of the new formula.
Then let $n = n_1 = n_2$, since balanced experiments have the greatest power, and use your specifications that $|p_t - p_0| \geq 0.1$, $p_0 = 0.2$. To attain a test statistic $|z| \geq 2$ (Type I error of about 5%), this works out to $n \approx 128$. This is a reasonable sample size for the normal approximation to work, but it's definitely a lower bound.
I'd recommend doing a similar calculation based on the desired power for the test to control Type II error, since an underpowered design has a high probability of missing an actual effect.
Once you've done all this basic spadework, start looking at the stuff whuber addresses. In particular, it's not clear from your problem statement whether the samples of poultry measured are different groups of subjects, or the same groups of subjects. If they're the same, you're into paired t test or repeated measures territory, and you need someone smarter than me to help out!
The two groups do not have to be equal. Problems can arise if one group becomes very small. King and Zeng have an interesting paper on "Logistic Regression in Rare Events Data". When talking about rare events they have situations in mind where one group makes up 1% or less in a sample.
On the one hand King and Zeng propose estimation techniques to overcome this problem. There is software implementing these techniques.
On the other hand King and Zeng also discuss data collection strategies to avoid rare events. This might be interesting in your case. Note that these methods are not always innocuous. King and Zeng show how to deal with them and discuss the potential pitfalls.
Before bringing out the heavy artillery, I would try to find out how unequal the distribution of 0's and 1's could be. You probably have some knowledge about that, such as e.g. from previous studies on the same topic. Some expert knowledge about the population and programs you want to assess might be useful too. Then you will see if rare events become an issue and if you need to correct whatsoever.
Best Answer
Your sample size is likely the number of tanks, not the number of fish. You can nest fish ID within tank in your statistical models to account for this.