I did some calculations to find the maximum flow rate into my 55 gallon (208 L) tank, given that the concentration of Chlorine (Cl2) shouldn't rise above 0.04 mg/L.
Known: Cl2 concentration varies from 0.5 mg/L to 2.0 mg/L. Assume an average value of (0.5+2.0)/2 = 1.25 mg Cl2 / L water
Known: Concentration of chlorine in the tank should be 0.04 mg/L or less.
Accumulation = In - Out + Generation - Consumption
Assuming that the system is in steady state, accumulation = 0.
Let the consumption term equal the evaporation rate out of the tank.
Let generation term equal zero because no chlorine is being generated in the tank. Due to the zero mg/L ammonia, nitrite, and nitrate concentration, the chloramine generation (and its equilibrium exchange with chlorine) is zero, and this assumption is probably valid.
Accumulation = In - Out + Generation - Consumption
0= (1.25 mg/L)*(X L/min) - (0.04 mg/L)*(X L/min) + 0 - Evaporation rate
Evaporation rate = (1.25 mg/L)*(X L/min) - (0.04 mg/L)*(X L/min)
That is on a per time (rate) setup. If we assume that this is happening over the course of one minute, then time cancels out across both sides of the equation.
n in mg = (1.25 mg/L)*(X L) - (0.04 mg/L)*(X L)
n in mg = X L *(1.25 mg/L - 0.04 mg/L)
The value of n can be found (according to Dr. Dai of the Chemical Engineering department of CWRU, I had to ask for help on this part) from the partial pressure. According to
http://pubs.acs.org/...021/ie50378a014 , the partial pressure of Cl2 in water at 25 degrees C equals 0.973 atm at 0.6 g Cl2 / 100 g water. If we convert that to mg/l, that is
(600 mg Cl2 / 100 g water)*(3787.5 gram / gallon)*(1 gallon / 3.7854 L ) = 6003 mg/L
The data comes from a solution of 6003 mg/L and we are talking about 0.5 mg/L, so this is a bad fitting region to get the volatility data. If anyone has any evaporation data for lower concentration chlorine gas in water, that would be helpful.
Recalling the ideal gas law, n = P V / R T
n = (0.972 atm * 208 L)/(298 K * 0.08206 (L atm / mol K))
n = 8.267 moles
n in grams = 8.267 moles * 71 grams Cl2 / mol
n in grams = 587 grams
587,003 mg = X L *(1.25 mg/L - 0.04 mg/L)
X = 485126 L/min
X = 128157 gal/min
That's a ridiculously high flow rate, which makes me think there has to be an error. I bet it's because the volatility was really, really off. But I think that getting the volatility from a region with higher concentration chlorine gas in water would inflate the evaporation term to an artificially higher value? I'm not sure on that way. I need better data, particularly the partial pressure of chlorine at something less than 10 mg/L. I'm going to try to find that and see if I can redo the math.
Edited by EricaWieser, 08 April 2011 - 12:27 PM.